##### Existence of Replica-Symmetry Breaking in Quantum Glasses

H. Leschke, C. Manai, R. Ruder, S. Warzel

Physical Review Letters 127, 207204 (2021).

By controlling quantum fluctuations via the Falk–Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington–Kirkpatrick model with a “transverse” magnetic field if the temperature and the field are sufficiently low. The argument also applies to the generalization of the model with multispin interactions, sometimes dubbed as the transverse p-spin model.H. Lesc

##### Exciton g-factors in monolayer and bilayer WSe2 from experiment and theory

J. Foerste, N.V. Tepliakov, S.Y. Kruchinin, J. Lindlau, V. Funk, M. Foerg, K. Watanabe, T. Taniguchi, A.S. Baimuratov, A. Hoegele

Nature Communications 11 (1), 4539 (2021).

The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. Here, we present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe2 monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton g-factors from first principles for all possible spin-valley configurations of excitons in monolayer and bilayer WSe2 including valley-indirect excitons. Our theoretical and experimental findings shed light on some of the characteristic photoluminescence peaks observed for monolayer and bilayer WSe2. In more general terms, the theoretical aspects of our work provide additional means for the characterization of single and few-layer transition metal dichalcogenides, as well as their heterostructures, in the presence of external magnetic fields.

##### Compound Channel Capacities under Energy Constraints and Application

A. Cacioppo, J. Nötzel, M. Rosati

IEEE International Symposium on Information Theory (ISIT) 640-645 (2021).

Compound channel models offer a simple and straightforward way of analyzing the stability of decoder design under model variations. With this work we provide a coding theorem for a large class of practically relevant compound channel models. We give explicit formulas for the cases of the Gaussian classical-quantum compound channels with unknown noise, unknown phase and unknown attenuation. We show analytically how the classical compound channel capacity formula motivates nontrivial choices of the displacement parameter of the Kennedy receiver. Our work demonstrates the value of the compound channel model as a method for the design of receivers in quantum communication.

##### Uniqueness of ground state and minimal-mass blow-up solutions for focusing NLS with Hardy potential

D. Mukherjee, P.T. Nam, P.-T. Nguyen

Journal of Functional Analysis 281, 109092 (2021).

We consider the focusing nonlinear Schrödinger equation with the critical inverse square potential. We give the first proof of the uniqueness of the ground state solution. Consequently, we obtain a sharp Hardy-Gagliardo-Nirenberg interpolation inequality. Moreover, we provide a complete characterization for the minimal mass blow-up solutions to the time dependent problem.

##### Excitons and emergent quantum phenomena in stacked 2D semiconductors

N.P. Wilson, W. Yao, J. Shan, X. Xu

(2021).

##### Entanglement-Assisted Data Transmission as an Enabling Technology: A Link-Layer Perspective

J. Nötzel, S. DiAdamo,

IEEE International Symposium on Information Theory (ISIT) 1955-1960 (2020).

Quantum entanglement as a resource has repeatedly proven to add performance improvements for various tasks in communication and computing, yet no current application justifies a wide spread use of entanglement as a commodity in communication systems. In this work, we detail how the addition of an entanglement storage system at the end-points of a communication link integrated seamlessly into the current Internet can benefit that link's capabilities via a protocol implementing the simple rule to "create entanglement when idle", and use entanglement-assisted communication whenever possible. The benefits are shown with regards to throughput, packet drop-rate, and average packet processing time. The modelling is done in an information-theoretic style, thereby establishing a connecting from information-theoretic capacities to statistical network analysis.

##### Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

P. Che, I. Stasinopoulos, A. Mucchietto, J. Li, H. Berger, A. Bauer, C. Pfleiderer, D. Grundler

Physical Review Research 3, 33104 (2021).

The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu2OSeO3 by means of introducing asymmetry in their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy, and we observe confined spin waves up to eleventh order in bulk Cu2OSeO3 in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to (47.2±0.05) nm attributed to the exchange interaction modulation. Our results suggest the DMI to be effective in creating exchange spin waves in a bulk sample without the challenging nanofabrication and thereby in exploring their scattering with noncollinear spin textures.

##### Efficient optomechanical mode-shape mapping of micromechanical devices

D. Hoch, K.-J. Haas, L. Moller, T. Sommer, P. Soubelet, J. Finley, M. Poot

Micromachines 12, 880 (2021).

Visualizing eigenmodes is crucial in understanding the behavior of state-of-the-art micromechanical devices. We demonstrate a method to optically map multiple modes of mechanical structures simultaneously. The fast and robust method, based on a modified phase-lock loop, is demonstrated on a silicon nitride membrane and shown to outperform three alternative approaches. Line traces and two-dimensional maps of different modes are acquired. The high quality data enables us to determine the weights of individual contributions in superpositions of degenerate modes.

##### Dynamical decoupling of spin ensembles with strong anisotropic interactions

B. Merkel, P. Cova Fariña, A. Reiserer

Physical Review Letters 127, 030501 (2021).

Ensembles of dopants have widespread applications in quantum technology. The miniaturization of corresponding devices is however hampered by dipolar interactions that reduce the coherence at increased dopant density. We theoretically and experimentally investigate this limitation. We find that dynamical decoupling can alleviate, but not fully eliminate, the decoherence in crystals with strong anisotropic spin-spin interactions that originate from an anisotropic g tensor. Our findings can be generalized to many quantum systems used for quantum sensing, microwave-to-optical conversion, and quantum memory.

##### Quantum Algorithms for Solving Ordinary Differential Equations via Classical Integration Methods

B. Zanger, C.B. Mendl, M. Schulz, M. Schreiber

Quantum 5, 502 (2021).

Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis encoding and fixed-point arithmetic on a digital quantum computer, and (ii) representing and solving high-order Runge-Kutta methods as optimization problems on quantum annealers. As realizations applied to two-dimensional linear ordinary differential equations, we devise and simulate corresponding digital quantum circuits, and implement and run a 6th order Gauss-Legendre collocation method on a D-Wave 2000Q system, showing good agreement with the reference solution. We find that the quantum annealing approach exhibits the largest potential for high-order implicit integration methods. As promising future scenario, the digital arithmetic method could be employed as an "oracle" within quantum search algorithms for inverse problems.

##### Rare thermal bubbles at the many-body localization transition from the Fock space point of view

G. De Tomasi, I.M. Khaymovich, F. Pollmann, S. Warzel

Physical Review B 104, 024202 (2021).

In this paper we study the many-body localization (MBL) transition and relate it to the eigenstate structure in the Fock space. Besides the standard entanglement and multifractal probes, we introduce the radial probability distribution of eigenstate coefficients with respect to the Hamming distance in the Fock space and relate the cumulants of this distribution to the properties of the quasilocal integrals of motion in the MBL phase. We demonstrate nonself-averaging property of the many-body fractal dimension Dq and directly relate it to the jump of Dq as well as of the localization length of the integrals of motion at the MBL transition. We provide an example of the continuous many-body transition confirming the above relation via the self-averaging of Dq in the whole range of parameters. Introducing a simple toy model, which hosts ergodic thermal bubbles, we give analytical evidences both in standard probes and in terms of newly introduced radial probability distribution that the MBL transition in the Fock space is consistent with the avalanche mechanism for delocalization, i.e., the Kosterlitz-Thouless scenario. Thus, we show that the MBL transition can been seen as a transition between ergodic states to nonergodic extended states and put the upper bound for the disorder scaling for the genuine Anderson localization transition with respect to the noninteracting case.

##### Collisions of ultracold molecules in bright and dark optical dipole traps

R. Bause, A. Schindewolf, R. Tao, M. Duda, X.-Y. Chen, G. Quéméner, T. Karman, A. Christianen, I. Bloch, X.-Y. Luo

Physical Review Research 3, 33013 (2021).

Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photo-excitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic 23Na40K molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood, and provide a benchmark for the development of new theories.

##### Optimal sampling of dynamical large deviations via matrix product states

L. Causer, M.C. Banuls, J. P. Garrahan

Physical Review E 103, 62144 (2021).

The large deviation (LD) statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute the relevant leading eigenvalues and eigenvectors accurately. However, the efficient generation of the corresponding rare trajectories is a harder task. Here we show how to exploit the MPS approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called "Doob") dynamics that realises the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models (KCMs), and the symmetric simple exclusion process (SSEP). We discuss how to generalise our approach to higher dimensions.

##### QuNetSim: A Software Framework for Quantum Networks

S. Diadamo, J. Nötzel, B. Zanger, M.M. Beşe

IEEE Transactions on Quantum Engineering 2 , 1-12 (2021).

As quantum network technologies develop, the need for teaching and engineering tools such as simulators and emulators rises. QuNetSim addresses this need. QuNetSim is a Python software framework that delivers an easy-to-use interface for simulating quantum networks at the network layer, which can be extended at little effort of the user to implement the corresponding link layer protocols. The goal of QuNetSim is to make it easier to investigate and test quantum networking protocols over various quantum network configurations and parameters. The framework incorporates many known quantum network protocols so that users can quickly build simulations using a quantum-networking toolbox in a few lines of code and so that beginners can easily learn to implement their own quantum networking protocols. Unlike most current tools, QuNetSim simulates with real time and is, therefore, well suited to control laboratory hardware. Here, we present a software design overview of QuNetSim and demonstrate examples of protocols implemented with it. We describe ongoing work, which uses QuNetSim as a library, and describe possible future directions for the development of QuNetSim.

##### Detecting an Itinerant Optical Photon Twice without Destroying It

E. Distante, S. Daiss, S. Langenfeld, L. Hartung, P. Thomas, O. Morin, G. Rempe, S. Welte

Physical Review Letters 126, 253603 (2021).

Nondestructive quantum measurements are central for quantum physics applications ranging from quantum sensing to quantum computing and quantum communication. Employing the toolbox of cavity quantum electrodynamics, we here concatenate two identical nondestructive photon detectors to repeatedly detect and track a single photon propagating through a 60 m long optical fiber. By demonstrating that the combined signal-to-noise ratio of the two detectors surpasses each single one by about 2 orders of magnitude, we experimentally verify a key practical benefit of cascaded nondemolition detectors compared to conventional absorbing devices.

##### Quantum algorithms for powering stable Hermitian matrices

G. González, R. Trivedi, J.I. Cirac

Physical Review A 103, 062420 (2021).

Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering and underlies the solution of time-homogeneous linear ordinary differential equations, simulation of discrete-time Markov chains, or discovering the spectral properties of matrices with iterative methods. In this paper, we investigate the possibility of speeding up matrix powering of sparse stable Hermitian matrices on a quantum computer. We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms: (i) a fast-forwarding algorithm that builds on construction of Apers and Sarlette [Quantum Inf. Comput. 19, 181 (2019)] and (ii) an algorithm based on Hamiltonian simulation. Furthermore, by mapping the N-bit parity determination problem to a matrix powering problem, we provide no-go theorems that limit the quantum speedups achievable in powering non-Hermitian matrices.

##### Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime

P.T. Nam, A. Triay

We consider an inhomogeneous system of N bosons in R3 confined by an external potential and interacting via a repulsive potential of the form N2V(N(x−y)). We prove that the low-energy excitation spectrum of the system is determined by the eigenvalues of an effective one-particle operator, which agrees with Bogoliubov's approximation.

##### Tensors cast their nets for quarks

M.C. Bañuls, K. Cichy

nature physics, News & views 17, 762–763 (2021).

Many aspects of gauge theories — such as the one underlying quantum chromodynamics, which describes quark physics — evade common numerical methods. Tensor networks are getting closer to a solution, having successfully tackled the related problem of a three-dimensional quantum link model.

##### Growth of aluminum nitride on a silicon nitride substrate for hybrid photonic circuits

G. Terrasanta, M. Müller, T. Sommer, S. Geprägs, R. Gross, M. Althammer, M. Poot

Materials for Quantum Technology 1, 21002 (2021).

Aluminum nitride (AlN) is an emerging material for integrated quantum photonics with its excellent linear and nonlinear optical properties. In particular, its second-order nonlinear susceptibility χ(2) allows single-photon generation. We have grown AlN thin films on silicon nitride (Si3N4) via reactive DC magnetron sputtering. The thin films have been characterized using x-ray diffraction (XRD), optical reflectometry, atomic force microscopy (AFM), and scanning electron microscopy. The crystalline properties of the thin films have been improved by optimizing the nitrogen to argon ratio and the magnetron DC power of the deposition process. XRD measurements confirm the fabrication of high-quality c-axis oriented AlN films with a full width at half maximum of the rocking curves of 3.9° for 300 nm-thick films. AFM measurements reveal a root mean square surface roughness below 1 nm. The AlN deposition on SiN allows us to fabricate hybrid photonic circuits with a new approach that avoids the challenging patterning of AlN.

##### Gauging the Kitaev chain

U. Borla, R. Verresen, J. Shah, S. Moroz

Scipost Physics 10 (6), 148 (2021).

We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.

##### Quantum coherence as a signature of chaos

N. Anand, G. Styliaris, M. Kumari, P. Zanardi

Physical Review Research 3, 023214 (2021).

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP)—a measure of how much coherence a dynamical process generates on average—emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.

##### On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

Ivan Bardet, Angela Capel, Angelo Lucia, David Perez-Gracia, Cambyse Rouzé

Journal of Mathematical Physics 62, 061901 (2021).

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.

##### Symmetry-enforced topological nodal planes in a chiral magnet

M.A. Wilde, M. Dodenhöft, A. Niedermayr, A. Bauer, M.M. Hirschmann, K. Alpin, A.P. Schnyder, C. Pfleiderer

Nature 594, 374 (2021).

Despite recent efforts to advance spintronics devices and quantum information technology using materials with non-trivial topological properties, three key challenges are still unresolved. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, the identification of generic topological degeneracies in large, multisheeted Fermi surfaces. By combining de Haas–van Alphen spectroscopy with density functional theory and band-topology calculations, here we show that the non-symmorphic symmetries in chiral, ferromagnetic manganese silicide (MnSi) generate nodal planes (NPs), which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1,651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs, which can be controlled with a magnetic field, on the FS of MnSi suggests the existence of similar properties—amenable for technological exploitation—in a large number of materials.

##### On the modified logarithmic Sobolev inequality for the heat-bath dynamics for 1D systems

I. Bardet, A. Capel, A. Lucia, D. Pérez-García, C. Rouzé

Journal of Mathematical Physics 62, 61901 (2021).

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.

##### Approximate tensorization of the relative entropy for noncommuting conditional expectations

Ivan Bardet, Angela Capel, Cambyse Rouzé

(2021).

In this paper, we derive a new generalisation of the strong subadditivity of the entropy to the setting of general conditional expectations onto arbitrary finite-dimensional von Neumann algebras. The latter inequality, which we call approximate tensorization of the relative entropy, can be expressed as a lower bound for the sum of relative entropies between a given density and its respective projections onto two intersecting von Neumann algebras in terms of the relative entropy between the same density and its projection onto an algebra in the intersection, up to multiplicative and additive constants. In particular, our inequality reduces to the so-called quasi-factorization of the entropy for commuting algebras, which is a key step in modern proofs of the logarithmic Sobolev inequality for classical lattice spin systems. We also provide estimates on the constants in terms of conditions of clustering of correlations in the setting of quantum lattice spin systems. Along the way, we show the equivalence between conditional expectations arising from Petz recovery maps and those of general Davies semigroups.

##### Synthesis of large-area rhombohedral few-layer graphene by chemical vapor deposition on copper

C. Bouhafs, S. Pezzini, F.R. Geisenhof , N. Mishra, V. Mišeikis, Y. Niu, C. Struzzi, R.T. Weitz, A.A. Zakharov, S. Forti, C. Coletti

Carbon 177, 282-290 (2021).

Rhombohedral-stacked few-layer graphene (FLG) displays peculiar electronic properties that could lead to phenomena such as high-temperature superconductivity and magnetic ordering. To date, experimental studies have been mainly limited by the difficulty in isolating rhombohedral FLG with thickness exceeding 3 layers and device-compatible size. In this work, we demonstrate the synthesis and transfer of rhombohedral graphene with thickness up to 9 layers and areas up to ∼50 μm2. The domains of rhombohedral FLG are identified by Raman spectroscopy and are found to alternate with Bernal regions within the same crystal in a stripe-like configuration. Near-field nano-imaging further confirms the structural integrity of the respective stacking orders. Combined spectroscopic and microscopic analyses indicate that rhombohedral-stacking formation is strongly correlated to the underlying copper step-bunching and emerges as a consequence of interlayer displacement along preferential crystallographic orientations. The growth and transfer of rhombohedral FLG with the reported thickness and size shall facilitate the observation of predicted unconventional physics and ultimately add to its technological relevance.

##### Dispersive readout of room-temperature ensemble spin sensors

J. Ebel, T. Joas, M. Schalk, P. Weinbrenner, A. Angerer, J. Majer, F. Reinhard

IOP Quant Sci. Info. 6, 03LT01 (2021).

We demonstrate dispersive readout of the spin of an ensemble of nitrogen-vacancy centers in a high-quality dielectric microwave resonator at room temperature. The spin state is inferred from the reflection phase of a microwave signal probing the resonator. Time-dependent tracking of the spin state is demonstrated, and is employed to measure the T1 relaxation time of the spin ensemble. Dispersive readout provides a microwave interface to solid state spins, translating a spin signal into a microwave phase shift. We estimate that its sensitivity can outperform optical readout schemes, owing to the high accuracy achievable in a measurement of phase. The scheme is moreover applicable to optically inactive spin defects and it is non-destructive, which renders it insensitive to several systematic errors of optical readout and enables the use of quantum feedback.

##### Complete entropic inequalities for Quantum Markov chains

Li Gao, Cambyse Rouzé

We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum channel satisfies a strong data processing inequality with respect to its decoherence free part. Moreover, we establish the first general approximate tensorization property of relative entropy. This extends the famous strong subadditivity of the quantum entropy (SSA) of two subsystems to the general setting of two subalgebras. All the three results are independent of the size of the environment and hence satisfy the tensorization property. They are obtained via a common, conceptually simple method for proving entropic inequalities via spectral or L2-estimates. As applications, we combine our results on the modified log-Sobolev inequality and approximate tensorization to derive bounds for examples of both theoretical and practical relevance, including representation of sub-Laplacians on SU(2) and various classes of local quantum Markov semigroups such as quantum Kac generators and continuous time approximate unitary designs. For the latter, our bounds imply the existence of local continuous time Markovian evolutions on nk qudits forming ε-approximate k-designs in relative entropy for times scaling as Õ(n poly(k)).

##### Coherent Control in the Ground and Optically Excited States of an Ensemble of Erbium Dopants

P. Cova Fariña, B. Merkel, N. Herrera Valencia, P. Yu, A. Ulanowski, and A. Reiserer

Physical Review Applied 15, 64028 (2021).

Ensembles of erbium dopants can realize quantum memories and frequency converters that operate in the minimal-loss wavelength band of fiber optical communication. Their operation requires the initialization, coherent control, and readout of the electronic spin state. In this work, we use a split-ring microwave resonator to demonstrate such control in both the ground and optically excited state. The presented techniques can also be applied to other combinations of dopant and host and may facilitate the further development of quantum memory protocols and sensing schemes.

##### Lokales Quantennetzwerk für Alice und Bob

F. Deppe, K.G. Fedorov, A. Marx

Akadmie Aktuell Heft 2 (74), 36-38 (2021).

Vom wissenschaftlichen Nischenthema zum international anerkannten Forschungsfeld: Quantenmikrowellen eröffnen viele Anwendungsperspektiven, für die sich auch die Industrie interessiert.

##### Quantum Repeater Node Demonstrating Unconditionally Secure Key Distribution

S. Langenfeld, P. Thomas, O.Morin, G. Rempe

Physical Review Letters 126, 230506 (2021).

Long-distance quantum communication requires quantum repeaters to overcome photon loss in optical fibers. Here we demonstrate a repeater node with two memory atoms in an optical cavity. Both atoms are individually and repeatedly entangled with photons that are distributed until each communication partner has independently received one of them. An atomic Bell-state measurement followed by classical communication serves to establish a key. We demonstrate scaling advantage of the key rate, increase the effective attenuation length by a factor of 2, and beat the error-rate threshold of 11% for unconditionally secure communication, the corner stones for repeater-based quantum networks.

##### Manganese doping for enhanced magnetic brightening and circular polarization control of dark excitons in paramagnetic layered hybrid metal-halide perovskites

T. Neumann, S. Feldmann, P. Moser, A. Delhomme, J. Zerhoch, T. van de Goor, S. Wang, M. Dyksik, T. Winkler, J.J. Finley, P. Plochocka, M.S. Brandt, C. Faugeras, A.V. Stier, F. Deschler

Nature Communications 12, 3489 (2021).

Materials combining semiconductor functionalities with spin control are desired for the advancement of quantum technologies. Here, we study the magneto-optical properties of novel paramagnetic Ruddlesden-Popper hybrid perovskites Mn:(PEA)2PbI4 (PEA = phenethylammonium) and report magnetically brightened excitonic luminescence with strong circular polarization from the interaction with isolated Mn2+ ions. Using a combination of superconducting quantum interference device (SQUID) magnetometry, magneto-absorption and transient optical spectroscopy, we find that a dark exciton population is brightened by state mixing with the bright excitons in the presence of a magnetic field. Unexpectedly, the circular polarization of the dark exciton luminescence follows the Brillouin-shaped magnetization with a saturation polarization of 13% at 4 K and 6 T. From high-field transient magneto-luminescence we attribute our observations to spin-dependent exciton dynamics at early times after excitation, with first indications for a Mn-mediated spin-flip process. Our findings demonstrate manganese doping as a powerful approach to control excitonic spin physics in Ruddlesden-Popper perovskites, which will stimulate research on this highly tuneable material platform with promise for tailored interactions between magnetic moments and excitonic states.

##### Critically slow operator dynamics in constrained many-body systems

J. Feldmeier, M. Knap

The far-from-equilibrium dynamics of generic interacting quantum systems is characterized by a handful of universal guiding principles, among them the ballistic spreading of initially local operators. Here, we show that in certain constrained many-body systems the structure of conservation laws can cause a drastic modification of this universal behavior. As an example, we study operator growth characterized by out-of-time-order correlations (OTOCs) in a dipole-conserving fracton chain. We identify a critical point with sub-ballistically moving OTOC front, that separates a ballistic from a dynamically frozen phase. This critical point is tied to an underlying localization transition and we use its associated scaling properties to derive an effective description of the moving operator front via a biased random walk with long waiting times. We support our arguments numerically using classically simulable automaton circuits.

##### Accelerating seminumerical Fock-exchange calculations using mixed single- and double-precision arithmethic

H. Laqua, J. Kussmann, C. Ochsenfeld

Journal of Chemical Physics 154 (4), 214116 (2021).

We investigate the applicability of single-precision (fp32) floating point operations within our linear-scaling, seminumerical exchange method sn-LinK [Laqua et al., J. Chem. Theory Comput. 16, 1456 (2020)] and find that the vast majority of the three-center-one-electron (3c1e) integrals can be computed with reduced numerical precision with virtually no loss in overall accuracy. This leads to a near doubling in performance on central processing units (CPUs) compared to pure fp64 evaluation. Since the cost of evaluating the 3c1e integrals is less significant on graphic processing units (GPUs) compared to CPU, the performance gains from accelerating 3c1e integrals alone is less impressive on GPUs. Therefore, we also investigate the possibility of employing only fp32 operations to evaluate the exchange matrix within the self-consistent-field (SCF) followed by an accurate one-shot evaluation of the exchange energy using mixed fp32/fp64 precision. This still provides very accurate (1.8 µEh maximal error) results while providing a sevenfold speedup on a typical “gaming” GPU (GTX 1080Ti). We also propose the use of incremental exchange-builds to further reduce these errors. The proposed SCF scheme (i-sn-LinK) requires only one mixed-precision exchange matrix calculation, while all other exchange-matrix builds are performed with only fp32 operations. Compared to pure fp64 evaluation, this leads to 4–7× speedups for the whole SCF procedure without any significant deterioration of the results or the convergence behavior.

##### The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions

Ángela Capel, Cambyse Rouzé, Daniel Stilck França

(2021).

Given a uniform, frustration-free family of local Lindbladians defined on a quantum lattice spin system in any spatial dimension, we prove a strong exponential convergence in relative entropy of the system to equilibrium under a condition of spatial mixing of the stationary Gibbs states and the rapid decay of the relative entropy on finite-size blocks. Our result leads to the first examples of the positivity of the modified logarithmic Sobolev inequality for quantum lattice spin systems independently of the system size. Moreover, we show that our notion of spatial mixing is a consequence of the recent quantum generalization of Dobrushin and Shlosman's complete analyticity of the free-energy at equilibrium. The latter typically holds above a critical temperature Tc. Our results have wide-ranging applications in quantum information. As an illustration, we discuss four of them: first, using techniques of quantum optimal transport, we show that a quantum annealer subject to a finite range classical noise will output an energy close to that of the fixed point after constant annealing time. Second, we prove Gaussian concentration inequalities for Lipschitz observables and show that the eigenstate thermalization hypothesis holds for certain high-temperture Gibbs states. Third, we prove a finite blocklength refinement of the quantum Stein lemma for the task of asymmetric discrimination of two Gibbs states of commuting Hamiltonians satisfying our conditions. Fourth, in the same setting, our results imply the existence of a local quantum circuit of logarithmic depth to prepare Gibbs states of a class of commuting Hamiltonians.

##### Universal signatures of Dirac fermions in entanglement and charge fluctuations

V. Crépel, A. Hackenbroich, N. Regnault, B. Estienne

Physical Review B 103, 235108 (2021).

We investigate the entanglement entropy (EE) and charge fluctuations in models where the low-energy physics is governed by massless Dirac fermions. We focus on the response to flux insertion which, for the EE, is widely assumed to be universal, i.e., independent of the microscopic details. We provide an analytical derivation of the EE and charge fluctuations for the seminal example of graphene, using the dimensional reduction of its tight-binding model to the one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the EE matches the conformal field theory prediction. We show that the charge variance has the same asymptotic behavior, up to a constant prefactor. To check the validity of universality arguments, we numerically consider several models, with different geometries and numbers of Dirac cones, and either for strictly two-dimensional models or for a gapless surface mode of three-dimensional topological insulators. We also show that the flux response does not depend on the entangling surface geometry as long as it encloses the flux. Finally we consider the universal corner contributions to the EE. We show that in the presence of corners, the Kitaev-Preskill subtraction scheme provides nonuniversal, geometry-dependent results.

##### Generating function for tensor network diagrammatic summation

W.L. Tu, H.K. Wu, N. Schuch, N. Kawashima, J.Y. Chen

Physical Review B 103, 205155 (2021).

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading-order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and the dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite-size systems and higher dimension are outlined.

##### On S-Matrix Exclusion of de Sitter and Naturalness

G. Dvali

The cosmological constant puzzle, traditionally viewed as a naturalness problem, is evidently nullified by the S-matrix formulation of quantum gravity/string theory. We point out an implication of this fact for another naturalness puzzle, the Hierarchy Problem between the weak and Planck scales. By eliminating the landscape of de Sitter vacua and eternal inflation, the S-matrix formulation exhibits an obvious tension with the explanations based on anthropic selection or cosmological relaxation of the Higgs mass. This sharpens the Hierarchy Problem in a profound way. On one hand, it strengthens the case for explanations based on new physics not far from the weak scale. At the same time, it opens up a question, whether instead the hierarchy is imposed by the S-matrix consistency between the Standard Model and gravity.

##### The nonlinear Schrödinger equation for orthonormal functions II. Applications to Lieb-Thirring inequalities

R.L. Frank, D. Gontier, M. Lewin

Commun. Math. Phys. 384, 1783- 1828 (2021).

In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a Schrödinger operator −Δ+V(x) are raised to the power κ is never given by the one-bound state case when κ>max(0,2−d/2) in space dimension d≥1. When in addition κ≥1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo–Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb–Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schrödinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. https://doi.org/10.1007/s00205-021-01634-7). In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.R. L. Frank, E. H. Lieb

##### Rényi free energy and variational approximations to thermal states

G. Giudice, A. Cakan, J.I. Cirac, M.C. Banuls

Physical Review B 103, 205128 (2021).

We propose the construction of thermodynamic ensembles that minimize the Rényi free energy, as an alternative to Gibbs states. For large systems, the local properties of these Rényi ensembles coincide with those of thermal equilibrium, and they can be used as approximations to thermal states. We provide algorithms to find tensor network approximations to the 2-Rényi ensemble. In particular, a matrix-product-state representation can be found by using gradient-based optimization on Riemannian manifolds, or via a non-linear evolution which yields the desired state as a fixed point. We analyze the performance of the algorithms and the properties of the ensembles on one-dimensional spin chains.

##### Algorithms for quantum simulation at finite energies

S. Lu, M.C. Banuls, J.I. Cirac

Physical Review X Quantum 2, 20321 (2021).

We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a finite energy interval around its mean energy. This algorithm is based on a filtering operator, similar to quantum phase estimation, which projects out energies outside the desired energy interval. However, instead of performing this operation on a physical state, it recovers the physical values by performing interferometric measurements without the need to prepare the filtered state. We show that the computational time scales polynomially with the number of qubits, the inverse of the prescribed variance, and the inverse error. In practice, the algorithm does not require the evolution for long times, but instead a significant number of measurements in order to obtain sensible results. Our second algorithm is a quantum-assisted Monte Carlo sampling method to compute other quantities which approach the expectation values for the microcanonical and canonical ensembles. Using classical Monte Carlo techniques and the quantum computer as a resource, this method circumvents the sign problem that is plaguing classical Quantum Monte Carlo simulations, as long as one can prepare states with suitable energies. All algorithms can be used with small quantum computers and analog quantum simulators, as long as they can perform the interferometric measurements. We also show that this last task can be greatly simplified at the expense of performing more measurements.

##### Preparation and verification of tensor network states

E. Cruz, F. Baccari, J. Tura, N. Schuch, J.I. Cirac

We consider a family of tensor network states defined on regular lattices that can be efficiently prepared with a quantum computer by adiabatic evolution. This family comprises relevant classes of states, such as injective Matrix Product and Projected Entangled-Pair States, and some corresponding to classical spin models. We show how uniform lower bounds to the gap of the parent Hamiltonian along the adiabatic trajectory can be efficiently computed using semi-definite programming. We also derive a set of observables whose expectation values can be easily determined and that form a complete set, in the sense that they uniquely characterize the state. We identify a subset of those observables which can be efficiently computed if one has access to the quantum state and local measurements, and analyze how they can be used in verification procedures.

##### Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem

Simon Becker, Nilanjana Datta, Ludovico Lami, Cambyse Rouzé

Physical Review Letters 126, 190504 (2021).

We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Secondly, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Thirdly, we establish a version of the Solovay--Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.

##### Energy-Constrained Discrimination of Unitaries, Quantum Speed Limits, and a Gaussian Solovay-Kitaev Theorem

S. Becker, N. Datta, L. Lami, C. Rouzé

Physical Review Letters 126, 190504 (2021).

We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. First, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Second, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We expect these results to be relevant for benchmarking internal dynamics of quantum devices. Third, we establish a version of the Solovay-Kitaev theorem that applies to the group of Gaussian unitaries over a finite number of modes, with the approximation error being measured with respect to the EC diamond norm relative to the photon number Hamiltonian.

##### Application of Optimal Control Theory to Fourier Transform Ion Cyclotron Resonance

V. Martikyan, C. Beluffi, S.J. Glaser, M.A. Delsuc, D. Sugny

Molecules 26 (10), 2860 (2021).

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

##### Ionic polaron in a Bose-Einstein condensate

G.E. Astrakharchik, L.A. Peña Ardila, R. Schmidt, K. Jachymski, A. Negretti

Communications Physics 4, 94 (2021).

The presence of strong interactions in a many-body quantum system can lead to a variety of exotic effects. Here we show that even in a comparatively simple setup consisting of a charged impurity in a weakly interacting bosonic medium the competition of length scales gives rise to a highly correlated mesoscopic state. Using quantum Monte Carlo simulations, we unravel its vastly different polaronic properties compared to neutral quantum impurities. Moreover, we identify a transition between the regime amenable to conventional perturbative treatment in the limit of weak atom-ion interactions and a many-body bound state with vanishing quasi-particle residue composed of hundreds of atoms. In order to analyze the structure of the corresponding states, we examine the atom-ion and atom-atom correlation functions which both show nontrivial properties. Our findings are directly relevant to experiments using hybrid atom-ion setups that have recently attained the ultracold regime.

##### Quantifying the spin mixing conductance of EuO/W heterostructures by spin Hall magnetoresistance experiments

P. Rosenberger, M. Opel, S. Geprägs, H. Huebl, R. Gross, M. Müller, M. Althammer

Applied Physics Letters 118, 192401 (2021).

The spin Hall magnetoresistance (SMR) allows to investigate the magnetic textures of magnetically ordered insulators in heterostructures with normal metals by magnetotransport experiments. We here report the observation of the SMR in in situ prepared ferromagnetic EuO/W thin film bilayers with magnetically and chemically well-defined interfaces. We characterize the magnetoresistance effects utilizing angle-dependent and field-dependent magnetotransport measurements as a function of temperature. Applying the established SMR model, we derive and quantify the real and imaginary parts of the complex spin mixing interface conductance. We find that the imaginary part is by one order of magnitude larger than the real part. Both decrease with increasing temperature. This reduction is in agreement with thermal fluctuations in the ferromagnet.

##### Charge Traps in All-Inorganic CsPbBr3 Perovskite Nanowire Field-Effect Phototransistors

F. Winterer, L.S. Walter, J. Lenz, S. Seebauer, Y. Tong, L. Polavarapu, R.T. Weitz

Advanced electronic Materials 7 (6), 2100105 (2021).

All-inorganic halide perovskite materials have recently emerged as outstanding materials for optoelectronic applications. However, although critical for developing novel technologies, the influence of charge traps on charge transport in all-inorganic systems still remains elusive. Here, the charge transport properties in cesium lead bromide, nanowire films are probed using a field-effect transistor geometry. Field-effect mobilities of μFET = 4 × 10−3 cm−2 V−1 s−1 and photoresponsivities in the range of R = 25 A W−1 are demonstrated. Furthermore, charge transport both with and without illumination is investigated down to cryogenic temperatures. Without illumination, deep traps dominate transport and the mobility freezes out at low temperatures. Despite the presence of deep traps, when illuminating the sample, the field-effect mobility increases by several orders of magnitude and even phonon-limited transport characteristics are visible. This can be seen as an extension to the notion of “defect tolerance” of perovskite materials that has solely been associated with shallow traps. These findings provide further insight in understanding charge transport in perovskite materials and underlines that managing deep traps can open up a route to optimizing optoelectronic devices such as solar cells or phototransistors operable also at low light intensities.

##### High-Performance Vertical Organic Transistors of Sub-5 nm Channel Length

J. Lenz, A.M. Seiler, F.R. Geisenhof, F. Winterer, K. Watanabe, T. Taniguchi, R.T. Weitz

Nano Letters 21 (10), 4430–4436 (2021).

Miniaturization of electronic circuits increases their overall performance. So far, electronics based on organic semiconductors has not played an important role in the miniaturization race. Here, we show the fabrication of liquid electrolyte gated vertical organic field effect transistors with channel lengths down to 2.4 nm. These ultrashort channel lengths are enabled by using insulating hexagonal boron nitride with atomically precise thickness and flatness as a spacer separating the vertically aligned source and drain electrodes. The transistors reveal promising electrical characteristics with output current densities of up to 2.95 MA cm–2 at −0.4 V bias, on–off ratios of up to 106, a steep subthreshold swing of down to 65 mV dec–1 and a transconductance of up to 714 S m–1. Realizing channel lengths in the sub-5 nm regime and operation voltages down to 100 μV proves the potential of organic semiconductors for future highly integrated or low power electronics.

##### Localizable quantum coherence

A. Hamma, G. Styliaris, P. Zanardi

Physics Letters A 397, 127264 (2021).

Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum system. In this paper, we put forward a notion of localizable coherence as the coherence that can be stored in a particular subsystem, either by measuring or just by disregarding the rest. We examine its spreading, its average properties in the Hilbert space and show that it can be applied to reveal the real-space structure of states of interest in quantum many-body theory, for example, localized or topological states.

##### Quantensysteme lernen gemeinsames Rechnen

S. Daiss, G. Rempe

Physik in unserer Zeit (2021).

Quantencomputer besitzen heute erst wenige Qubits in einzelnen Aufbauten. Jetzt ist es gelungen, ein Quantengatter zwischen zwei Qubits in sechzig Metern Entfernung zu realisieren: ein Prototyp eines verteilt rechnenden Quantencomputers.

##### Optical Signatures of Periodic Charge Distribution in a Mott-like Correlated Insulator State

Y. Shimazaki, C. Kuhlenkamp, I. Schwartz, T. Smoleński, K. Watanabe, T. Taniguchi, M. Kroner, R. Schmidt, M. Knap, A. Imamoğlu

Physical Review X 11 (2), 21027 (2021).

The elementary optical excitations in two-dimensional semiconductors hosting itinerant electrons are attractive and repulsive polarons—excitons that are dynamically screened by electrons. Exciton polarons have hitherto been studied in translationally invariant degenerate Fermi systems. Here, we show that periodic distribution of electrons breaks the excitonic translational invariance and leads to a direct optical signature in the exciton-polaron spectrum. Specifically, we demonstrate that new optical resonances appear due to spatially modulated interactions between excitons and electrons in an incompressible Mott-like correlated state. Our observations demonstrate that resonant optical spectroscopy provides an invaluable tool for studying strongly correlated states, such as Wigner crystals and density waves, where exciton-electron interactions are modified by the emergence of charge order.

##### A nondestructive Bell-state measurement on two distant atomic qubits

S. Welte, P. Thomas, L. Hartung, S. Daiss, S. Langenfeld, O. Morin, G. Rempe, and E. Distante

Nature Photonics 15, 504–509 (2021).

One of the most fascinating aspects of quantum networks is their capability to distribute entanglement as a nonlocal communication resource. In a first step, this requires network-ready devices that can generate and store entangled states. Another crucial step, however, is to develop measurement techniques that allow for entanglement detection. Demonstrations for different platforms suffer from being not complete, destructive or local. Here, we demonstrate a complete and nondestructive measurement scheme that always projects any initial state of two spatially separated network nodes onto a maximally entangled state. Each node consists of an atom trapped inside an optical resonator from which two photons are successively reflected. Polarization measurements on the photons discriminate between the four maximally entangled states. Remarkably, such states are not destroyed by our measurement. In the future, our technique might serve to probe the decay of entanglement and to stabilize it against dephasing via repeated measurements.

##### Correlation energy of a weakly interacting Fermi gas

N. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer

Inventiones mathematicae 225, 885–979 (2021).

We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.

##### A nondestructive Bell-state measurement on two distant atomic qubits

S. Welte, P. Thomas, L. Hartung, S. Daiss, S. Langenfeld, O. Morin, G. Rempe, E. Distante

Nature Photonics 15, 504–509 (2021).

One of the most fascinating aspects of quantum networks is their capability to distribute entanglement as a nonlocal communication resource. In a first step, this requires network-ready devices that can generate and store entangled states. Another crucial step, however, is to develop measurement techniques that allow for entanglement detection. Demonstrations for different platforms suffer from being not complete, destructive or local. Here, we demonstrate a complete and nondestructive measurement scheme that always projects any initial state of two spatially separated network nodes onto a maximally entangled state. Each node consists of an atom trapped inside an optical resonator from which two photons are successively reflected. Polarization measurements on the photons discriminate between the four maximally entangled states. Remarkably, such states are not destroyed by our measurement. In the future, our technique might serve to probe the decay of entanglement and to stabilize it against dephasing via repeated measurements.

##### Tunable Feshbach resonances and their spectral signatures in bilayer semiconductors

C. Kuhlenkamp, M. Knap, M. Wagner, R. Schmidt, A. Imamoglu

Feshbach resonances are an invaluable tool in atomic physics, enabling precise control of interactions and the preparation of complex quantum phases of matter. Here, we theoretically analyze a solid-state analogue of a Feshbach resonance in two dimensional semiconductor heterostructures. In the presence of inter-layer electron tunneling, the scattering of excitons and electrons occupying different layers can be resonantly enhanced by tuning an applied electric field. The emergence of an inter-layer Feshbach molecule modifies the optical excitation spectrum, and can be understood in terms of Fermi polaron formation. We discuss potential implications for the realization of correlated Bose-Fermi mixtures in bilayer semiconductors.

##### Generalization of group-theoretic coherent states for variational calculations

T. Guaita, L. Hackl, T. Shi, E. Demler, J.I. Cirac

Physical Review Research 3, 023090 (2021).

We introduce families of pure quantum states that are constructed on top of the well-known Gilmore-Perelomov group-theoretic coherent states. We do this by constructing unitaries as the exponential of operators quadratic in Cartan subalgebra elements and by applying these unitaries to regular group-theoretic coherent states. This enables us to generate entanglement not found in the coherent states themselves, while retaining many of their desirable properties. Most importantly, we explain how the expectation values of physical observables can be evaluated efficiently. Examples include generalized spin-coherent states and generalized Gaussian states, but our construction can be applied to any Lie group represented on the Hilbert space of a quantum system. We comment on their applicability as variational families in condensed matter physics and quantum information.

##### Estimates on derivatives of Coulombic wave functions and their electron densities

S. Fournais, T.Ø. Sørensen

Journal für die reine und angewandte Mathematik 775, 1-38 (2021).

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the corresponding one-electron densities ρ, involving negative powers of the distance from the nuclei. The results are both natural and optimal, as seen from the ground state of Hydrogen.

##### Weakly invasive metrology: quantum advantage and physical implementations

M. Perarnau-Llobet, D. Malz, J.I. Cirac

Quantum 5, 446 (2021).

We consider the estimation of a Hamiltonian parameter of a set of highly photosensitive samples, which are damaged after a few photons Nabs are absorbed, for a total time T. The samples are modelled as a two mode photonic system, where photons simultaneously acquire information on the unknown parameter and are absorbed at a fixed rate. We show that arbitrarily intense coherent states can obtain information at a rate that scales at most linearly with Nabs and T, whereas quantum states with finite intensity can overcome this bound. We characterise the quantum advantage as a function of Nabs and T, as well as its robustness to imperfections (non-ideal detectors, finite preparation and measurement rates for quantum photonic states). We discuss an implementation in cavity QED, where Fock states are both prepared and measured by coupling atomic ensembles to the cavities. We show that superradiance, arising due to a collective coupling between the cavities and the atoms, can be exploited for improving the speed and efficiency of the measurement.

##### Coupling a mobile hole to an antiferromagnetic spin background: Transient dynamics of a magnetic polaron

G. Ji, M. Xu, L.H. Kendrick, C.S. Chiu, J.C. Brüggenjürgen, D. Greif, A. Bohrdt, F. Grusdt, E. Demler, M. Lebrat, M. Greiner

Physical Review X 11, 21022 (2021).

Understanding the interplay between charge and spin and its effects on transport is a ubiquitous challenge in quantum many-body systems. In the Fermi-Hubbard model, this interplay is thought to give rise to magnetic polarons, whose dynamics may explain emergent properties of quantum materials such as high-temperature superconductivity. In this work, we use a cold-atom quantum simulator to directly observe the formation dynamics and subsequent spreading of individual magnetic polarons. Measuring the density- and spin-resolved evolution of a single hole in a 2D Hubbard insulator with short-range antiferromagnetic correlations reveals fast initial delocalization and a dressing of the spin background, indicating polaron formation. At long times, we find that dynamics are slowed down by the spin exchange time, and they are compatible with a polaronic model with strong density and spin coupling. Our work enables the study of out-of-equilibrium emergent phenomena in the Fermi-Hubbard model, one dopant at a time.

##### Radiofrequency spectroscopy of one-dimensional trapped Bose polarons: crossover from the adiabatic to the diabatic regime

S. I. Mistakidis, G. M. Koutentakis, F. Grusdt, H. R. Sadeghpour, P. Schmelcher

New Journal of Physics 23, 43051 (2021).

We investigate the crossover of the impurity-induced dynamics, in trapped one-dimensional Bose polarons subject to radio frequency (RF) pulses of varying intensity, from an adiabatic to a diabatic regime. Utilizing adiabatic pulses for either weak repulsive or attractive impurity-medium interactions, a multitude of polaronic excitations or mode-couplings of the impurity-bath interaction with the collective breathing motion of the bosonic medium are spectrally resolved. We find that for strongly repulsive impurity-bath interactions, a temporal orthogonality catastrophe manifests in resonances in the excitation spectra where impurity coherence vanishes. When two impurities are introduced, impurity–impurity correlations, for either attractive or strong repulsive couplings, induce a spectral shift of the resonances with respect to the single impurity. For a heavy impurity, the polaronic peak is accompanied by a series of equidistant side-band resonances, related to interference of the impurity spin dynamics and the sound waves of the bath. In all cases, we enter the diabatic transfer regime for an increasing bare Rabi frequency of the RF field with a Lorentzian spectral shape featuring a single polaronic resonance. The findings in this work on the effects of external trap, RF pulse and impurity–impurity interaction should have implications for the new generations of cold-atom experiments.

##### Cooperation and dependencies in multipartite systems

W. Kłobus, M. Miller, M. Pandit, R.Ganardi, L. Knips, J. Dziewior, J. Meinecke, H. Weinfurter, W. Laskowski, T. Paterek

NJP 23, 63057 (2021).

We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations.

##### Stability of a Szegő-type asymptotics

P. Müller, R. Schulte

We consider a multi-dimensional continuum Schrödinger operator H which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the second-order Szegő-type asymptotics for the spatially truncated Fermi projection of H is independent of the potential and, thus, identical to the known asymptotics of the Laplacian.

##### Fractional Chiral Hinge Insulator

A. Hackenbroich, A. Hudomal, N. Schuch, B.A. Bernevig, N. Regnault

Physical Review B 103, L161110 (2021).

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two noninteracting second-order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge c=1 and Luttinger parameter K=1/2, like the edge modes of a Laughlin 1/2 state. The bulk and surface topology is characterized by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host an unconventional two-dimensional topological phase. In a clear departure from the physics of a Laughlin 1/2 state, we find a TEE per surface compatible with (ln√2)/2, half that of a Laughlin 1/2 state. This value cannot be obtained from topological quantum field theory for purely two-dimensional systems. For the sake of completeness, we also investigate the topological degeneracy.

##### Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit

D. Malz, A. Smith

Physical Review Letters 126, 163602 (2021).

Current noisy intermediate-scale quantum (NISQ) devices constitute powerful platforms for analog quantum simulation. The exquisite level of control offered by state-of-the-art quantum computers make them especially promising to implement time-dependent Hamiltonians. We implement quasiperiodic driving of a single qubit in the IBM Quantum Experience and thus experimentally realize a temporal version of the half-Bernevig-Hughes-Zhang Chern insulator. Using simple error mitigation, we achieve consistently high fidelities of around 97%. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Motivated by these results, we theoretically study the many-qubit case, and show that one can implement a wide class of Floquet Hamiltonians, or time-dependent Hamiltonians in general. Our study highlights promises and limitations when studying many-body systems through multifrequency driving of quantum computers.

##### BaOsO3: A Hund's metal in the presence of strong spin-orbit coupling

M. Bramberger, J. Mravlje, M. Grundner, U. Schollwöck, M. Zingl

Physical Review B 103, 165133 (2021).

We investigate the 5d transition metal oxide BaOsO3 within a combination of density functional theory and dynamical mean-field theory, using a matrix-product-state impurity solver. BaOsO3 has four electrons in the t2g shell akin to ruthenates but stronger spin-orbit coupling (SOC) and is thus expected to reveal an interplay of Hund's metal behavior with SOC. We explore the paramagnetic phase diagram as a function of SOC and Hubbard interaction strengths, identifying metallic, band (van Vleck) insulating, and Mott insulating regions. At the physical values of the two couplings, we find that BaOsO3 is still situated inside the metallic region and has a moderate quasiparticle renormalization m∗/m≈2, consistent with specific heat measurements. SOC leads to a splitting of a van Hove singularity close to the Fermi energy and a subsequent reduction of electronic correlations (found in the vanishing SOC case), but the SOC strength is insufficient to push the material into an insulating van Vleck regime. In spite of the strong effect of SOC, BaOsO3 can be best pictured as a moderately correlated Hund's metal.

##### Atomistic investigation of surface characteristics and electronic features at high-purity FeSi(110) presenting interfacial metallicity

B. Yang, M. Uphoff, Y.-Q. Zhang, J. Reichert, A.P. Seitsonen, A. Bauer, C. Pfleiderer, J.V. Barth

PNAS 118 , e2021203118 (2021).

Iron silicide (FeSi) provides multiple fascinating features whereby intriguing functional properties bearing significant application prospects were recognized. FeSi is understood notably as a correlated d-electron narrow-gap semiconductor and a putative Kondo insulator, hosting unconventional quasiparticles. Recently, metallic surface conduction channels were identified at cryogenic conditions and suggested to play a key role in the resistivity of high-quality single-crystalline specimens. Motivated by these findings, we prepared and closely examined a FeSi(110) surface with atomistically defined termination and topography. In the low-temperature regime, where surface metallicity emerges, the electronic band gap undergoes a subtle evolution. The pertaining key features, asymmetrization of the gap shape and formation of in-gap states, underscore the similarity of FeSi to unequivocal topological Kondo insulator materials.

##### On the spectrum of the Kronig-Penney model in a constant electric field

R.L. Frank, S. Larson

We are interested in the nature of the spectrum of the one-dimensional Schrödinger operator

−d2dx2−Fx+∑n∈Zgnδ(x−n)in L2(R)

with F>0 and two different choices of the coupling constants {gn}n∈Z. In the first model gn≡λ and we prove that if F∈π2Q then the spectrum is R and is furthermore absolutely continuous away from an explicit discrete set of points. In the second model gn are independent random variables with mean zero and variance λ2. Under certain assumptions on the distribution of these random variables we prove that almost surely the spectrum is R and it is dense pure point if F<λ2/2 and purely singular continuous if F>λ2/2.

##### Gaussian continuous tensor network states for simple bosonic field theories

T. D. Karanikolaou, P. Emonts, and A. Tilloy.

Physical Review Research 3, 023059 (2021).

Tensor networks states allow one to find the low-energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow one to renormalize away simple divergences variationally. In the end our study makes it plausible that CTNSs are indeed a good manifold to approximate the low-energy states of QFTs.

##### Gaussian continuous tensor network states for simple bosonic field theories

T.D. Karanikolaou, P. Emonts, A. Tilloy

Physical Review Research 3, 023059 (2021).

Tensor networks states allow one to find the low-energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow one to renormalize away simple divergences variationally. In the end our study makes it plausible that CTNSs are indeed a good manifold to approximate the low-energy states of QFTs.

##### Exact Thermalization Dynamics in the “Rule 54” Quantum Cellular Automaton

K. Klobas, B. Bertini, L. Piroli

Physical Review Letters 126, 160602 (2021).

We study the out-of-equilibrium dynamics of the quantum cellular automaton known as “Rule 54.” For a class of low-entangled initial states, we provide an analytic description of the effect of the global evolution on finite subsystems in terms of simple quantum channels, which gives access to the full thermalization dynamics at the microscopic level. As an example, we provide analytic formulas for the evolution of local observables and Rényi entropies. We show that, in contrast to other known examples of exactly solvable quantum circuits, Rule 54 does not behave as a simple Markovian bath on its own parts, and displays typical nonequilibrium features of interacting integrable many-body quantum systems such as finite relaxation rate and interaction-induced dressing effects. Our study provides a rare example where the full thermalization dynamics can be solved exactly at the microscopic level.

##### Topological Lower Bound on Quantum Chaos by Entanglement Growth

Z.-P. Gong, L. Piroli, J.I. Cirac

Physical Review Letters 126, 160601 (2021).

A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the evolution operator. Here we show that, for one-dimensional quantum cellular automata (QCA), there exists a lower bound on quantum chaos quantified by such entanglement entropy. This lower bound is equal to twice the index of the QCA, which is a topological invariant that measures the chirality of information flow, and holds for all the Rényi entropies, with its strongest Rényi-∞ version being tight. The rigorous bound rules out the possibility of any sublinear entanglement growth behavior, showing in particular that many-body localization is forbidden for unitary evolutions displaying nonzero index. Since the Rényi entropy is measurable, our findings have direct experimental relevance. Our result is robust against exponential tails which naturally appear in quantum dynamics generated by local Hamiltonians.

##### Field tensor network states

A.E.B. Nielsen, B. Herwerth, J.I. Cirac, G. Sierra

Physical Review B 103, 155130 (2021).

We define a class of tensor network states for spin systems where the individual tensors are functionals of fields. The construction is based on the path-integral representation of correlators of operators in quantum field theory. These tensor network states are infinite-dimensional versions of matrix product states and projected entangled pair states. We find the field tensor that generates the Haldane-Shastry wave function and extend it to two dimensions. We give evidence that the latter underlies the topological chiral state described by the Kalmeyer-Laughlin wave function.

##### Synthetic control over the binding configuration of luminescent sp3-defects in single-walled carbon nanotubes

S. Settele, F. Berger, S. Lindenthal, S. Zhao, A. Ali El Yumin, N. Zorn, A. Asyuda, M. Zharnikov, A. Högele, J. Zaumseil

Nature Communications 12, 2119 (2021).

The controlled functionalization of single-walled carbon nanotubes with luminescent sp3-defects has created the potential to employ them as quantum-light sources in the near-infrared. For that, it is crucial to control their spectral diversity. The emission wavelength is determined by the binding configuration of the defects rather than the molecular structure of the attached groups. However, current functionalization methods produce a variety of binding configurations and thus emission wavelengths. We introduce a simple reaction protocol for the creation of only one type of luminescent defect in polymer-sorted (6,5) nanotubes, which is more red-shifted and exhibits longer photoluminescence lifetimes than the commonly obtained binding configurations. We demonstrate single-photon emission at room temperature and expand this functionalization to other polymer-wrapped nanotubes with emission further in the near-infrared. As the selectivity of the reaction with various aniline derivatives depends on the presence of an organic base we propose nucleophilic addition as the reaction mechanism.

##### Generation of photonic matrix product states with Rydberg atomic arrays

Z.-Y. Wei, D. Malz, A. González-Tudea, J.I. Cirac

Physical Review Research 3, 023021 (2021).

We show how one can deterministically generate photonic matrix product states with high bond and physical dimensions with an atomic array if one has access to a Rydberg-blockade mechanism. We develop both a quantum gate and an optimal control approach to universally control the system and analyze the photon retrieval efficiency of atomic arrays. Comprehensive modeling of the system shows that our scheme is capable of generating a large number of entangled photons. We further develop a multi-port photon emission approach that can efficiently distribute entangled photons into free space in several directions, which can become a useful tool in future quantum networks.

##### Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model

F. A. Palm, M. Buser, J. Léonard, M. Aidelsburger, U. Schollwöck, F. Grusdt

Physical Review B 103, L161101 (2021).

Topological states of matter, such as fractional quantum Hall states, are an active field of research due to their exotic excitations. In particular, ultracold atoms in optical lattices provide a highly controllable and adaptable platform to study such new types of quantum matter. However, finding a clear route to realize non-Abelian quantum Hall states in these systems remains challenging. Here we use the density-matrix renormalization-group (DMRG) method to study the Hofstadter-Bose-Hubbard model at filling factor ν=1 and find strong indications that at α=1/6 magnetic flux quanta per plaquette the ground state is a lattice analog of the continuum non-Abelian Pfaffian. We study the on-site correlations of the ground state, which indicate its paired nature at ν=1, and find an incompressible state characterized by a charge gap in the bulk. We argue that the emergence of a charge density wave on thin cylinders and the behavior of the two- and three-particle correlation functions at short distances provide evidence for the state being closely related to the continuum Pfaffian. The signatures discussed in this letter are accessible in current cold atom experiments and we show that the Pfaffian-like state is readily realizable in few-body systems using adiabatic preparation schemes.

##### Revealing the phase diagram of Kitaev materials by Machine Learning: Cooperation and Competition between spin Liquids

K. Liu, N. Sadoune, N. Rao, J. Greitemann, L. Pollet

Physical Review Research 3, 023016 (2021).

Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases. We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-Γ model in a magnetic field. Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic S3 magnets, and two modulated S3×Z3 magnets. We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-S limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level. Moreover, the two S3×Z3 orders are induced by competition between Kitaev and Γ spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors. Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.

##### Realizing topologically ordered states on a quantum processor

K. J. Satzinger, Y. Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, J. Basso, A. Bengtsson, A. Bilmes, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. R. Derk, D. Eppens, C. Erickson, E. Farhi, L. Foaro, A. G. Fowler, B. Foxen, M. Giustina, A. Greene, J. A. Gross, M. P. Harrigan, S. D. Harrington, J. Hilton, S. Hong, T. Huang, W. J. Huggins, L. B. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, T. Khattar, S. Kim, P. V. Klimov, A.N. Korotkov, F. Kostritsa, D. Landhuis, P. Laptev, A. Locharla, E. Lucero, O. Martin, J. R. McClean, M. McEwen, K. C. Miao, M. Mohseni, S. Montazeri, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Neeley, C. Neill, M. Y. Niu, T. E. O'Brien, A. Opremcak, B. Pató, A. Petukhov, N. C. Rubin, D. Sank, V. Shvarts, D. Strain, M. Szalay, B. Villalonga, T. C. White, Z. Yao, P. Yeh, J. Yoo, A. Zalcman, H. Neven, S. Boixo, A. Megrant, Y. Chen, J. Kelly, V. Smelyanskiy, A. Kitaev, M. Knap, F. Pollmann, P. Roushan

The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven to be extremely challenging in both condensed matter and synthetic quantum systems. Here, we prepare the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measure a topological entanglement entropy near the expected value of ln2, and simulate anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigate key aspects of the surface code, including logical state injection and the decay of the non-local order parameter. Our results demonstrate the potential for quantum processors to provide key insights into topological quantum matter and quantum error correction.

##### Quantum Teleportation between Remote Qubit Memories with Only a Single Photon as a Resource

S. Langenfeld, S. Welte, L. Hartung, S. Daiss, P. Thomas, O. Morin, E. Distante, G. Rempe

Physical Review Letters 126, 130502 (2021).

Quantum teleportation enables the deterministic exchange of qubits via lossy channels. While it is commonly believed that unconditional teleportation requires a preshared entangled qubit pair, here we demonstrate a protocol that is in principle unconditional and requires only a single photon as an ex-ante prepared resource. The photon successively interacts, first, with the receiver and then with the sender qubit memory. Its detection, followed by classical communication, heralds a successful teleportation. We teleport six mutually unbiased qubit states with average fidelity ¯F=(88.3±1.3)% at a rate of 6 Hz over 60 m.

##### Quantum Gravity in Species Regime

G. Dvali

A large number of particle species allows to formulate quantum gravity in a special double-scaling limit, the species limit. In this regime, quantum gravitational amplitudes simplify substantially. An infinite set of perturbative corrections, that usually blur the picture, vanishes, whereas the collective and non-perturbative effects can be cleanly extracted. Such are the effects that control physics of black holes and of de Sitter and their entanglement curves. In string theory example, we show that the entropy of open strings matches the Gibbons-Hawking entropy of a would-be de Sitter state at the point of saturation of the species bound. This shows, from yet another angle, why quantum gravity/string theory cannot tolerate a de Sitter vacuum. Finally, we discuss various observational implications.

##### Functional Theory for Bose-Einstein Condensates

J. Liebert, C. Schilling

Physical Review Research 3, 13282 (2021).

One-particle reduced density matrix functional theory would potentially be the ideal approach for describing Bose-Einstein condensates. It namely replaces the macroscopically complex wave function by the simple one-particle reduced density matrix, and therefore provides direct access to the degree of condensation and still recovers quantum correlations in an exact manner. We initiate and establish this theory by deriving the respective universal functional F for homogeneous Bose-Einstein condensates with arbitrary pair interaction. Most importantly, the successful derivation necessitates a particle-number conserving modification of Bogoliubov theory and a solution of the common phase dilemma of functional theories. We then illustrate this approach in several bosonic systems such as homogeneous Bose gases and the Bose-Hubbard model. Remarkably, the general form of F reveals the existence of a universal Bose-Einstein condensation force which provides an alternative and more fundamental explanation for quantum depletion.

##### In-situ tunable nonlinearity and competing signal paths in coupled superconducting resonators

M. Fischer, Q.-M. Chen, C. Besson, P. Eder, J. Goetz, S. Pogorzalek, M. Renger, E. Xie, M.J. Hartmann, K.G. Fedorov, A. Marx, F. Deppe, R. Gross

Physical Review B 103, 94515 (2021).

We have fabricated and studied a system of two tunable and coupled nonlinear superconducting resonators. The nonlinearity is introduced by galvanically coupled dc superconducting quantum interference devices. We simulate the system response by means of a circuit model, which includes an additional signal path introduced by the electromagnetic environment. Furthermore, we present two methods allowing us to experimentally determine the nonlinearity. First, we fit the measured frequency and flux dependence of the transmission data to simulations based on the equivalent circuit model. Second, we fit the power dependence of the transmission data to a model that is predicted by the nonlinear equation of motion describing the system. Our results show that we are able to tune the nonlinearity of the resonators by almost two orders of magnitude via an external coil and two on-chip antennas. The studied system represents a basic building block for larger systems, allowing for quantum simulations of bosonic many-body systems with a larger number of lattice sites.

##### Nondestructive detection of photonic qubits

D. Niemietz, P. Farrera, S. Langenfeld, G. Rempe

Nature 591, 570-574 (2021).

One of the biggest challenges in experimental quantum information is to sustain the fragile superposition state of a qubit. Long lifetimes can be achieved for material qubit carriers as memories, at least in principle, but not for propagating photons that are rapidly lost by absorption, diffraction or scattering. The loss problem can be mitigated with a nondestructive photonic qubit detector that heralds the photon without destroying the encoded qubit. Such a detector is envisioned to facilitate protocols in which distributed tasks depend on the successful dissemination of photonic qubits, improve loss-sensitive qubit measurements and enable certain quantum key distribution attacks. Here we demonstrate such a detector based on a single atom in two crossed fibre-based optical resonators, one for qubit-insensitive atom–photon coupling and the other for atomic-state detection. We achieve a nondestructive detection efficiency upon qubit survival of 79 ± 3 per cent and a photon survival probability of 31 ± 1 per cent, and we preserve the qubit information with a fidelity of 96.2 ± 0.3 per cent. To illustrate the potential of our detector, we show that it can, with the current parameters, improve the rate and fidelity of long-distance entanglement and quantum state distribution compared to previous methods, provide resource optimization via qubit amplification and enable detection-loophole-free Bell tests.

##### Design of an optomagnonic crystal: Towards optimal magnon-photon mode matching at the microscale

J. Graf, S. Sharma, H. Huebl, S.V. Kusminskiy

Physical Review Research 3 (1), 013277 (2021).

We put forward the concept of an optomagnonic crystal: a periodically patterned structure at the microscale based on a magnetic dielectric, which can co-localize magnon and photon modes. The co-localization in small volumes can result in large values of the photon-magnon coupling at the single quanta level, which opens perspectives for quantum information processing and quantum conversion schemes with these systems. We study theoretically a simple geometry consisting of a one-dimensional array of holes with an abrupt defect, considering the ferrimagnet yttrium iron garnet (YIG) as the basis material. We show that both magnon and photon modes can be localized at the defect, and use symmetry arguments to select an optimal pair of modes in order to maximize the coupling. We show that an optomagnonic coupling in the kHz range is achievable in this geometry, and discuss possible optimization routes in order to improve both coupling strengths and optical losses.

##### Continuous quantum light from a dark atom

K.N. Tolazzi, B. Wang, C. Ianzano, J. Neumeier, C.J. Villas-Boas, G. Rempe

Communications Physics 4, 57 (2021).

Cycling processes are important in many areas of physics ranging from lasers to topological insulators, often offering surprising insights into dynamical and structural aspects of the respective system. Here we report on a quantum-nonlinear wave-mixing experiment where resonant lasers and an optical cavity define a closed cycle between several ground and excited states of a single atom. We show that, for strong atom–cavity coupling and steady-state driving, the entanglement between the atomic states and intracavity photon number suppresses the excited-state population via quantum interference, effectively reducing the cycle to the atomic ground states. The system dynamics then result from transitions within a harmonic ladder of entangled dark states, one for each cavity photon number, and a quantum Zeno blockade that generates antibunching in the photons emitted from the cavity. The reduced cycle suppresses unwanted optical pumping into atomic states outside the cycle, thereby enhancing the number of emitted photons.

##### Nondestructive detection of photonic qubits

D. Niemietz, P. Farrera, S. Langenfeld, G. Rempe

Nature 591, 570–574 (2021).

One of the biggest challenges in experimental quantum information is to sustain the fragile superposition state of a qubit1. Long lifetimes can be achieved for material qubit carriers as memories2, at least in principle, but not for propagating photons that are rapidly lost by absorption, diffraction or scattering3. The loss problem can be mitigated with a nondestructive photonic qubit detector that heralds the photon without destroying the encoded qubit. Such a detector is envisioned to facilitate protocols in which distributed tasks depend on the successful dissemination of photonic qubits4,5, improve loss-sensitive qubit measurements6,7 and enable certain quantum key distribution attacks8. Here we demonstrate such a detector based on a single atom in two crossed fibre-based optical resonators, one for qubit-insensitive atom–photon coupling and the other for atomic-state detection9. We achieve a nondestructive detection efficiency upon qubit survival of 79 ± 3 per cent and a photon survival probability of 31 ± 1 per cent, and we preserve the qubit information with a fidelity of 96.2 ± 0.3 per cent. To illustrate the potential of our detector, we show that it can, with the current parameters, improve the rate and fidelity of long-distance entanglement and quantum state distribution compared to previous methods, provide resource optimization via qubit amplification and enable detection-loophole-free Bell tests.

##### All-electrical detection of skyrmion lattice state and chiral surface twists

A. Aqeel, M. Azhar, N. Vlietstra, A. Pozzi, J. Sahliger, H. Huebl, T.T.M. Palstra, C.H. Back, M. Mostovoy

Physical Review B 103 (10), L100410 (2021).

We study the high-temperature phase diagram of the chiral magnetic insulator Cu2OSeO3 by measuring the spin-Hall magnetoresistance (SMR) in a thin Pt electrode. We find distinct changes in the phase and amplitude of the SMR signal at critical lines separating different magnetic phases of bulk Cu2OSeO3. The skyrmion lattice state appears as a strong dip in the SMR phase. A strong enhancement of the SMR amplitude is observed in the conical spiral state, which we explain by an additional symmetry-allowed contribution to the SMR present in noncollinear magnets. We demonstrate that the SMR can be used as an all-electrical probe of chiral surface twists and skyrmions in magnetic insulators.

##### Spin to charge conversion in Si/Cu/ferromagnet systems investigated by ac inductive measurements

E. Shigematsu, L. Liensberger, M. Weiler, R. Ohshima, Y. Ando, T. Shinjo, H. Huebl, M. Shiraishi

Physical Review B 103, 094430 (2021).

Semiconductor/ferromagnet hybrid systems are attractive platforms for investigation of spin conversion physics, such as the (inverse) spin Hall effect. However, the superimposed rectification currents originating from anisotropic magnetoresistance have been a serious problem preventing unambiguous detection of dc spin Hall electric signals in semiconductors. In this study, we applied a microwave frequency inductive technique immune to such rectification effects to investigate the spin to charge conversion in heterostructures based on Si, one of the primitive semiconductors. The Si doping dependence of the spin-orbit torque conductivity was obtained for the Si/Cu/NiFe trilayer system. A monotonous modulation of the spin-orbit torque conductivity by doping and relative sign change of spin to charge conversion between the degenerate n- and p-type Si samples were observed. These results unveil spin to charge conversion mechanisms in semiconductor/metal heterostructures and show a pathway for further exploration of spin-conversion physics in metal/semiconductor heterostructures.

##### Microscopic electronic structure tomography of Rydberg macrodimers

S. Hollerith, J. Rui, A. Rubio-Abadal, K. Srakaew, D. Wei, J. Zeiher, C. Gross, I. Bloch

Rhys. Rev. Research 3, 13252 (2021).

Precise control and study of molecules is challenging due to the variety of internal degrees of freedom and local coordinates that are typically not controlled in an experiment. Employing quantum gas microscopy to position and resolve the atoms in Rydberg macrodimer states solves almost all of these challenges and enables unique access to the molecular frame. Here, we demonstrate the power of this approach and present first photoassociation studies for different molecular symmetries in which the molecular orientation relative to an applied magnetic field, the polarization of the excitation light and the initial atomic state are fully controlled. The observed characteristic dependencies allow for an electronic structure tomography of the molecular state. We additionally observe an orientation-dependent Zeeman shift and reveal a significant influence on it caused by the hyperfine interaction of the macrodimer state. Finally, we demonstrate controlled engineering of the electrostatic binding potential by opening a gap in the energetic vicinity of two crossing pair potentials.

##### Emergent fracton dynamics in a nonplanar dimer model

J. Feldmeier, F. Pollmann, M. Knap

Physical Review B 103 (9), 94303 (2021).

We study the late time relaxation dynamics of a pure U(1) lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's nonequilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional “tubes” within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The timescale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for nonergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of “statistically localized integrals of motion,” whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.

##### Entanglement and complexity of purification in (1+1)-dimensional free conformal field theories

H.A. Camargo, L. Hackl, M.P. Heller, A. Jahn, T. Takayanagi, B. Windt

Physical Review Research 3, 013248 (2021).

Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using the most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theory and the corresponding behavior of the mutual information, as well as the Hilbert space structure under the Jordan-Wigner mapping in the spin chain model of the Ising conformal field theory.

##### The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

K. Kögler, P.T. Nam

Archive for Rational Mechanics and Analysis 240, 1169–1202 (2021).

We consider an analogue of the Lieb–Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb–Thirring constant converges to the optimal constant of the one-body Gagliardo–Nirenberg interpolation inequality without interaction.

##### Bosonization of Fermionic Many-Body Dynamics

N. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer

We consider the quantum many-body evolution of a homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We study a class of initial data describing collective particle-hole pair excitations on the Fermi ball. Using a rigorous version of bosonization for non-solvable models, we prove that the many-body evolution can be approximated in Fock space norm by a quasifree bosonic evolution of the collective particle-hole excitations.

##### Moire excitons in MoSe2-WSe2 heterobilayers and heterotrilayers

M. Foerg, A.S. Baimuratov, S.Y. Kruchinin, I.A. Vovk, J. Scherzer, J. Foerste, V. Funk, K. Watanabe, T. Taniguchi, A. Hoegele

Nature Communications 12 (1), 1656 (2021).

Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moire interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe2-WSe2 stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlayer moire excitons in different spin and valley configurations. We conclude that the photoluminescence of MoSe2-WSe2 heterobilayer is consistent with joint contributions from radiatively decaying valley-direct interlayer excitons and phonon-assisted emission from momentum-indirect reservoirs that reside in spatially distinct regions of moire supercells, whereas the heterotrilayer emission is entirely due to momentum-dark interlayer excitons of hybrid-layer valleys. Our results highlight the profound role of interlayer hybridization for transition metal dichalcogenide heterostacks and other realizations of multi-layered semiconductor van der Waals heterostructures. Here, the authors show that the photoluminescence of MoSe2/WSe2 heterobilayers is dominated by valley-direct excitons, whereas, in heterotrilayers, interlayer hybridization turns momentum-indirect interlayer excitons into energetically lowest states with phonon-assisted emission.

##### Group Transference Techniques for the Estimation of the Decoherence Times and Capacities of Quantum Markov Semigroups

I. Bardet, M. Junge, N. LaRacuente, C. Rouzé, D.S. França

IEEE Transactions on Information Theory 67, 2878-2909 (2021).

Capacities of quantum channels and decoherence times both quantify the extent to which quantum information can withstand degradation by interactions with its environment. However, calculating capacities directly is known to be intractable in general. Much recent work has focused on upper bounding certain capacities in terms of more tractable quantities such as specific norms from operator theory. In the meantime, there has also been substantial recent progress on estimating decoherence times with techniques from analysis and geometry, even though many hard questions remain open. In this article, we introduce a class of continuous-time quantum channels that we called transferred channels , which are built through representation theory from a classical Markov kernel defined on a compact group. In particular, we study two subclasses of such kernels: Hörmander systems on compact Lie-groups and Markov chains on finite groups. Examples of transferred channels include the depolarizing channel, the dephasing channel, and collective decoherence channels acting on d qubits. Some of the estimates presented are new, such as those for channels that randomly swap subsystems. We then extend tools developed in earlier work by Gao, Junge and LaRacuente to transfer estimates of the classical Markov kernel to the transferred channels and study in this way different non-commutative functional inequalities. The main contribution of this article is the application of this transference principle to the estimation of decoherence time, of private and quantum capacities, of entanglement-assisted classical capacities as well as estimation of entanglement breaking times, defined as the first time for which the channel becomes entanglement breaking. Moreover, our estimates hold for non-ergodic channels such as the collective decoherence channels, an important scenario that has been overlooked so far because of a lack of techniques.

##### Entropy bound and unitarity of scattering amplitudes

G. Dvali

JHEP 3, 126 (2021).

We establish that unitarity of scattering amplitudes imposes universal entropy bounds. The maximal entropy of a self-sustained quantum field object of radius R is equal to its surface area and at the same time to the inverse running coupling α evaluated at the scale R. The saturation of these entropy bounds is in one-to-one correspondence with the non-perturbative saturation of unitarity by 2 → N particle scattering amplitudes at the point of optimal truncation. These bounds are more stringent than Bekenstein’s bound and in a consistent theory all three get saturated simultaneously. This is true for all known entropy-saturating objects such as solitons, instantons, baryons, oscillons, black holes or simply lumps of classical fields. We refer to these collectively as saturons and show that in renormalizable theories they behave in all other respects like black holes. Finally, it is argued that the confinement in SU(N) gauge theory can be understood as a direct consequence of the entropy bounds and unitarity.

##### Local optimization on pure Gaussian state manifolds

B. Windt, A. Jahn, J. Eisert, L. Hackl

SciPost Physics 10, 066 (2021).

We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

##### On the Algorithmic Solvability of Channel Dependent Classification Problems in Communication Systems

H. Boche, R.F. Schaefer, H.V. Poor

IEEE/ACM Transactions on Networking 29 (3), 1155 - 1168 (2021).

For communication systems there is a recent trend towards shifting functionalities from the physical layer to higher layers by enabling software-focused solutions. Having obtained a (physical layer-based) description of the communication channel, such approaches exploit this knowledge to enable various services by subsequently processing it on higher layers. For this it is a crucial task to first find out in which state the underlying communication channel is. This paper develops a framework based on Turing machines and studies whether or not it is in principle possible to algorithmically solve such classification tasks, i.e., to decide in which state the communication system is. Turing machines have no limitations on computational complexity, computing capacity and storage, and can simulate any given algorithm and therewith are a simple but very powerful model of computation. They characterize the fundamental performance limits for today's digital computers. It is shown that there exists no Turing machine that takes the physical description of the communication channel as an input and solves a non-trivial classification task. Subsequently, this general result is used to study communication under adversarial attacks and it is shown that it is impossible to algorithmically detect denial-of-service (DoS) attacks on the transmission. Jamming attacks on ACK/NACK feedback cannot be detected as well and, in addition, ACK/NACK feedback is shown to be useless for the detection of DoS on the actual message transmission. Further applications are discussed including DoS attacks on the Post Shannon task of identification, and on physical layer security and resilience by design.

##### Approximating the long time average of the density operator: Diagonal ensemble

A. Cakan, J.I. Cirac, M.C. Banuls

Physical Review B 103, 115113 (2021).

For an isolated generic quantum system out of equilibrium, the long time average of observables is given by the diagonal ensemble, i.e. the mixed state with the same probability for energy eigenstates as the initial state but without coherences between different energies. In this work we present a method to approximate the diagonal ensemble using tensor networks. Instead of simulating the real time evolution, we adapt a filtering scheme introduced earlier in [Phys. Rev. B 101, 144305 (2020)] to this problem. We analyze the performance of the method on a non-integrable spin chain, for which we observe that local observables converge towards thermal values polynomially with the inverse width of the filter.

##### Efficient Numerical Evaluation of Thermodynamic Quantities on Infinite (Semi-)classical Chains

C.B. Mendl, F. Bornemann

Journal of Statistical Physics 182, 57 (2021).

This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical discretization of integral kernels using quadrature rules. For analytic kernels, the technique exhibits exponential convergence in the number of quadrature points. As demonstration, we apply the method to a classical particle chain, to the semiclassical nonlinear Schrödinger (NLS) equation and to a classical system on a cylindrical lattice. A comparison with molecular dynamics simulations performed for the NLS model shows very good agreement.

##### String order parameters for symmetry fractionalization in an enriched toric code

J. Garre-Rubio, M. Iqbal, D.T. Stephen

Physical Review B 103, 125104 (2021).

We study a simple model of symmetry-enriched topological order obtained by decorating a toric code model with lower-dimensional symmetry-protected topological states. We show that the symmetry fractionalization in this model can be characterized by string order parameters, and that these signatures are robust under the effects of external fields and interactions, up to the phase transition point. This extends the recent proposal of Garre-Rubio and Iblisdir [New J. Phys. 21, 113016 (2019)] beyond the setting of fixed-point tensor network states, and solidifies string order parameters as a useful tool to characterize and detect symmetry fractionalization. In addition to this, we observe how the condensation of an anyon that fractionalizes a symmetry forces that symmetry to spontaneously break, and we give a proof of this in the framework of projected entangled pair states. This phenomenon leads to a notable change in the phase diagram of the toric code in parallel magnetic fields

##### Uncertainty in Identification Systems

M.T. Vu, T.J. Oechtering, M. Skoglund, H. Boche

IEEE Transactions on Information Theory 67 (3), 1400-1414 (2021).

High-dimensional identification systems consisting of two groups of users in the presence of statistical uncertainties are considered in this work. The task is to design enrollment mappings to compress users' information and an identification mapping that combines the stored information in the database and an observation to estimate the underlying user index. The compression-identification trade-off regions are established for the compound, extended compound, general and mixture settings. It is shown that several settings admit the same compression-identification trade-offs. We then study a connection between the Wyner-Ahlswede-Korner network and the identification setting. It indicates that a strong converse for the WAK network is equivalent to a strong converse for the identification setting. Finally, we present strong converse arguments for the discrete identification setting that are extensible to the Gaussian scenario.

##### Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid

V. Leeb, K. Polyudov, S. Mashhadi, S. Biswas, R. Valenti, M. Burghard, J. Knolle

Physical Review Letters 126 (9), 097201 (2021).

The quasi-two-dimensional Mott insulator alpha-RuCl3 is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of alpha-RuCl3 on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such alpha-RuCl3 and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using ab initio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

##### Optomechanical wave mixing by a single quantum dot

M. Weiß, D. Wigger, M. Nägele, K. Müller, J.J. Finley, T. Kuhn, P. Machnikowski, H.J. Krenner

Optica 8 (3), 291-300 (2021).

Wave mixing is an archetypical phenomenon in bosonic systems. In optomechanics, the bidirectional conversion between electromagnetic waves or photons at optical frequencies and elastic waves or phonons at radio frequencies is building on precisely this fundamental principle. Surface acoustic waves (SAWs) provide a versatile interconnect on a chip and thus enable the optomechanical control of remote systems. Here we report on the coherent nonlinear three-wave mixing between the coherent fields of two radio frequency SAWs and optical laser photons via the dipole transition of a single quantum dot exciton. In the resolved sideband regime, we demonstrate fundamental acoustic analogues of sum and difference frequency generation between the two SAWs and employ phase matching to deterministically enhance or suppress individual sidebands. This transfer between the acoustic and optical domains is described by theory that fully takes into account direct and virtual multiphonon processes. Finally, we show that the precision of the wave mixing is limited by the frequency accuracy of modern radio frequency electronics.

##### Selective and robust time-optimal rotations of spin systems

Q. Ansel, S.J. Glaser, D. Sugny

Journal of Physics A-Mathematical and Theoretical 54 (8), 085204 (2021).

We study the selective and robust time-optimal rotation control of several spin-1/2 particles with different offset terms. For that purpose, the Pontryagin maximum principle is applied to a model of two spins, which is simple enough for analytic computations and sufficiently complex to describe inhomogeneity effects. We find that selective and robust controls are respectively described by singular and regular trajectories. Using a geometric analysis combined with numerical simulations, we determine the optimal solutions of different control problems. Selective and robust controls can be derived analytically without numerical optimization. We show the optimality of several standard control mechanisms in Nuclear Magnetic Resonance, but new robust controls are also designed.

##### 3D Deep Learning Enables Accurate Layer Mapping of 2D Materials

X.C. Dong, H.W. Li, Z.T. Jiang, T. Grunleitner, I. Gueler, J. Dong, K. Wang, M.H. Koehler, M. Jakobi, B.H. Menze, A.K. Yetisen, I.D. Sharp, A.V. Stier, J.J. Finley, A.W. Koch

ACS Nano 15 (2), 3139-3151 (2021).

Layered, two-dimensional (2D) materials are promising for next-generation photonics devices. Typically, the thickness of mechanically cleaved flakes and chemical vapor deposited thin films is distributed randomly over a large area, where accurate identification of atomic layer numbers is time-consuming. Hyperspectral imaging microscopy yields spectral information that can be used to distinguish the spectral differences of varying thickness specimens. However, its spatial resolution is relatively low due to the spectral imaging nature. In this work, we present a 3D deep learning solution called DALM (deep-learning-enabled atomic layer mapping) to merge hyperspectral reflection images (high spectral resolution) and RGB images (high spatial resolution) for the identification and segmentation of MoS2 flakes with mono-, bi-, tri-, and multilayer thicknesses. DALM is trained on a small set of labeled images, automatically predicts layer distributions and segments individual layers with high accuracy, and shows robustness to illumination and contrast variations. Further, we show its advantageous performance over the state-of-the-art model that is solely based on RGB microscope images. This AI-supported technique with high speed, spatial resolution, and accuracy allows for reliable computer-aided identification of atomically thin materials.

##### Temperature-Dependent Spin Transport and Current-Induced Torques in Superconductor-Ferromagnet Heterostructures

M. Mueller, L. Liensberger, L. Flacke, H. Huebl, A. Kamra, W. Belzig, R. Gross, M. Weiler, M. Althammer

Physical Review Letters 126 (8), 087201 (2021).

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent ferromagnetic metal layer. To this end, we use NbN-Ni80Fe20(Py) heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Permalloy layer by placing the samples onto a coplanar waveguide. A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between the sample and the coplanar waveguide, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature T-c, we observe a suppression of the dampinglike torque generated in the Pt layer by the inverse spin Hall effect, which can be understood by the changes in spin current transport in the superconducting NbN layer. Moreover, below T-c we find a large fieldlike current-induced torque.

##### Highly Efficient Resolution-of-Identity Density Functional Theory Calculations on Central and Graphics Processing Units

J. Kussmann, H. Laqua, C. Ochsenfeld

Journal of Chemical Theory and Computation 17, 1512-1521 (2021).

We present an efficient method to evaluate Coulomb potential matrices using the resolution of identity approximation and semilocal exchange-correlation potentials on central (CPU) and graphics processing units (GPU). The new GPU-based RI-algorithm shows a high performance and ensures the favorable scaling with increasing basis set size as the conventional CPU-based method. Furthermore, our method is based on the J-engine algorithm [White; , Head-Gordon, J. Chem. Phys. 1996, 7, 2620], which allows for further optimizations that also provide a significant improvement of the corresponding CPU-based algorithm. Due to the increased performance for the Coulomb evaluation, the calculation of the exchange-correlation potential of density functional theory on CPUs quickly becomes a bottleneck to the overall computational time. Hence, we also present a GPU-based algorithm to evaluate the exchange-correlation terms, which results in an overall high-performance method for density functional calculations. The algorithms to evaluate the potential and nuclear derivative terms are discussed, and their performance on CPUs and GPUs is demonstrated for illustrative calculations.

##### Temperature-Dependent Spin Transport and Current-Induced Torques in Superconductor-Ferromagnet Heterostructures

M. Müller, L. Liensberger, L. Flacke, H. Huebl, A. Kamra, W. Belzig, R. Gross, M. Weiler, M. Althammer

Physical Review Letters 126 (8), 087201 (2021).

We investigate the injection of quasiparticle spin currents into a superconductor via spin pumping from an adjacent ferromagnetic metal layer. To this end, we use NbN-Ni80Fe20(Py) heterostructures with a Pt spin sink layer and excite ferromagnetic resonance in the Permalloy layer by placing the samples onto a coplanar waveguide. A phase sensitive detection of the microwave transmission signal is used to quantitatively extract the inductive coupling strength between the sample and the coplanar waveguide, interpreted in terms of inverse current-induced torques, in our heterostructures as a function of temperature. Below the superconducting transition temperature Tc, we observe a suppression of the dampinglike torque generated in the Pt layer by the inverse spin Hall effect, which can be understood by the changes in spin current transport in the superconducting NbN layer. Moreover, below Tc we find a large fieldlike current-induced torque.

##### Spectral Gaps and Incompressibility in a ?? = 1/3 Fractional Quantum Hall System

B. Nachtergaele, S. Warzel, A. Young

Communications in Mathematical Physics 383, 1093–1149 (2021).

We study an effective Hamiltonian for the standard ν=1/3 fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice. We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values. As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states. We also show that all the ground states labeled by a tiling have a finite correlation length, for which we give an upper bound. We demonstrate by example, however, that not all superpositions of tiling states have exponential decay of correlations.

##### Vacancy-Induced Low-Energy Density of States in the Kitaev Spin Liquid

W.H. Kao, J. Knolle, G.B. Halasz, R. Moessner, N.B. Perkins

Physical Review X 11 (1), 011034 (2021).

The Kitaev honeycomb model has attracted significant attention due to its exactly solvable spin-liquid ground state with fractionalized Majorana excitations and its possible materialization in magnetic Mott insulators with strong spin-orbit couplings. Recently, the 5d-electron compound H3LiIr2O6 has shown to be a strong candidate for Kitaev physics considering the absence of any signs of a long-range ordered magnetic state. In this work, we demonstrate that a finite density of random vacancies in the Kitaev model gives rise to a striking pileup of low-energy Majorana eigenmodes and reproduces the apparent power-law upturn in the specific heat measurements of H3LiIr2O6. Physically, the vacancies can originate from various sources such as missing magnetic moments or the presence of nonmagnetic impurities (true vacancies), or from local weak couplings of magnetic moments due to strong but rare bond randomness (quasivacancies). We show numerically that the vacancy effect is readily detectable even at low vacancy concentrations and that it is not very sensitive either to the nature of vacancies or to different flux backgrounds. We also study the response of the site-diluted Kitaev spin liquid to the three-spin interaction term, which breaks time-reversal symmetry and imitates an external magnetic field. We propose a field-induced flux-sector transition where the ground state becomes flux-free for larger fields, resulting in a clear suppression of the low-temperature specific heat. Finally, we discuss the effect of dangling Majorana fermions in the case of true vacancies and show that their coupling to an applied magnetic field via the Zeeman interaction can also account for the scaling behavior in the high-field limit observed in H3LiIr2O6.

##### Interaction of Luminescent Defects in Carbon Nanotubes with Covalently Attached Stable Organic Radicals

F.J. Berger, J.A. de Sousa, S. Zhao, N.F. Zorn, A.A. El Yumin, A.Q. García, S. Settele, A. Högele , N. Crivillers, J. Zaumseil

ACS Nano 15, 5147–5157 (2021).

The functionalization of single-walled carbon nanotubes (SWCNTs) with luminescent sp3 defects has greatly improved their performance in applications such as quantum light sources and bioimaging. Here, we report the covalent functionalization of purified semiconducting SWCNTs with stable organic radicals (perchlorotriphenylmethyl, PTM) carrying a net spin. This model system allows us to use the near-infrared photoluminescence arising from the defect-localized exciton as a highly sensitive probe for the short-range interaction between the PTM radical and the SWCNT. Our results point toward an increased triplet exciton population due to radical-enhanced intersystem crossing, which could provide access to the elusive triplet manifold in SWCNTs. Furthermore, this simple synthetic route to spin-labeled defects could enable magnetic resonance studies complementary to in vivo fluorescence imaging with functionalized SWCNTs and facilitate the scalable fabrication of spintronic devices with magnetically switchable charge transport.

##### Engineering the Luminescence and Generation of Individual Defect Emitters in Atomically Thin MoS2

J. Klein, L. Sigl, S. Gyger, K. Barthelmi, M. Florian, S. Rey T. Taniguchi K. Watanabe, F. Jahnke, C. Kastl, V. Zwiller, K.D. Jons, K. Mueller, U. Wurstbauer, J.J. Finley, A.W. Holleitner

ACS Photonics 8 (2), 669-677 (2021).

We demonstrate the on-demand creation and positioning of photon emitters in atomically thin MoS2 with very narrow ensemble broadening and negligible background luminescence. Focused helium-ion beam irradiation creates 100s to 1000s of such mono-typical emitters at specific positions in the MoS2 monolayers. Individually measured photon emitters show anti-bunching behavior with a g(2)(0) similar to 0.23 and 0.27. From a statistical analysis, we extract the creation yield of the He-ion induced photon emitters in MoS2 as a function of the exposed area, as well as the total yield of single emitters as a function of the number of He ions when single spots are irradiated by He ions. We reach probabilities as high as 18% for the generation of individual and spectrally clean photon emitters per irradiated single site. Our results firmly establish 2D materials as a platform for photon emitters with unprecedented control of position as well as photophysical properties owing to the all-interfacial nature.

##### How creating one additional well can generate Bose-Einstein condensation

M. Máté, Ö. Legeza, R. Schilling, M. Yousif, C. Schilling

Communications Physics 4, 29 (2021).

The realization of Bose-Einstein condensation in ultracold trapped gases has led to a revival of interest in this fascinating quantum phenomenon. This experimental achievement necessitated both extremely low temperatures and sufficiently weak interactions. Particularly in reduced spatial dimensionality even an infinitesimal interaction immediately leads to a departure to quasi-condensation. We propose a system of strongly interacting bosons, which overcomes those obstacles by exhibiting a number of intriguing related features: (i) The tuning of just a single control parameter drives a transition from quasi-condensation to complete condensation, (ii) the destructive influence of strong interactions is compensated by the respective increased mobility, (iii) topology plays a crucial role since a crossover from one- to ‘infinite’-dimensionality is simulated, (iv) a ground state gap opens, which makes the condensation robust to thermal noise. Remarkably, all these features can be derived by analytical and exact numerical means despite the non-perturbative character of the system.

##### Convergence rates for the quantum central limit theorem

Simon Becker, Nilanjana Datta, Ludovico Lami Cambyse Rouzé

Communications in Mathematical Physics 383, 223-279 (2021).

Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It implies that the state in any single output arm of an n-splitter, which is fed with n copies of a centred state ρ with finite second moments, converges to the Gaussian state with the same first and second moments as ρ. Here we exploit the phase space formalism to carry out a refined analysis of the rate of convergence in this quantum central limit theorem. For instance, we prove that the convergence takes place at a rate O(n−1/2) in the Hilbert--Schmidt norm whenever the third moments of ρ are finite. Trace norm or relative entropy bounds can be obtained by leveraging the energy boundedness of the state. Via analytical and numerical examples we show that our results are tight in many respects. An extension of our proof techniques to the non-i.i.d. setting is used to analyse a new model of a lossy optical fibre, where a given m-mode state enters a cascade of n beam splitters of equal transmissivities λ1/n fed with an arbitrary (but fixed) environment state. Assuming that the latter has finite third moments, and ignoring unitaries, we show that the effective channel converges in diamond norm to a simple thermal attenuator, with a rate O(n−12(m+1)). This allows us to establish bounds on the classical and quantum capacities of the cascade channel. Along the way, we derive several results that may be of independent interest. For example, we prove that any quantum characteristic function χρ is uniformly bounded by some ηρ<1 outside of any neighbourhood of the origin; also, ηρ can be made to depend only on the energy of the state ρ.

##### Convergence Rates for the Quantum Central Limit Theorem

S. Becker, N. Datta, L. Lami, C. Rouzé

Communications in Mathematical Physics 383, 223–279 (2021).

Various quantum analogues of the central limit theorem, which is one of the cornerstones of probability theory, are known in the literature. One such analogue, due to Cushen and Hudson, is of particular relevance for quantum optics. It implies that the state in any single output arm of an n-splitter, which is fed with n copies of a centred state ρ with finite second moments, converges to the Gaussian state with the same first and second moments as ρ. Here we exploit the phase space formalism to carry out a refined analysis of the rate of convergence in this quantum central limit theorem. For instance, we prove that the convergence takes place at a rate O(n−1/2) in the Hilbert–Schmidt norm whenever the third moments of ρ are finite. Trace norm or relative entropy bounds can be obtained by leveraging the energy boundedness of the state. Via analytical and numerical examples we show that our results are tight in many respects. An extension of our proof techniques to the non-i.i.d. setting is used to analyse a new model of a lossy optical fibre, where a given m-mode state enters a cascade of n beam splitters of equal transmissivities λ1/n fed with an arbitrary (but fixed) environment state. Assuming that the latter has finite third moments, and ignoring unitaries, we show that the effective channel converges in diamond norm to a simple thermal attenuator, with a rate O(n−12(m+1)). This allows us to establish bounds on the classical and quantum capacities of the cascade channel. Along the way, we derive several results that may be of independent interest. For example, we prove that any quantum characteristic function χρ is uniformly bounded by some ηρ<1 outside of any neighbourhood of the origin; also, ηρ can be made to depend only on the energy of the state ρ.

##### Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model

A. Imamoglu, O. Cotlet, R. Schmidt

Comptes Rendus. Physique 22, 1 (2021).

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton–polarons is subject of ongoing debate. Here, we use an analogy to the Tavis–Cummings model of quantum optics to show that an exciton–polaron can be understood as a hybrid quasiparticle—a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors.

##### Seasonal epidemic spreading on small-world networks: Biennial outbreaks and classical discrete time crystals

D. Malz, A. Pizzi, A. Nunnenkamp, J. Knolle

Physical Review Research 3, 013124 (2021).

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible model on small-world graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase transition between annual and biennial outbreaks. A numerical scaling analysis exhibits a diverging autocorrelation time in the thermodynamic limit, which confirms the presence of a classical discrete time crystalline phase. We derive the phase diagram of the model both from mean-field theory and from numerics. Our paper demonstrates that small worldness and non-Markovianity can stabilize a classical discrete time crystal, and links recent efforts to understand such dynamical phases of matter to the century-old problem of biennial epidemics.

##### Ionic liquid gating of single-walled carbon nanotube devices with ultra-short channel length down to 10nm

A. Jannisek, J. Lenz, F. del Giudice, M. Gaulke, F. Pyatkov, S. Dehm, F. Hennrich, L. Wei, Y. Chen, A. Fediai, M. Kappes, W. Wenzel, R. Krupke, R.T. Weitz

Applied Physics Letters 118 (6), 063101 (2021).

Ionic liquids enable efficient gating of materials with nanoscale morphology due to the formation of a nanoscale double layer that can also follow strongly vaulted surfaces. On carbon nanotubes, this can lead to the formation of a cylindrical gate layer, allowing an ideal control of the drain current even at small gate voltages. In this work, we apply ionic liquid gating to chirality-sorted (9, 8) carbon nanotubes bridging metallic electrodes with gap sizes of 20nm and 10nm. The single-tube devices exhibit diameter-normalized current densities of up to 2.57mA/mu m, on-off ratios up to 10(4), and a subthreshold swing down to 100mV/dec. Measurements after long vacuum storage indicate that the hysteresis of ionic liquid gated devices depends not only on the gate voltage sweep rate and the polarization dynamics but also on charge traps in the vicinity of the carbon nanotube, which, in turn, might act as trap states for the ionic liquid ions. The ambipolar transfer characteristics are compared with calculations based on the Landauer-Buttiker formalism. Qualitative agreement is demonstrated, and the possible reasons for quantitative deviations and possible improvements to the model are discussed. Besides being of fundamental interest, the results have potential relevance for biosensing applications employing high-density device arrays.

##### Experimental evidence for Zeeman spin-orbit coupling in layered antiferromagnetic conductors

R. Ramazashvili, P.D. Grigoriev, T. Helm, F. Kollmannsberger, M. Kunz, W. Biberacher, E. Kampert, H. Fujiwara, A. Erb, J. Wosnitza, R. Gross, M.V. Kartsovnik

NPJ Quantum Materials 6 (1), 11 (2021).

Most of solid-state spin physics arising from spin-orbit coupling, from fundamental phenomena to industrial applications, relies on symmetry-protected degeneracies. So does the Zeeman spin-orbit coupling, expected to manifest itself in a wide range of antiferromagnetic conductors. Yet, experimental proof of this phenomenon has been lacking. Here we demonstrate that the Neel state of the layered organic superconductor kappa-(BETS)(2)FeBr4 shows no spin modulation of the Shubnikov-de Haas oscillations, contrary to its paramagnetic state. This is unambiguous evidence for the spin degeneracy of Landau levels, a direct manifestation of the Zeeman spin-orbit coupling. Likewise, we show that spin modulation is absent in electron-doped Nd1.85Ce0.15CuO4, which evidences the presence of Neel order in this cuprate superconductor even at optimal doping. Obtained on two very different materials, our results demonstrate the generic character of the Zeeman spin-orbit coupling.

##### A quantum-logic gate between distant quantum-network modules

S. Daiss, S. Langenfeld, S. Welte, E. Distante, P. Thomas, L. Hartung, O. Morin, G. Rempe

Science 371, 614-617 (2021).

The big challenge in quantum computing is to realize scalable multi-qubit systems with cross-talk–free addressability and efficient coupling of arbitrarily selected qubits. Quantum networks promise a solution by integrating smaller qubit modules to a larger computing cluster. Such a distributed architecture, however, requires the capability to execute quantum-logic gates between distant qubits. Here we experimentally realize such a gate over a distance of 60 meters. We employ an ancillary photon that we successively reflect from two remote qubit modules, followed by a heralding photon detection, which triggers a final qubit rotation. We use the gate for remote entanglement creation of all four Bell states. Our nonlocal quantum-logic gate could be extended both to multiple qubits and many modules for a tailor-made multi-qubit computing register.

##### The view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet

J. Greitemann, K. Liu, L. Pollet

Journal of Physics-Condensed Matter 33 (5), 054002 (2021).

We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial D-3h spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and an SVM bias parameter. For completeness we mention that the machine also picks up the leading 3x3<i correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.

##### Simulating 2+1D Z(3) Lattice Gauge Theory with an Infinite Projected Entangled-Pair State

D. Robaina, M.C. Banuls, J.I. Cirac

Physical Review Letters 126 (5), 050401 (2021).

We simulate a zero-temperature pure Z(3) lattice gauge theory in 2 + 1 dimensions by using an iPEPS (infmite projected entangled-pair state) Ansatz for the ground state. Our results are therefore directly valid in the thermodynamic limit. They clearly show two distinct phases separated by a phase transition. We introduce an update strategy that enables plaquette terms and Gauss-law constraints to be applied as sequences of two-body operators. This allows the use of the most up-to-date iPEPS algorithms. From the calculation of spatial Wilson loops we are able to prove the existence of a confined phase. We show that with relatively low computational cost it is possible to reproduce crucial features of gauge theories. We expect that the strategy allows the extension of iPEPS studies to more general LGTs.

##### Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor

X.G. Qiang, Y.Z. Wang, S.C. Xue, R.Y. Ge, L.F. Chen, Y.W. Liu, A.Q. Huang, X. Fu, P. Xu, T. Yi, F.F. Xu, M.T. Deng, J.B. Wang, J.D.A. Meinecke, J.C.F. Matthews, X.L. Cai, X.J. Yang, J.J. Wu

Science Advances 7 (9), eabb8375 (2021).

Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.

##### The quantum random energy model as a limit of p-spin interactions

C. Manai, S. Warzel

Reviews in Mathematical Physics 33 (1), 2060013 (2021).

We consider the free energy of a mean-field quantum spin glass described by a p-spin interaction and a transversal magnetic field. Recent rigorous results for the case p = infinity, i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the p-spin model converges in a joint thermodynamic and p -> infinity limit to the free energy of the QREM.

##### Revisiting Groeneveld's approach to the virial expansion

S. Jansen

Journal of Mathematical Physics 62 (2), 023302 (2021).

A generalized version of Groeneveld's convergence criterion for the virial expansion and generating functionals for weighted two-connected graphs is proven. This criterion works for inhomogeneous systems and yields bounds for the density expansions of the correlation functions rho (s) (a.k.a. distribution functions or factorial moment measures) of grand-canonical Gibbs measures with pairwise interactions. The proof is based on recurrence relations for graph weights related to the Kirkwood-Salsburg integral equation for correlation functions. The proof does not use an inversion of the density-activity expansion; however, a Mobius inversion on the lattice of set partitions enters the derivation of the recurrence relations.

##### Lagrange Inversion and Combinatorial Species with Uncountable Color Palette

S. Jansen, T. Kuna, D. Tsagkarogiannis

Annales Henri Poincare

We prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. We clarify the cancellations that take place between the two aforementioned formulas and draw connections with similar approaches in a range of applications.

##### Random Multipolar Driving: Tunably Slow Heating through Spectral Engineering

H.Z. Zhao, F. Mintert, R. Moessner, J. Knolle

Physical Review Letters 126 (4), 040601 (2021).

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n >= 1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n + 1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n -> infinity limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.

##### A scaled explicitly correlated F12 correction to second-order MOller-Plesset perturbation theory

L. Urban, T.H. Thompson, C. Ochsenfeld

Journal of Chemical Physics 154 (4), 044101 (2021).

An empirically scaled version of the explicitly correlated F12 correction to second-order MOller-Plesset perturbation theory (MP2-F12) is introduced. The scaling eliminates the need for many of the most costly terms of the F12 correction while reproducing the unscaled explicitly correlated F12 interaction energy correction to a high degree of accuracy. The method requires a single, basis set dependent scaling factor that is determined by fitting to a set of test molecules. We present factors for the cc-pVXZ-F12 (X = D, T, Q) basis set family obtained by minimizing interaction energies of the S66 set of small- to medium-sized molecular complexes and show that our new method can be applied to accurately describe a wide range of systems. Remarkably good explicitly correlated corrections to the interaction energy are obtained for the S22 and L7 test sets, with mean percentage errors for the double-zeta basis of 0.60% for the F12 correction to the interaction energy, 0.05% for the total electron correlation interaction energy, and 0.03% for the total interaction energy, respectively. Additionally, mean interaction energy errors introduced by our new approach are below 0.01 kcal mol(-1) for each test set and are thus negligible for second-order perturbation theory based methods. The efficiency of the new method compared to the unscaled F12 correction is shown for all considered systems, with distinct speedups for medium- to large-sized structures.

##### Quantum-Zeno Fermi polaron in the strong dissipation limit

T. Wasak, R. Schmidt, F. Piazza

Physical Review Research 3, 13086 (2021).

The interplay between measurement and quantum correlations in many-body systems can lead to novel types of collective phenomena which are not accessible in isolated systems. In this work, we merge the Zeno paradigm of quantum measurement theory with the concept of polarons in condensed-matter physics. The resulting quantum-Zeno Fermi polaron is a quasiparticle which emerges for lossy impurities interacting with a quantum-degenerate bath of fermions. For loss rates of the order of the impurity-fermion binding energy, the quasiparticle is short lived. However, we show that in the strongly dissipative regime of large loss rates a long-lived polaron branch reemerges. This quantum-Zeno Fermi polaron originates from the nontrivial interplay between the Fermi surface and the surface of the momentum region forbidden by the quantum-Zeno projection. The situation we consider here is realized naturally for polaritonic impurities in charge-tunable semiconductors and can be also implemented using dressed atomic states in ultracold gases.

##### Gate-Switchable Arrays of Quantum Light Emitters in Contacted Monolayer MoS2 van der Waals Heterodevices

A. Hoetger, J. Klein, K. Barthelmi, L. Sigl, F. Sigger, W. Manner, S. Gyger, M. Florian, M. Lorke, F. Jahnke, T. Taniguchi, K. Watanabe, K.D. Jons, U. Wurstbauer, C. Kastl, K. Mueller, J.J. Finley, A.W. Holleitner

Nano Letters 21 (2), 1040-1046 (2021).

We demonstrate electrostatic switching of individual, site-selectively generated matrices of single photon emitters (SPEs) in MoS2 van der Waals heterodevices. We contact monolayers of MoS2 in field-effect devices with graphene gates and hexagonal boron nitride as the dielectric and graphite as bottom gates. After the assembly of such gate-tunable heterodevices, we demonstrate how arrays of defects, that serve as quantum emitters, can be site-selectively generated in the monolayer MoS2 by focused helium ion irradiation. The SPEs are sensitive to the charge carrier concentration in the MoS2 and switch on and off similar to the neutral exciton in MoS2 for moderate electron doping. The demonstrated scheme is a first step for producing scalable, gate-addressable, and gate-switchable arrays of quantum light emitters in MoS2 heterostacks.

##### Charged Exciton Kinetics in Monolayer MoSe2 near Ferroelectric Domain Walls in Periodically Poled LiNbO3

P. Soubelet, J. Klein, J. Wierzbowski, R. Silvioli, F. Sigger, A.V. Stier, K. Gallo, J.J. Finley

Nano Letter 21 (2), 959-966 (2021).

Monolayer semiconducting transition metal dichal-cogenides are a strongly emergent platform for exploring quantum phenomena in condensed matter, building novel optoelectronic devices with enhanced functionalities. Because of their atomic thickness, their excitonic optical response is highly sensitive to their dielectric environment. In this work, we explore the optical properties of monolayer thick MoSe2 straddling domain wall boundaries in periodically poled LiNbO3. Spatially resolved photoluminescence experiments reveal spatial sorting of charge and photogenerated neutral and charged excitons across the boundary. Our results reveal evidence for extremely large in-plane electric fields of similar or equal to 4000 kV/cm at the domain wall whose effect is manifested in exciton dissociation and routing of free charges and trions toward oppositely poled domains and a nonintuitive spatial intensity dependence. By modeling our result using drift-diffusion and continuity equations, we obtain excellent qualitative agreement with our observations and have explained the observed spatial luminescence modulation using realistic material parameters.

##### Mobile impurity in a Bose-Einstein condensate and the orthogonality catastrophe

N.E. Guenther, R. Schmidt, G.M. Bruun, V. Gurarie, P. Massignan

Physical Review A 103 (1), 013317 (2021).

We analyze the properties of an impurity in a dilute Bose-Einstein condensate (BEC). The quasiparticle residue of a static impurity in an ideal BEC is known to vanish exponentially with increasing particle number, leading to a bosonic orthogonality catastrophe. Here we introduce a conceptually simple variational ansatz for mobile impurities which accurately describes their macroscopic dressing in the regime close to orthogonality, including back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs in the mobile case, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with recent experimental results.

##### Robust all-optical single-shot readout of nitrogen-vacancy centers in diamond

D.M. Irber, F. Poggiali, F. Kong, M. Kieschnick, T. Luehmann, D. Kwiatkowski, J. Meijer, J.F. Du, F.Z. Shi, F. Reinhard

Nature Communications 12 (1), 532 (2021).

High-fidelity projective readout of a qubit's state in a single experimental repetition is a prerequisite for various quantum protocols of sensing and computing. Achieving single-shot readout is challenging for solid-state qubits. For Nitrogen-Vacancy (NV) centers in diamond, it has been realized using nuclear memories or resonant excitation at cryogenic temperature. All of these existing approaches have stringent experimental demands. In particular, they require a high efficiency of photon collection, such as immersion optics or all-diamond micro-optics. For some of the most relevant applications, such as shallow implanted NV centers in a cryogenic environment, these tools are unavailable. Here we demonstrate an all-optical spin readout scheme that achieves single-shot fidelity even if photon collection is poor (delivering less than 10(3) clicks/second). The scheme is based on spin-dependent resonant excitation at cryogenic temperature combined with spin-to-charge conversion, mapping the fragile electron spin states to the stable charge states. We prove this technique to work on shallow implanted NV centers, as they are required for sensing and scalable NV-based quantum registers. The NV center in diamond has been used extensively in sensing; however single shot readout of its spin remains challenging, requiring complex optical setups. Here, Irber et al. demonstrate a more robust scheme that achieves single-shot readout even when using inefficient detection optics.

##### Erbium dopants in nanophotonic silicon waveguides

Lorenz Weiss, Andreas Gritsch, Benjamin Merkel, and Andreas Reiserer

Optica 8, 40–41 (2021).

We perform resonant spectroscopy of erbium implanted into nanophotonic silicon waveguides, finding 1 GHz inhomogeneous broadening and homogeneous linewidths below 0.1 GHz. Our study thus introduces a promising materials platform for on-chip quantum information processing.

##### Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality

G. Styliaris, N. Anand, P. Zanardi

Physical Review Letters 126, 030601 (2021).

In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this “bipartite OTOC” is equal to the operator entanglement of the evolution, and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.

##### Probing the Hall Voltage in Synthetic Quantum Systems

M. Buser, S. Greschner, U. Schollwoeck, T. Giamarchi

Physical Review Letters 126 (3), 030501 (2021).

YIn the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.

##### A Statistical Theory of Heavy Atoms: Asymptotic Behavior of the Energy and Stability of Matter

H. Siedentop

We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizsäcker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation of the lower bound, we show stability of matter.

##### Raman spectrum of Janus transition metal dichalcogenide monolayers WSSe and MoSSe

M.M. Petric, M. Kremser, M. Barbone, Y. Qin, Y. Sayyad, Y.X. Shen, S. Tongay, J.J. Finley, A.R. Botello-Mendez, K. Mueller

Physical Review B 103 (3), 035414 (2021).

Janus transition metal dichalcogenides (TMDs) lose the horizontal mirror symmetry of ordinary TMDs, leading to the emergence of additional features, such as native piezoelectricity, Rashba effect, and enhanced catalytic activity. While Raman spectroscopy is an essential nondestructive, phase- and composition-sensitive tool to monitor the synthesis of materials, a comprehensive study of the Raman spectrum of Janus monolayers is still missing. Here, we discuss the Raman spectra of WSSe and MoSSe measured at room and cryogenic temperatures, near and off resonance. By combining polarization-resolved Raman data with calculations of the phonon dispersion and using symmetry considerations, we identify the four first-order Raman modes and higher-order two-phonon modes. Moreover, we observe defect-activated phonon processes, which provide a route toward a quantitative assessment of the defect concentration and, thus, the crystal quality of the materials. Our work establishes a solid background for future research on material synthesis, study, and application of Janus TMD monolayers.

##### Laser stabilization to a cryogenic fiber ring resonator

B. Merkel, D. Repp, and A. Reiserer

Optics Letters 46, 444-447 (2021).

The frequency stability of lasers is limited by thermal noise in state-of-the-art frequency references. Further improvement requires operation at cryogenic temperature. In this context, we investigate a fiber-based ring resonator. Our system exhibits a first-order temperature-insensitive point around 3.55K, much lower than that of crystalline silicon. The observed low sensitivity with respect to vibrations (<5⋅10−11m−1s2), temperature (−22(1)⋅10−9K−2), and pressure changes (4.2(2)⋅10−11mbar−2) makes our approach promising for future precision experiments.

##### High-resolution spectroscopy of a quantum dot driven bichromatically by two strong coherent fields

C. Gustin, L. Hanschke, K. Boos, J.R.A. Müller, M. Kremser, J. J. Finley, S. Hughes, K. Müller

Physical Review Research 3, 13044 (2021).

We present spectroscopic experiments and theory of a quantum dot driven bichromatically by two strong coherent lasers. In particular, we explore the regime where the drive strengths are substantial enough to merit a general nonperturbative analysis, resulting in a rich higher-order Floquet dressed-state energy structure. We show high-resolution spectroscopy measurements with a variety of laser detunings performed on a single InGaAs quantum dot, with the resulting features well explained with a time-dependent quantum master equation and Floquet analysis. Notably, driving the quantum dot resonance and one of the subsequent Mollow triplet sidepeaks, we observe the disappearance and subsequent reappearance of the central transition and transition resonant with detuned laser at high detuned-laser pump strengths and additional higher-order effects, e.g., emission triplets at higher harmonics and signatures of higher-order Floquet states. For a similar excitation condition but with an off-resonant primary laser, we observe similar spectral features but with an enhanced inherent spectral asymmetry.

##### Fermionic quantum cellular automata and generalized matrix-product unitaries

L. Piroli, A. Turzillo, S.K Shukla, J.I. Cirac

Journal of Statistical Mechanics: Theory and Experiment 013107 (2021).

In this paper, we study matrix-product unitary operators (MPUs) for fermionic one-dimensional chains. In stark contrast to the case of 1D qudit systems, we show that (i) fermionic MPUs (fMPUs) do not necessarily feature a strict causal cone and (ii) not all fermionic quantum cellular automata (QCA) can be represented as fMPUs. We then introduce a natural generalization of the latter, obtained by allowing for an additional operator acting on their auxiliary space. We characterize a family of such generalized MPUs that are locality-preserving, and show that, up to appending inert ancillary fermionic degrees of freedom, any representative of this family is a fermionic QCA (fQCA) and vice versa. Finally, we prove an index theorem for generalized MPUs, recovering the recently derived classification of fQCA in one dimension. As a technical tool for our analysis, we also introduce a graded canonical form for fermionic matrix product states, proving its uniqueness up to similarity transformations.

##### Dominant Fifth-Order Correlations in Doped Quantum Antiferromagnets

A. Bohrdt, Y. Wang, J. Koepsell, M. Kanasz-Nagy, E. Demler, F. Grusdt.

Physical Review Letters 126 (2), 026401 (2021).

Traditionally, one- and two-point correlation functions are used to characterize many-body systems. In strongly correlated quantum materials, such as the doped 2D Fermi-Hubbard system, these may no longer be sufficient, because higher-order correlations are crucial to understanding the character of the many-body system and can be numerically dominant. Experimentally, such higher-order correlations have recently become accessible in ultracold atom systems. Here, we reveal strong non-Gaussian correlations in doped quantum antiferromagnets and show that higher-order correlations dominate over lower-order terms. We study a single mobile hole in the t - J model using the density matrix renormalization group and reveal genuine fifth-order correlations which are directly related to the mobility of the dopant. We contrast our results to predictions using models based on doped quantum spin liquids which feature significantly reduced higher-order correlations. Our predictions can be tested at the lowest currently accessible temperatures in quantum simulators of the 2D Fermi-Hubbard model. Finally, we propose to experimentally study the same fifth-order spin-charge correlations as a function of doping. This will help to reveal the microscopic nature of charge carriers in the most debated regime of the Hubbard model, relevant for understanding high-T-c superconductivity.

##### Low-Scaling Tensor Hypercontraction in the Cholesky Molecular Orbital Basis Applied to Second-Order Moller-Plesset Perturbation Theory

F.H. Bangerter, M. Glasbrenner, C. Ochsenfeld

Journal of Chemical Theory and Computation 17 (1), 211-221 (2021).

We employ various reduced scaling techniques to accelerate the recently developed least-squares tensor hypercontraction (LS-THC) approximation [Parrish, R M., Hohenstein, E. G., Martinez, T. J., Sherrill, C. D. J. Chem. Phys. 137, 224106 (2012)] for electron repulsion integrals (ERIs) and apply it to second-order Moller-Plesset perturbation theory (MP2). The grid-projected ERI tensors are efficiently constructed using a localized Cholesky molecular orbital basis from density-fitted integrals with an attenuated Coulomb metric. Additionally, rigorous integral screening and the natural blocking matrix format are applied to reduce the complexity of this step. By recasting the equations to form the quantized representation of the 1/r operator Z into the form of a system of linear equations, the bottleneck of inverting the grid metric via pseudoinversion is removed. This leads to a reduced scaling THC algorithm and application to MP2 yields the (sub-)quadratically scaling THC-omega-RI-CDD-SOS-MP2 method. The efficiency of this method is assessed for various systems including DNA fragments with over 8000 basis functions and the subquadratic scaling is illustrated.

##### Concept of Orbital Entanglement and Correlation in Quantum Chemistry

L.X. Ding, S. Mardazad, S. Das, S. Szalay, U. Schollwoeck, Z. Zimboras, C. Schilling

Journal of Chemical Theory and Computation 17 (1), 79-95 (2021).

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements in numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement seen previously. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

##### Crossed optical cavities with large mode diameters

A. Heinz, J. Trautmann, N. Šantić, A. J. Park, I. Bloch, and S. Blatt

Optics Letters 46 (2), 250-253 (2021).

We report on a compact, ultrahigh-vacuum compatible optical assembly to create large-scale, two-dimensional optical lattices for use in experiments with ultracold atoms. The assembly consists of an octagon-shaped spacer made from ultra-low-expansion glass, to which we optically contact four fused-silica cavity mirrors, making it highly mechanically and thermally stable. The mirror surfaces are nearly plane-parallel which allows us to create two perpendicular cavity modes with diameters ∼1 mm. Such large mode diameters are desirable to increase the optical lattice homogeneity, but lead to strong angular sensitivities of the coplanarity between the two cavity modes. We demonstrate a procedure to precisely position each mirror substrate that achieves a deviation from coplanarity of d=1(5) μm. Creating large optical lattices at arbitrary visible and near infrared wavelengths requires significant power enhancements to overcome limitations in the available laser power. The cavity mirrors have a customized low-loss mirror coating that enhances the power at a set of relevant wavelengths from the visible to the near infrared by up to three orders of magnitude.

##### Microwave Spectroscopy of the Low-Temperature Skyrmion State in Cu2OSeO3

A. Aqeel, J. Sahliger, T. Taniguchi, S. Maendl, D. Mettus, H. Berger, A. Bauer, M. Garst, C. Pfleiderer, C.H. Back.

Physical Review Letters 126 (1), 017202 (2021).

In the cubic chiral magnet Cu2OSeO3 a low-temperature skyrmion state (LTS) and a concomitant tilted conical state are observed for magnetic fields parallel to h100i. Here, we report on the dynamic resonances of these novel magnetic states. After promoting the nucleation of the LTS by means of field cycling, we apply broadband microwave spectroscopy in two experimental geometries that provide either predominantly in-plane or out-of-plane excitation. By comparing the results to linear spin-wave theory, we clearly identify resonant modes associated with the tilted conical state, the gyrational and breathing modes associated with the LTS, as well as the hybridization of the breathing mode with a dark octupole gyration mode mediated by the magnetocrystalline anisotropies. Most intriguingly, our findings suggest that under decreasing fields the hexagonal skyrmion lattice becomes unstable with respect to an oblique deformation, reflected in the formation of elongated skyrmions.

##### Charge-neutral nonlocal response in superconductor-InAs nanowire hybrid devices

A.O. Denisov, A.V. Bubis, S.U. Piatrusha, N.A. Titova, A.G. Nasibulin, J. Becker, J. Treu, D. Ruhstorfer, G. Koblmueller, E.S. Tikhonov, V.S. Khrapai

arXiv:2101.02128 (2021).

Nonlocal quasiparticle transport in normal-superconductor-normal (NSN) hybrid structures probes sub-gap states in the proximity region and is especially attractive in the context of Majorana research. Conductance measurement provides only partial information about nonlocal response composed from both electron-like and hole-like quasiparticle excitations. In this work, we show how a nonlocal shot noise measurement delivers a missing puzzle piece in NSN InAs nanowire-based devices. We demonstrate that in a trivial superconducting phase quasiparticle response is practically charge-neutral, dominated by the heat transport component with a thermal conductance being on the order of conductance quantum. This is qualitatively explained by numerous Andreev reflections of a diffusing quasiparticle, that makes its charge completely uncertain. Consistently, strong fluctuations and sign reversal are observed in the sub-gap nonlocal conductance, including occasional Andreev rectification signals. Our results prove conductance and noise as complementary measurements to characterize quasiparticle transport in superconducting proximity devices.

##### Existence and nonexistence in the liquid drop model

R.L. Frank, P.T. Nam

We revisit the liquid drop model with a general Riesz potential. Our new result is the existence of minimizers for the conjectured optimal range of parameters. We also prove a conditional uniqueness of minimizers and a nonexistence result for heavy nuclei.

##### Coherent terahertz radiation from a nonlinear oscillator of viscous electrons

C.B. Mendl, M. Polini, A. Lucas

Applied Physics Letters 118, 013105 (2021).

Compressible electron flow through a narrow cavity is theoretically unstable, and the oscillations occurring during the instability have been proposed as a method of generating terahertz radiation. We numerically demonstrate that the end point of this instability is a nonlinear hydrodynamic oscillator, consisting of an alternating shock wave and rarefaction-like relaxation flowing back and forth in the device. This qualitative physics is robust to cavity inhomogeneity and changes in the equation of state of the fluid. We discuss the frequency and amplitude dependence of the emitted radiation on physical parameters (viscosity, momentum relaxation rate, and bias current) beyond linear response theory, providing clear predictions for future experiments.

##### Erste Demonstration von Quantenüberlegenheit

M.J. Hartmann, F. Deppe

Physik in unserer Zeit 52, 12 (2021).

Mit dem Sycamore-Quantenprozessor von Google gelang zum ersten Mal überzeugend ein Experiment, in dem ein Quantensystem ein Problem besser löst als derzeit verfügbare herkömmliche Supercomputer. Die Hardware basiert auf der Technologie der supraleitenden Quantenschaltkreise. Ihr wird schon länger ein besonders großes Skalierungspotenzial hin zu mehr Quantenbits bescheinigt. Der verwendete Chip besitzt 53 Qubits. Sie sind in einem zweidimensionalen quadratischen Gitter angeordnet und durch Nächste-Nachbar-Wechselwirkung gekoppelt. Somit stellt das Experiment einen großen technologischen Fortschritt für das gesamte Feld der Quantenwissenschaften und -technologien dar. Obwohl der praktische Nutzen derzeit noch gering erscheint, sind die Arbeiten des Google-Teams ein wichtiger Schritt hin zu skalierbarem Quantenrechnen. Damit erscheint erstmals eine fehlerkorrigierte, supraleitende Quantencomputer-Architektur in nicht allzu ferner Zukunft möglich.

##### Semantic Security via Seeded Modular Coding Schemes and Ramanujan Graphs

M. Wiese, H. Boche

IEEE Transactions on Information Theory 67 (1), 52-80 (2021).

A novel type of functions called biregular irreducible functions is introduced and applied as security components (instead of, e.g., universal hash functions) in seeded modular wiretap coding schemes, whose second component is an error-correcting code. These schemes are called modular BRI schemes. An upper bound on the semantic security information leakage of modular BRI schemes in a one-shot setting is derived which separates the effects of the biregular irreducible function on the one hand and the error-correcting code plus the channel on the other hand. The effect of the biregular irreducible function is described by the second-largest eigenvalue of an associated stochastic matrix. A characterization of biregular irreducible functions is given in terms of connected edge-disjoint biregular graphs. It allows for the construction of new biregular irreducible functions from families of edge-disjoint Ramanujan graphs, which are shown to exist. A concrete and frequently used arithmetic universal hash function can be converted into a biregular irreducible function for certain parameters. Sequences of Ramanujan biregular irreducible functions are constructed which exhibit an optimal trade-off between the size of the regularity set and the rate of decrease of the associated second-largest eigenvalue. Together with the one-shot bound on the information leakage, the existence of these sequences implies an asymptotic coding result for modular BRI schemes applied to discrete and Gaussian wiretap channels. It shows that the separation of error correction and security as done in a modular BRI scheme is secrecy capacity-achieving for every discrete and Gaussian wiretap channel. The same holds for a derived construction where the seed is generated locally by the sender and reused several times. It is shown that the optimal sequences of biregular irreducible functions used in the above constructions must be nearly Ramanujan.

##### Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

M. Lewin, P.T. Nam, N. Rougerie

Inventiones Mathematicae (2021).

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrodinger-type classical field theory, in terms of partition functions and reduced density matrices. The Gibbs measure thus describes the behavior of the infinite Bose gas at criticality, that is, close to the phase transition to a Bose-Einstein condensate. The Gibbs measure is concentrated on singular distributions and has to be appropriately renormalized, while the quantum system is well defined without any renormalization. By tuning a single real parameter (the chemical potential), we obtain a counter-term for the diverging repulsive interactions which provides the desired Wick renormalization of the limit classical theory. The proof relies on a new estimate on the entropy relative to quasi-free states and a novel method to control quantum variances.

##### Classical field theory limit of many-body quantum Gibbs states in 2D and 3D

M. Lewin, P.T. Nam, N. Rougerie

Inventiones mathematicae 224, 315–444 (2021).

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrödinger-type classical field theory, in terms of partition functions and reduced density matrices. The Gibbs measure thus describes the behavior of the infinite Bose gas at criticality, that is, close to the phase transition to a Bose–Einstein condensate. The Gibbs measure is concentrated on singular distributions and has to be appropriately renormalized, while the quantum system is well defined without any renormalization. By tuning a single real parameter (the chemical potential), we obtain a counter-term for the diverging repulsive interactions which provides the desired Wick renormalization of the limit classical theory. The proof relies on a new estimate on the entropy relative to quasi-free states and a novel method to control quantum variances.

##### The periodic Lieb-Thirring inequality

R.L. Frank, D. Gontier, M. Lewin

Book: Partial Differential Equations, Spectral theory and Mathematical Physics 135-154 (2021).

We discuss the Lieb–Thirring inequality for periodic systems, which has the same optimal constant as the original inequality for finite systems. This allows us to formulate a new conjecture about the value of its best constant. To demonstrate the importance of periodic states, we prove that the 1D Lieb–Thirring inequality at the special exponent γ=32 admits a one-parameter family of periodic optimizers, interpolating between the one-bound state and the uniform potential. Finally, we provide numerical simulations in 2D which support our conjecture that optimizers could be periodic.

##### On tensor network representations of the (3+1)d toric code

C. Delcamp, N. Schuch

We define two dual tensor network representations of the (3+1)d toric code ground state subspace. These two representations, which are obtained by initially imposing either family of stabilizer constraints, are characterized by different virtual symmetries generated by string-like and membrane-like operators, respectively. We discuss the topological properties of the model from the point of view of these virtual symmetries, emphasizing the differences between both representations. In particular, we argue that, depending on the representation, the phase diagram of boundary entanglement degrees of freedom is naturally associated with that of a (2+1)d Hamiltonian displaying either a global or a gauge Z2-symmetry.

##### On the stability of topological order in tensor network states

D.J. Williamson, C. Delcamp, F. Verstraete, N. Schuch

We construct a tensor network representation of the 3d toric code ground state that is stable to all local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The stability is established by mapping the phase diagram of the perturbed tensor network to that of the 3d Ising gauge theory, which has a non-zero finite temperature transition. More generally, we find that the stability of a topological tensor network state is determined by the form of its virtual symmetries and the topological excitations created by virtual operators that break those symmetries. In particular, a dual representation of the 3d toric code ground state, as well as representations of the X-cube and cubic code ground states, for which point-like excitations are created by such operators, are found to be unstable.

##### Time crystallinity and finite-size effects in clean Floquet systems

A. Pizzi, D. Malz, G. De Tomasi, J. Knolle, A. Nunnenkamp

Physical Review B 102 (21), 214207 (2020).

A cornerstone assumption that most literature on discrete time crystals has relied on is that homogeneous Floquet systems generally heat to a featureless infinite temperature state, an expectation that motivated researchers in the field to mostly focus on many-body localized systems. Some works have, however, shown that the standard diagnostics for time crystallinity apply equally well to clean settings without disorder. This fact raises the question whether a homogeneous discrete time crystal is possible in which the originally expected heating is evaded. Studying both a localized and an homogeneous model with short-range interactions, we clarify this issue showing explicitly the key differences between the two cases. On the one hand, our careful scaling analysis confirms that, in the thermodynamic limit and in contrast to localized discrete time crystals, homogeneous systems indeed heat. On the other hand, we show that, thanks to a mechanism reminiscent of quantum scars, finite-size homogeneous systems can still exhibit very crisp signatures of time crystallinity. A subharmonic response can in fact persist over timescales that are much larger than those set by the integrability-breaking terms, with thermalization possibly occurring only at very large system sizes (e.g., of hundreds of spins). Beyond clarifying the emergence of heating in disorder-free systems, our work casts a spotlight on finite-size homogeneous systems as prime candidates for the experimental implementation of nontrivial out-of-equilibrium physics.

##### Static magnetic proximity effects and spin Hall magnetoresistance in Pt/Y3Fe5O12 and inverted Y3Fe5O12/Pt bilayers

S. Gepraegs, C. Klewe, S. Meyer, D. Graulich, F. Schade, M. Schneider, S. Francoual, S.P. Collins, K. Ollefs, F. Wilhelm, A. Rogalev, Y. Joly, S.T.B. Goennenwein, M. Opel, T. Kuschel, R. Gross

Physical Review B 102 (21), 214438 (2020).

The magnetic state of heavy metal Pt thin films in proximity to the ferrimagnetic insulator Y3Fe5O12 has been investigated systematically by means of x-ray magnetic circular dichroism and x-ray resonant magnetic reflectivity measurements combined with angle-dependent magnetotransport studies. To reveal intermixing effects as the possible cause for induced magnetic moments in Pt, we compare thin film heterostructures with different orders of the layer stacking and different interface properties. For standard Pt layers on Y3Fe5O12 thin films, we do not detect any static magnetic polarization in Pt. These samples show an angle-dependent magnetoresistance behavior, which is consistent with the established spin Hall magnetoresistance. In contrast, for the inverted layer sequence, Y3Fe5O12 thin films grown on Pt layers, Pt displays a finite induced magnetic moment comparable to that of all-metallic Pt/Fe bilayers. This magnetic moment is found to originate from finite intermixing at the Y3Fe5O12/Pt interface. As a consequence, we found a complex angle-dependent magnetoresistance indicating a superposition of the spin Hall and the anisotropic magnetoresistance in these types of samples. Both effects can be disentangled from each other due to their different angle dependence and their characteristic temperature evolution.

##### A range-separated generalized Kohn-Sham method including a long-range nonlocal random phase approximation correlation potential

D. Graf, C. Ochsenfeld

Journal of Chemical Physics 153 (24), 244118 (2020).

Based on our recently published range-separated random phase approximation (RPA) functional [Kreppel et al., "Range-separated density-functional theory in combination with the random phase approximation: An accuracy benchmark," J. Chem. Theory Comput. 16, 2985-2994 (2020)], we introduce self-consistent minimization with respect to the one-particle density matrix. In contrast to the range-separated RPA methods presented so far, the new method includes a long-range nonlocal RPA correlation potential in the orbital optimization process, making it a full-featured variational generalized Kohn-Sham (GKS) method. The new method not only improves upon all other tested RPA schemes including the standard post-GKS range-separated RPA for the investigated test cases covering general main group thermochemistry, kinetics, and noncovalent interactions but also significantly outperforms the popular G(0)W(0) method in estimating the ionization potentials and fundamental gaps considered in this work using the eigenvalue spectra obtained from the GKS Hamiltonian.

##### Special issue on Mathematical Results in Quantum Mechanics

M. Christandl, H. Cornean, S. Fournais, P. Müller, J.Schach Møller (Editors)

Rev. Math. Phys. 33 (1), (2020).

##### Which magnetic fields support a zero mode?

R.L. Frank, M. Loss

This paper presents some results concerning the size of magnetic fields that support zero modes for the three dimensional Dirac equation and related problems for spinor equations. It is a well known fact that for the Schrödinger in three dimensions to have a negative energy bound state, the 3/2- norm of the potential has to be greater than the Sobolev constant. We prove an analogous result for the existence of zero modes, namely that the 3/2 - norm of the magnetic field has to greater than twice the Sobolev constant. The novel point here is that the spinorial nature of the wave function is crucial. It leads to an improved diamagnetic inequality from which the bound is derived. While the results are probably not sharp, other equations are analyzed where the results are indeed optimal.

##### Obstacles to Variational Quantum Optimization from Symmetry Protection

S. Bravyi, A. Kliesch, R. Koenig, E. Tang

Physical Review Letters 125, 260505 (2020).

The quantum approximate optimization algorithm (QAOA) employs variational states generated by a parameterized quantum circuit to maximize the expected value of a Hamiltonian encoding a classical cost function. Whether or not the QAOA can outperform classical algorithms in some tasks is an actively debated question. Our work exposes fundamental limitations of the QAOA resulting from the symmetry and the locality of variational states. A surprising consequence of our results is that the classical Goemans-Williamson algorithm outperforms the QAOA for certain instances of MaxCut, at any constant level. To overcome these limitations, we propose a nonlocal version of the QAOA and give numerical evidence that it significantly outperforms the standard QAOA for frustrated Ising models.

##### Gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations

J. Bender, E. Zohar

Physical Review D 102 (11), 114517 (2020).

We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating frame, where the matter is decoupled from the gauge constraints, we can express the gauge field operators in terms of dual operators. In two space dimensions, the dual representation is completely free of any local constraints. In three space dimensions, local constraints among the dual operators remain but involve only the gauge field degrees of freedom (and not the matter degrees of freedom). These formulations, which reduce the required Hilbert space dimension, could be useful for both numerical (classical) Hamiltonian computations and quantum simulation or computation.

##### S-Matrix and Anomaly of de Sitter

G. Dvali

Symmetry 13, 3 (2020).

S-matrix formulation of gravity excludes de Sitter vacua. In particular, this is organic to string theory. The S-matrix constraint is enforced by an anomalous quantum break-time proportional to the inverse values of gravitational and/or string couplings. Due to this, de Sitter can satisfy the conditions for a valid vacuum only at the expense of trivializing the graviton and closed-string S-matrices. At non-zero gravitational and string couplings, de Sitter is deformed by corpuscular 1/N effects, similarly to Witten–Veneziano mechanism in QCD with N colors. In this picture, an S-matrix formulation of Einstein gravity, such as string theory, nullifies an outstanding cosmological puzzle. We discuss possible observational signatures which are especially interesting in theories with a large number of particle species. Species can enhance the primordial quantum imprints to potentially observable level even if the standard inflaton fluctuations are negligible.

##### Fast Computation of Spherical Phase-Space Functions of Quantum Many-Body States

B. Koczor, R. Zeier, S.J. Glaser,

Physical Review A 102 (6), 62421 (2020).

Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We focus on spherical phase spaces for finite-dimensional quantum states of single qudits or permutationally symmetric states of multiple qubits. We present methods to efficiently compute the corresponding spherical phase-space functions which are at least an order of magnitude faster than traditional methods. Quantum many-body states in much larger dimensions can now be effectively studied by experimentalists and theorists using spherical phase-space techniques.

##### Analyzing non-equilibrium quantum states through snapshots with artificial neural networks

A. Bohrdt, S. Kim, A. Lukin, M. Rispoli, R. Schittko, M. Knap, M. Greiner, J. Léonard

Current quantum simulation experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. Therefore, the question emerges which observables are best suited to study the dynamics in such quantum many-body systems. Using machine learning techniques, we investigate the dynamics and in particular the thermalization behavior of an interacting quantum system which undergoes a dynamical phase transition from an ergodic to a many-body localized phase. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We test our methods with experimental snapshots of ultracold atoms taken with a quantum gas microscope. Our results provide a path to analyze highly-entangled large-scale quantum states for system sizes where numerical calculations of conventional observables become challenging.

##### Sideband-resolved resonator electromechanics based on a nonlinear Josephson inductance probed on the single-photon level

P. Schmidt, M.T. Amawi, S. Pogorzalek, F. Deppe, A. Marx, R. Gross, H. Huebl

Communication Physics 3 (1), 233 (2020).

Light-matter interaction in optomechanical systems is the foundation for ultra-sensitive detection schemes as well as the generation of phononic and photonic quantum states. Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280Hz. Complementary, early proposals and experiments suggest that inductive coupling schemes are tunable and have the potential to reach the single-photon strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62kHz, realizing sub-aNHz(-1/2) force sensitivities. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian. Recently, inductively-coupled optomechanical systems have been realized. They represent an important step forward towards achieving strong light-matter interaction, offer extreme sensitivity to mechanical displacement, and allow to study quantum phenomena on a single quantum level. In this work, a superconducting device is inductively coupled to a microwave resonator forming an electromechanical system operating at the single-photon level.

##### Z(2) Parton Phases in the Mixed-Dimensional t - J(z) Model

F. Grusdt, L. Pollet

Physical Review Letters 125 (25), 256401 (2020).

We study the interplay of spin and charge degrees of freedom in a doped Ising antiferromagnet, where the motion of charges is restricted to one dimension. The phase diagram of this mixed-dimensional t - J(z) model can be understood in terms of spinless chargons coupled to a Z(2) lattice gauge field. The antiferromagnetic couplings give rise to interactions between Z(2) electric field lines which, in turn, lead to a robust stripe phase at low temperatures. At higher temperatures, a confined meson-gas phase is found for low doping whereas at higher doping values, a robust deconfined chargon-gas phase is seen, which features hidden antiferromagnetic order. We confirm these phases in quantum Monte Carlo simulations. Our model can be implemented and its phases detected with existing technology in ultracold atom experiments. The critical temperature for stripe formation with a sufficiently high hole concentration is around the spin-exchange energy J(z), i.e., well within reach of current experiments.

##### Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions

S. Birnkammer, A. Bohrdt, F. Grusdt, M. Knap

Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. Based on analytical and numerical arguments, we show that this model features a quantum phase transition from a spin liquid to a valence bond solid that spontaneously breaks lattice translational symmetry and is reminiscent of the Majumdar-Ghosh state. The different phases can be probed dynamically by measuring the evolution of a fully dimerized state. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of our interacting many-body system.

##### Magneto-optical conductivity in generic Weyl semimetals

M. Stalhammar, J. Larana-Aragon, J. Knolle, E.J. Bergholtz

Physical Review B 102 (23), 235134 (2020).

Magneto-optical studies of Weyl semimetals have been proposed as a versatile tool for observing low-energy Weyl fermions in candidate materials including the chiral Landau level. However, previous theoretical results have been restricted to the linearized regime around the Weyl node and are at odds with experimental findings. Here, we derive a closed form expression for the magneto-optical conductivity of generic Weyl semimetals in the presence of an external magnetic field aligned with the tilt of the spectrum. The systems are taken to have linear dispersion in two directions, while the tilting direction can consist of any arbitrary continuously differentiable function. This general calculation is then used to analytically evaluate the magneto-optical conductivity of Weyl semimetals expanded to cubic order in momentum. In particular, systems with arbitrary tilt, as well as systems hosting trivial Fermi pockets are investigated. The higher-order terms in momentum close the Fermi pockets in the type-II regime, removing the need for unphysical cutoffs when evaluating the magneto-optical conductivity. Crucially, the ability to take into account closed over-tilted and additional trivial Fermi pockets allows us to treat model systems closer to actual materials and we propose a simple explanation why the presence of parasitic trivial Fermi pockets can mask the characteristic signature of Weyl fermions in magneto-optical conductivity measurements.

##### Integrability of one-dimensional Lindbladians from operator-space fragmentation

F.H.L. Essler, L. Piroli

Physical Review E 102 (6), 062210 (2020).

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) The space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; (ii) the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 XXZ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimensions.

##### Symmetry-adapted decomposition of tensor operators and the visualization of coupled spin systems

D. Leiner, R. Zeier, S.J. Glaser

Journal of Physics A - Mathematical and Theoretical 53 (49), 495301 (2020).

We study the representation and visualization of finite-dimensional, coupled quantum systems. To establish a generalizedWigner representation, multi-spin operators are decomposed into a symmetry-adapted tensor basis and are mapped to multiple spherical plots that are each assembled from linear combinations of spherical harmonics. We explicitly determine the corresponding symmetry-adapted tensor basis for up to six coupled spins 1/2 (qubits) using a first step that relies on a Clebsch-Gordan decomposition and a second step which is implemented with two different approaches based on explicit projection operators and coefficients of fractional parentage. The approach based on explicit projection operators is currently only applicable for up to four spins 1/2. The resulting generalized Wigner representation is illustrated with various examples for the cases of four to six coupled spins 1/2. We also treat the case of two coupled spins with arbitrary spin numbers (qudits) not necessarily equal to 1/2 and highlight a quantum system of a spin 1/2 coupled to a spin 1 (qutrit). Our work offers a much more detailed understanding of the symmetries appearing in coupled quantum systems.

##### Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Lukas Homeier, Christian Schweizer, Monika Aidelsburger, Arkady Fedorov, Fabian Grusdt

(2020).

Kitaev's toric code is an exactly solvable model with Z2-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for Z2 lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a π-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.

##### Observation of Antiferromagnetic Magnon Pseudospin Dynamics and the Hanle Effect

T. Wimmer, A. Kamra, J. Gueckelhorn, M. Opel, S. Gepraegs, R. Gross, H. Huebl, M. Althammer

Physical Review Letters 125 (24), 247204 (2020).

We report on experiments demonstrating coherent control of magnon spin transport and pseudospin dynamics in a thin film of the antiferromagnetic insulator hematite utilizing two Pt strips for all-electrical magnon injection and detection. The measured magnon spin signal at the detector reveals an oscillation of its polarity as a function of the externally applied magnetic field. We quantitatively explain our experiments in terms of diffusive magnon transport and a coherent precession of the magnon pseudospin caused by the easy-plane anisotropy and the Dzyaloshinskii-Moriya interaction. This experimental observation can be viewed as the magnonic analog of the electronic Hanle effect and the Datta-Das transistor, unlocking the high potential of antiferromagnetic magnonics toward the realization of rich electronics-inspired phenomena.

##### Anomalous Diffusion in Dipole- and Higher-Moment-Conserving Systems

J. Feldmeier, P. Sala, G. De Tomasi, F. Pollmann, M. Knap

Physical Review Letters 125 (24), 245303 (2020).

The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher-moment generalizations thereof, escape this scenario, displaying subdiffusive decay instead. Modeling the time evolution as cellular automata for specific cases of dipole- and quadrupole conservation, we numerically find distinct anomalous exponents of the late time relaxation. We explain these findings by analytically constructing a general hydrodynamic model that results in a series of exponents depending on the number of conserved moments, yielding an accurate description of the scaling form of charge correlation functions. We analyze the spatial profile of the correlations and discuss potential experimentally relevant signatures of higher-moment conservation.

##### Spontaneous conformal symmetry breaking in fishnet CFT

G. Karananas, V. Kazakov, M. Shaposhnikov

Phys. Lett. B 811, 135922 (2020).

Quantum field theories with exact but spontaneously broken conformal invariance have an intriguing feature: their vacuum energy (cosmological constant) is equal to zero. Up to now, the only known ultraviolet complete theories where conformal symmetry can be spontaneously broken were associated with supersymmetry (SUSY), with the most prominent example being the =4 SUSY Yang-Mills. In this Letter we show that the recently proposed conformal “fishnet” theory supports at the classical level a rich set of flat directions (moduli) along which conformal symmetry is spontaneously broken. We demonstrate that, at least perturbatively, some of these vacua survive in the full quantum theory (in the planar limit, at the leading order of expansion) without any fine tuning. The vacuum energy is equal to zero along these flat directions, providing the first non-SUSY example of a four-dimensional quantum field theory with “natural” breaking of conformal symmetry.

##### Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations

A.Schuckert, M.Knap

Physical Review Research 2 (4), 43315 (2020).

The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input. This leaves many of the general assumptions of ETH untested. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH. We discuss and propose protocols to independently measure fluctuations and dissipations as well as higher order time-ordered correlation functions. We first show how the emergence of fluctuation-dissipation relations from a nonequilibrium initial state can be observed for the two-dimensional (2D) Bose-Hubbard model in superconducting qubits or quantum gas microscopes. Then we focus on the long-range transverse field Ising model (LTFI), which can be realized with trapped ions. The LTFI exhibits rich thermalization phenomena: For strong transverse fields, we observe prethermalization to an effective magnetization-conserving Hamiltonian in the fluctuation-dissipation relations. For weak transverse fields, confined excitations lead to nonthermal features, resulting in a violation of the fluctuation-dissipation relations up to long times. Moreover, in an integrable region of the LTFI, thermalization to a generalized Gibbs ensemble occurs and the fluctuation-dissipation relations enable an experimental diagonalization of the Hamiltonian. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.

##### Precise control of J(eff)=1/2 magnetic properties in Sr2IrO4 epitaxial thin films by variation of strain and thin film thickness

S. Geprags, B.E. Skovdal , M. Scheufele, M. Opel, D. Wermeille, P. Thompson, A. Bombardi, V. Simonet, S. Grenier, P. Lejay, G.A. Chahine, D.L. Quintero-Castro, R. Gross, D. Mannix

Physical Review B 102 (21), 214402 (2020).

We report on a comprehensive investigation of the effects of strain and film thickness on the structural and magnetic properties of epitaxial thin films of the prototypal J(eff) = 1/2 compound Sr2IrO4 by advanced x-ray scattering. We find that the Sr2IrO4 thin films can be grown fully strained up to a thickness of 108 nm. By using x-ray resonant scattering, we show that the out-of-plane magnetic correlation length is strongly dependent on the thin film thickness, but independent of the strain state of the thin films. This can be used as a finely tuned dial to adjust the out-of-plane magnetic correlation length and transform the magnetic anisotropy from two-dimensional to three-dimensional behavior by incrementing film thickness. These results provide a clearer picture for the systematic control of the magnetic degrees of freedom in epitaxial thin films of Sr2IrO4 and bring to light the potential for a rich playground to explore the physics of 5d transition-metal compounds.

##### Room-Temperature Synthesis of 2D Janus Crystals and their Heterostructures

D.B. Trivedi, G. Turgut, Y. Qin, M.Y. Sayyad, D. Hajra, M. Howell, L. Liu, S.J. Yang, N.H. Patoary, H. Li, M.M. Petric, M. Meyer, M. Kremser, M. Barbone, G. Soavi, A.V. Stier, K. Mueller, S.Z. Yang, I.S. Esqueda, H.L. Zhuang, J.J. Finley, S. Tongay

Advanced Materials 32 (50), 2006320 (2020).

Janus crystals represent an exciting class of 2D materials with different atomic species on their upper and lower facets. Theories have predicted that this symmetry breaking induces an electric field and leads to a wealth of novel properties, such as large Rashba spin-orbit coupling and formation of strongly correlated electronic states. Monolayer MoSSe Janus crystals have been synthesized by two methods, via controlled sulfurization of monolayer MoSe2 and via plasma stripping followed thermal annealing of MoS2. However, the high processing temperatures prevent growth of other Janus materials and their heterostructures. Here, a room-temperature technique for the synthesis of a variety of Janus monolayers with high structural and optical quality is reported. This process involves low-energy reactive radical precursors, which enables selective removal and replacement of the uppermost chalcogen layer, thus transforming classical transition metal dichalcogenides into a Janus structure. The resulting materials show clear mixed character for their excitonic transitions, and more importantly, the presented room-temperature method enables the demonstration of first vertical and lateral heterojunctions of 2D Janus TMDs. The results present significant and pioneering advances in the synthesis of new classes of 2D materials, and pave the way for the creation of heterostructures from 2D Janus layers.

##### Time-domain photocurrent spectroscopy based on a common-path birefringent interferometer

L. Wolz, C. Heshmatpour, A. Perri, D. Polli, G. Cerullo, J.J. Finley, E. Thyrhaug, J. Hauer, A.V. Stier

Review of Scientific Instruments 91 (12), 123101 (2020).

We present diffraction-limited photocurrent (PC) microscopy in the visible spectral range based on broadband excitation and an inherently phase-stable common-path interferometer. The excellent path-length stability guarantees high accuracy without the need for active feedback or post-processing of the interferograms. We illustrate the capabilities of the setup by recording PC spectra of a bulk GaAs device and compare the results to optical transmission data.

##### Turing Meets Circuit Theory: Not Every Continuous-Time LTI System Can be Simulated on a Digital Computer

H. Boche, V. Pohl

IEEE Transactions on Circuits and Systems I-Regular Papers 67 (12), 5051-5064 (2020).

Solving continuous problems on digital computers gives generally only approximations of the continuous solutions. It is therefore crucial that the error between the continuous solution and the digital approximation can effectively be controlled. This paper investigates the possibility of simulating linear, time-invariant (LTI) systems on Turing machines. It is shown that there exist elementary LTI systems for which an admissible and computable input signal results in a non-computable output signal. For these LTI systems, the paper gives sharp characterizations of input spaces such that the output is guaranteed to be computable. The second part of the paper discusses the computability of the impulse and step response of LTI systems. It is shown that the computability of the step response implies not the computability of the impulse response. Moreover, there exist impulse responses which cannot be computed from the transfer function using the inverse Laplace transform. Finally, the paper gives a stronger version of a classical non-computability result, showing that there exist admissible and computable initial values for the wave equation so that the solution cannot be computed at certain points in space and time.

##### Crux of Using the Cascaded Emission of a Three-Level Quantum Ladder System to Generate Indistinguishable Photons

E. Scholl, L. Schweickert, L. Hanschke, K.D. Zeuner, F. Sbresny, T. Lettner, R. Trivedi, M. Reindl, S.F.C. da Silva, R. Trotta, J.J. Finley, J. Vuckovic, K. Mueller, A. Rastelli, V. Zwiller, K.D. Jons

Physical Review Letters 125 (23), 233605 (2020).

We investigate the degree of indistinguishability of cascaded photons emitted from a three-level quantum ladder system; in our case the biexciton-exciton cascade of semiconductor quantum dots. For the three-level quantum ladder system we theoretically demonstrate that the indistinguishability is inherently limited for both emitted photons and determined by the ratio of the lifetimes of the excited and intermediate states. We experimentally confirm this finding by comparing the quantum interference visibility of noncascaded emission and cascaded emission from the same semiconductor quantum dot. Quantum optical simulations produce very good agreement with the measurements and allow us to explore a large parameter space. Based on our model, we propose photonic structures to optimize the lifetime ratio and overcome the limited indistinguishability of cascaded photon emission from a three-level quantum ladder system.

##### Dynamical formation of a magnetic polaron in a two-dimensional quantum antiferromagnet

A. Bohrdt, F. Grusdt, M. Knap

New Journal of Physics 22 (12), 123023 (2020).

Tremendous recent progress in the quantum simulation of the Hubbard model paves the way to controllably study doped antiferromagnetic Mott insulators. Motivated by these experimental advancements, we numerically study the real-time dynamics of a single hole created in an antiferromagnet on a square lattice, as described by the t-J model. Initially, the hole spreads ballistically with a velocity proportional to the hopping matrix element. At intermediate to long times, the dimensionality as well as the spin background determine the hole dynamics. A hole created in the ground state of a two dimensional (2D) quantum antiferromagnet propagates again ballistically at long times but with a velocity proportional to the spin exchange coupling, showing the formation of a magnetic polaron. We provide an intuitive explanation of this dynamics in terms of a parton construction, which leads to a good quantitative agreement with the numerical tensor network state simulations. In the limit of infinite temperature and no spin exchange couplings, the dynamics can be approximated by a quantum random walk on a Bethe lattice with coordination number

z

x303;

4

Adding Ising interactions corresponds to an effective disordered potential, which can dramatically slow down the hole propagation, consistent with subdiffusive dynamics. The study of the hole dynamics paves the way for understanding the microscopic constituents of this strongly correlated quantum state.

##### Strict positivity and D-majorization

F. vom Ende

Linear & Multilinear Algebra (2020).

Motivated by quantum thermodynamics, we first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action on any full-rank state, and that the image of non-strictly positive maps lives inside a lower-dimensional subalgebra. This implies that the distance of such maps to the identity channel is lower bounded by one. The notion of strict positivity comes in handy when generalizing the majorization ordering on real vectors with respect to a positive vector d to majorization on square matrices with respect to a positive definite matrix D. For the two-dimensional case, we give a characterization of this ordering via finitely many trace norm inequalities and, moreover, investigate some of its order properties. In particular it admits a unique minimal and a maximal element. The latter is unique as well if and only if minimal eigenvalue of D has multiplicity one.

##### Antiferromagnetic magnon pseudospin: Dynamics and diffusive transport

A. Kamra, T. Wimmer, H. Huebl, M. Althammer

Physical Review B 102 (17), 174445 (2020).

We formulate a theoretical description of antiferromagnetic magnons and their transport in terms of an associated pseudospin. The need and strength of this formulation emerges from the antiferromagnetic eigenmodes being formed from superpositions of spin-up and -down magnons, depending on the material anisotropies. Consequently, a description analogous to that of spin-1/2 electrons is demonstrated while accounting for the bosonic nature of the antiferromagnetic eigenmodes. Introducing the concepts of a pseudospin chemical potential together with a pseudofield and relating magnon spin to pseudospin allows a consistent description of diffusive spin transport in antiferromagnetic insulators with any given anisotropies and interactions. Employing the formalism developed, we elucidate the general features of recent nonlocal spin transport experiments in antiferromagnetic insulators hosting magnons with different polarizations. The pseudospin formalism developed herein is valid for any pair of coupled bosons and is likely to be useful in other systems comprising interacting bosonic modes.

##### Low-complexity eigenstates of a ν = 1/3 fractional quantum Hall system

B. Nachtergaele, S. Warzel, A. Young

Journal of Physics A: Mathematical and Theoretical 54, 1 (2020).

We identify the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in the thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice tilings and their properties are discussed. We also report on a proof of a spectral gap, which implies the incompressibility of the underlying fractional quantum Hall liquid at maximal filling ν = 1/3. Low-energy excitations and an extensive number of many-body scars at positive energy density, but nevertheless low complexity, are also identified using the concept of tilings.

##### Two-photon frequency comb spectroscopy of atomic hydrogen

A. Grinin, A. Matveev, D. C. Yost, L. Maisenbacher, V. Wirthl, R. Pohl, T. W. Hänsch, T. Udem

Science 370, 1061 (2020).

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R∞ = 10,973,731.568226(38) per meter] and the proton charge radius [rp = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

##### Dynamics and large deviation transitions of the XOR-Fredrickson-Andersen kinetically constrained model

L. Causer, I. Lesanovsky, M.C. Banuls, J.P. Garrahan

Physical Review E 102 (5), 052132 (2020).

We study a one-dimensional classical stochastic kinetically constrained model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbors is excited. We call this model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) model. We describe the dynamics of the XOR-FA model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.

##### Entanglement-Enhanced Communication Networks

J. Nötzel, S. DiAdamo

IEEE International Conference on Quantum Computing and Engineering (QCE) 242-248 (2020).

Building quantum networks ultimately requires strong use cases. As today's design and use of the Internet solely rests on the interconnection of classical computing devices, the development of hardware should take this dependence on an existing market into account. One might think quantum secure communication would be such a use case, but the entire design of the current Internet is built on the end-to-end argument and may reject the idea of implementing security as a physical layer protocol. On the other hand, higher data rates and reduced latency have been successfully used as key arguments for the conception of new communication standards. We thus argue that exactly these two figures of merit should be used again. We define two new initial stages of development of the quantum Internet, where in the first phase entanglement is only generated and used between network nodes, and in second phase entanglement swapping and thus distribution of entanglement over increasing distances becomes possible. In both phases, we show by simulation how the available new protocols increase the network capacity. Interestingly, following this envisioned approach can serve the needs of current market participants while paving the road for fully quantum applications in the future.

##### Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems

I. Cirac, D. Perez-Garcia, N. Schuch, F. Verstraete

The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their symmetries are reflections of the global entanglement patterns in the full system. We will discuss how tensor networks enable the construction of real-space renormalization group flows and fixed points, and examine the entanglement structure of states exhibiting topological quantum order. Finally, we provide a summary of the mathematical results of matrix product states and projected entangled pair states, highlighting the fundamental theorem of matrix product vectors and its applications.

##### Probing transport and slow relaxation in the mass-imbalanced Fermi-Hubbard model

N. D. Oppong, G. Pasqualetti, O. Bettermann, P. Zechmann, M. Knap, I. Bloch, S. Fölling

Constraints in the dynamics of quantum many-body systems can dramatically alter transport properties and relaxation time scales even in the absence of static disorder. Here, we report on the observation of such constrained dynamics arising from the distinct mobility of two species in the one-dimensional mass-imbalanced Fermi-Hubbard model, realized with ultracold ytterbium atoms in a state-dependent optical lattice. By displacing the trap potential and monitoring the dynamical response of the system, we identify suppressed transport and slow relaxation with a strong dependence on the mass imbalance and interspecies interaction strength, suggesting eventual thermalization for long times. Our observations are supported by numerical simulations and pave the way to study metastability arising from dynamical constraints in other quantum many-body systems.

##### Extending Quantum Links: Modules for Fiber- and Memory-Based Quantum Repeaters

P. van Loock, W. Alt, C. Becher, O. Benson, H. Boche, C. Deppe, J. Eschner, S. Höfling, D. Meschede, P. Michler, F. Schmidt, H. Weinfurter.

Advancing Quantum Technologies - Chances and Challenges Advanced Quantum Technologies, (2020).

Elementary building blocks for quantum repeaters based on fiber channels and memory stations are analyzed. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. The performances of basic quantum repeater links for these platforms are evaluated and compared, both for present‐day, state‐of‐the‐art experimental parameters as well as for parameters that can in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances—up to a few 100 km—in which the repeater‐assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. Two different protocols are considered, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, nondestructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.

##### Projected Entangled Pair States: Fundamental analytical and numerical limitations

G. Scarpa, A. Molnár, Y. Ge, J. J. García-Ripoll, N. Schuch, D. Pérez-García, S. Iblisdir

Physical Review Letters 125, 210504 (2020).

Matrix product states and projected entangled pair states (PEPS) are powerful analytical and numerical tools to assess quantum many-body systems in one and higher dimensions, respectively. While matrix product states are comprehensively understood, in PEPS fundamental questions, relevant analytically as well as numerically, remain open, such as how to encode symmetries in full generality, or how to stabilize numerical methods using canonical forms. Here, we show that these key problems, as well as a number of related questions, are algorithmically undecidable, that is, they cannot be fully resolved in a systematic way. Our work thereby exposes fundamental limitations to a full and unbiased understanding of quantum many-body systems using PEPS.

##### Zero-temperature phases of the two-dimensional Hubbard-Holstein model: A non-Gaussian exact diagonalization study

Y. Wang, I. Esterlis, T. Shi, J.I. Cirac, E. Demler

Physical Review Research 2 (4), 043258 (2020).

We propose a numerical method which embeds the variational non-Gaussian wave-function approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wave function that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wave function exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

##### Black hole metamorphosis and stabilization by memory burden

G. Dvali, L. Eisemann, M. Michel, S. Zell

Phys. Rev. D 102, 103523 (2020).

Systems of enhanced memory capacity are subjected to a universal effect of memory burden, which suppresses their decay. In this paper, we study a prototype model to show that memory burden can be overcome by rewriting stored quantum information from one set of degrees of freedom to another one. However, due to a suppressed rate of rewriting, the evolution becomes extremely slow compared to the initial stage. Applied to black holes, this predicts a metamorphosis, including a drastic deviation from Hawking evaporation, at the latest after losing half of the mass. This raises a tantalizing question about the fate of a black hole. As two likely options, it can either become extremely long lived or decay via a new classical instability into gravitational lumps. The first option would open up a new window for small primordial black holes as viable dark matter candidates.

##### Interacting bosonic flux ladders with a synthetic dimension: Ground-state phases and quantum quench dynamics

M. Buser, D. Hubig, U. Schollwoeck, L. Tarruell, F. Heidrich-Meisner

Physical Review A 102 (5), 053314 (2020).

Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.

##### Ultrathin catalyst-free InAs nanowires on silicon with distinct 1D sub-band transport properties

F. del Giudice, J. Becker, C. de Rose, M. Doeblinger, D. Ruhstorfer, L. Suomenniemi, J. Treu, H. Riedl, J.J. Finley, G. Koblmueller

Nanoscale 12 (42), 21857-21868 (2020).

Ultrathin InAs nanowires (NW) with a one-dimensional (1D) sub-band structure are promising materials for advanced quantum-electronic devices, where dimensions in the sub-30 nm diameter limit together with post-CMOS integration scenarios on Si are much desired. Here, we demonstrate two site-selective synthesis methods that achieve epitaxial, high aspect ratio InAs NWs on Si with ultrathin diameters below 20 nm. The first approach exploits direct vapor-solid growth to tune the NW diameter by interwire spacing, mask opening size and growth time. The second scheme explores a unique reverse-reaction growth by which the sidewalls of InAs NWs are thermally decomposed under controlled arsenic flux and annealing time. Interesting kinetically limited dependencies between interwire spacing and thinning dynamics are found, yielding diameters as low as 12 nm for sparse NW arrays. We clearly verify the 1D sub-band structure in ultrathin NWs by pronounced conductance steps in low-temperature transport measurements using back-gated NW-field effect transistors. Correlated simulations reveal single- and double degenerate conductance steps, which highlight the rotational hexagonal symmetry and reproduce the experimental traces in the diffusive 1D transport limit. Modelling under the realistic back-gate configuration further evidences regimes that lead to asymmetric carrier distribution and breakdown of the degeneracy depending on the gate bias.

##### The Strong Scott Conjecture: the Density of Heavy Atoms Close to the Nucleus

H. Siedentop

in Book: Spectral Theory and Mathematical Physics 257-272 (2020).

We review what is known about the atomic density close to the nucleus of heavy atoms.

##### Transverse instability and universal decay of spin spiral order in the Heisenberg model

J. F. Rodriguez-Nieva, A. Schuckert, D. Sels, M. Knap, E. Demler

We analyze the stability of spin spiral states in the two-dimensional Heisenberg model. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse deformations---both in real and spin space---of the spiral order. The instability is universal in the sense that it applies to systems with any spin number, spiral wavevector, and spiral amplitude. Unlike the Landau or modulational instabilities which require impurities or periodic potential modulation of an optical lattice, quantum fluctuations alone are sufficient to trigger the transverse instability. We analytically find the most unstable mode and its growth rate, and compare our analysis with phase space methods. By adding an easy plane exchange coupling that reduces the Hamiltonian symmetry from SU(2) to U(1), the stability boundary is shown to continuously interpolate between the modulational instability and the transverse instability. This suggests that the transverse instability is an important mechanism that hinders the formation of a spin superfluid, even in the presence of strong exchange anisotropy.

##### Entanglement order parameters and critical behavior for topological phase transitions and beyond

M. Iqbal, N. Schuch

Topological phases are exotic quantum phases which are lacking the characterization in terms of order parameters. In this paper, we develop a unified framework based on variational iPEPS for the quantitative study of both topological and conventional phase transitions through entanglement order parameters. To this end, we employ tensor networks with suitable physical and/or entanglement symmetries encoded, and allow for order parameters detecting the behavior of any of those symmetries, both physical and entanglement ones. First, this gives rise to entanglement-based order parameters for topological phases. These topological order parameters allow to quantitatively probe topological phase transitions and to identify their universal behavior. We apply our framework to the study of the Toric Code model in different magnetic fields, which in some cases maps to the (2+1)D Ising model. We identify 3D Ising critical exponents for the entire transition, consistent with those special cases and general belief. However, we moreover find an unknown critical exponent beta=0.021. We then apply our framework of entanglement order parameters to conventional phase transitions. We construct a novel type of disorder operator (or disorder parameter), which is non-zero in the disordered phase and measures the response of the wavefunction to a symmetry twist in the entanglement. We numerically evaluate this disorder operator for the (2+1)D transverse field Ising model, where we again recover a critical exponent hitherto unknown in the model, beta=0.024, consistent with the findings for the Toric Code. This shows that entanglement order parameters can provide additional means of characterizing the universal data both at topological and conventional phase transitions, and altogether demonstrates the power of this framework to identify the universal data underlying the transition.

##### On contraction coefficients, partial orders and approximation of capacities for quantum channels

Christoph Hirche, Cambyse Rouzé, Daniel Stilck França

(2020).

The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel. It is the centerpiece of many results in information theory and justifies the operational interpretation of most entropic quantities. In this work, we revisit the notion of contraction coefficients of quantum channels, which provide sharper and specialized versions of the data processing inequality. A concept closely related to data processing are partial orders on quantum channels. We discuss several quantum extensions of the well known less noisy ordering and then relate them to contraction coefficients. We further define approximate versions of the partial orders and show how they can give strengthened and conceptually simple proofs of several results on approximating capacities. Moreover, we investigate the relation to other partial orders in the literature and their properties, particularly with regards to tensorization. We then investigate further properties of contraction coefficients and their relation to other properties of quantum channels, such as hypercontractivity. Next, we extend the framework of contraction coefficients to general f-divergences and prove several structural results. Finally, we consider two important classes of quantum channels, namely Weyl-covariant and bosonic Gaussian channels. For those, we determine new contraction coefficients and relations for various partial orders.

##### Efficient Reduced-Scaling Second-Order Moller-Plesset Perturbation Theory with Cholesky-Decomposed Densities and an Attenuated Coulomb Metric

M. Glasbrenner, D. Graf, C. Ochsenfeld

Journal of Chemical Theory and Computation 16 (11), 6856-6868 (2020).

We present a novel, highly efficient method for the computation of second-order Moller-Plesset perturbation theory (MP2) correlation energies, which uses the resolution of the identity (RI) approximation and local molecular orbitals obtained from a Cholesky decomposition of pseudodensity matrices (CDD), as in the RI-CDD-MP2 method developed previously in our group [Maurer, S. A.; Clin, L.; Ochsenfeld, C. J. Chem. Phys. 2014, 140, 224112]. In addition, we introduce an attenuated Coulomb metric and subsequently redesign the RI-CDD-MP2 method in order to exploit the resulting sparsity in the three-center integrals. Coulomb and exchange energy contributions are computed separately using specialized algorithms. A simple, yet effective integral screening protocol based on Schwarz estimates is used for the MP2 exchange energy. The Coulomb energy computation and the preceding transformations of the three-center integrals are accelerated using a modified version of the natural blocking approach [Jung, Y.; Head-Gordon, M. Phys. Chem. Chem. Phys. 2006, 8, 2831-2840]. Effective subquadratic scaling for a wide range of molecule sizes is demonstrated in test calculations in conjunction with a low prefactor. The method is shown to enable cost-efficient MP2 calculations on large molecular systems with several thousand basis functions.

##### Enhanced noise resilience of the surface–Gottesman-Kitaev-Preskill code via designed bias

L. Hänggli, M. Heinze, R. König

Physical Review A 102, 52408 (2020).

We study the code obtained by concatenating the standard single-mode Gottesman-Kitaev-Preskill (GKP) code with the surface code. We show that the noise tolerance of this surface–GKP code with respect to (Gaussian) displacement errors improves when a single-mode squeezing unitary is applied to each mode, assuming that the identification of quadratures with logical Pauli operators is suitably modified. We observe noise-tolerance thresholds of up to σ≈0.58 shift-error standard deviation when the surface code is decoded without using GKP syndrome information. In contrast, prior results by K. Fukui, A. Tomita, A. Okamoto, and K. Fujii, High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction, Phys. Rev. X 8, 021054 (2018) and C. Vuillot, H. Asasi, Y. Wang, L. P. Pryadko, and B. M. Terhal, Quantum error correction with the toric Gottesman-Kitaev-Preskill code, Phys. Rev. A 99, 032344 (2019) report a threshold between σ≈0.54 and σ≈0.55 for the standard (toric, respectively) surface–GKP code. The modified surface–GKP code effectively renders the mode-level physical noise asymmetric, biasing the logical-level noise on the GKP qubits. The code can thus benefit from the resilience of the surface code against biased noise. We use the approximate maximum likelihood decoding algorithm of S. Bravyi, M. Suchara, and A. Vargo, Efficient algorithms for maximum likelihood decoding in the surface code, Phys. Rev. A 90, 032326 (2014) to obtain our threshold estimates. Throughout, we consider an idealized scenario where measurements are noiseless and GKP states are ideal. Our paper demonstrates that Gaussian encodings of individual modes can enhance concatenated codes.

##### Coherent and Purcell-Enhanced Emission from Erbium Dopants in a Cryogenic High-Q Resonator

Benjamin Merkel, Alexander Ulanowski, and Andreas Reiserer

Physical Review X 10, 041025 (2020).

The stability and outstanding coherence of dopants and other atomlike defects in tailored host crystals make them a leading platform for the implementation of distributed quantum information processing and sensing in quantum networks. Albeit the required efficient light-matter coupling can be achieved via the integration into nanoscale resonators, in this approach the proximity of interfaces is detrimental to the coherence of even the least-sensitive emitters. Here, we establish an alternative: By integrating a 19 μm thin crystal into a cryogenic Fabry-Perot resonator with a quality factor of 9×106, we achieve a two-level Purcell factor of 530(50). In our specific system, erbium-doped yttrium orthosilicate, this leads to a 59(6)-fold enhancement of the emission rate with an out-coupling efficiency of 46(8)%. At the same time, we demonstrate that the emitter properties are not degraded in our approach. We thus observe ensemble-averaged optical coherence up to 0.54(1) ms, which exceeds the 0.19(2) ms lifetime of dopants at the cavity field maximum. While our approach is also applicable to other solid-state quantum emitters, such as color centers in diamond, our system emits at the minimal-loss wavelength of optical fibers and thus enables coherent and efficient nodes for long-distance quantum networks.

##### Robust control of an ensemble of springs: Application to ion cyclotron resonance and two-level quantum systems

V. Martikyan, A. Devra, D. Guery-Odelin, S.J. Glaser, D. Sugny

Physical Review A 102 (5), 053104 (2020).

We study the simultaneous control of an ensemble of springs with different frequencies by means of an adiabatic shortcut to adiabaticity and optimal processes. The linearity of the system allows us to derive analytical expressions for the control fields and the time evolution of the dynamics. We discuss the relative advantages of the different solutions. These results are applied in two different examples. For ion cyclotron resonance, we show how to optimally control ions by means of electric field. Using a mapping between spins and springs, we derive analytical shortcut protocols to realize robust and selective excitations of two-level quantum systems.

##### Quantitative comparison of magnon transport experiments in three-terminal YIG/Pt nanostructures acquired via dc and ac detection techniques

J. Gueckelhorn, T. Wimmer, S. Gepraegs, H. Huebl, R. Gross, M. Althammer

Applied Physics Letters 117 (18), 182401 (2020).

All-electrical generation and detection of pure spin currents are promising ways toward controlling the diffusive magnon transport in magnetically ordered insulators. We quantitatively compare two measurement schemes, which allow us to measure the magnon spin transport in a three-terminal device based on a yttrium iron garnet thin film. We demonstrate that the dc charge current method based on the current reversal technique and the ac charge current method utilizing first and second harmonic lock-in detection can both efficiently distinguish between electrically and thermally injected magnons. In addition, both measurement schemes allow us to investigate the modulation of magnon transport induced by an additional dc charge current applied to the center modulator strip. However, while at a low modulator charge current both schemes yield identical results, we find clear differences above a certain threshold current. This difference originates from nonlinear effects of the modulator current on the magnon conductance.

##### Quantum Cellular Automata, Tensor Networks, and Area Laws

L. Piroli, J.I. Cirac

Physical Review Letters 125 (19), 190402 (2020).

Quantum cellular automata are unitary maps that preserve locality and respect causality. We identify them, in any dimension, with simple tensor networks (projected entangled pair unitary) whose bond dimension does not grow with the system size. As a result, they satisfy an area law for the entanglement entropy they can create. We define other classes of nonunitary maps, the so-called quantum channels, that either respect causality or preserve locality. We show that, whereas the latter obey an area law for the number of quantum correlations they can create, as measured by the quantum mutual information, the former may violate it. We also show that neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size.

##### Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting

D.X. Nguyen, A. Gromov, S. Moroz

Scipost Physics 9 (5), 076 (2020).

Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex supersolid phase.

##### Variational Approach for Many-Body Systems at Finite Temperature

T. Shi, E. Demler, J.I. Cirac

Physical Review Letters 125 (18), 180602 (2020).

We introduce an equation for density matrices that ensures a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal. We build a variational approach for many-body systems that can be applied to a broad class of states, including all bosonic and fermionic Gaussian, as well as their generalizations obtained by unitary transformations, such as polaron transformations in electron-phonon systems. We apply it to the Holstein model on 20 x 20 and 50 x 50 square lattices, and predict phase separation between the superconducting and charge-density wave phases in the strong interaction regime.

##### Observation of a Smooth Polaron-Molecule Transition in a Degenerate Fermi Gas

G. Ness, C. Shkedrov, Y. Florshaim, O.K. Diessel, J. von Milczewski, R. Schmidt, Y. Sagi

Physical Review X 10, 041019 (2020).

Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoretically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact parameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition. Our findings establish Raman spectroscopy as a powerful experimental tool for probing the physics of mobile quantum impurities and shed new light on the competition between emerging fermionic and bosonic quasiparticles in non-Fermi-liquid phases.

##### Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states

J. Bender, P. Emonts, E. Zohar, J.I. Cirac

Physical Review Research 2 (4), 043145 (2020).

We introduce a class of variational states to study ground-state properties and real-time dynamics in (2+1)-dimensional compact QED. These are based on complex Gaussian states which are made periodic to account for the compact nature of the U(1) gauge field. Since the evaluation of expectation values involves infinite sums, we present an approximation scheme for the whole variational manifold. We calculate the ground-state energy density for lattice sizes up to 20×20 and extrapolate to the thermodynamic limit for the whole coupling region. Additionally, we study the string tension both by fitting the potential between two static charges and by fitting the exponential decay of spatial Wilson loops. As the ansatz does not require a truncation in the local Hilbert spaces, we analyze truncation effects which are present in other approaches. The variational states are benchmarked against exact solutions known for the one plaquette case and exact diagonalization results for a Z3 lattice gauge theory. Using the time-dependent variational principle, we study real-time dynamics after various global quenches, e.g., the time evolution of a strongly confined electric field between two charges after a quench to the weak-coupling regime. Up to the points where finite-size effects start to play a role, we observe equilibrating behavior.

##### Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains

Sebastian Scherg, Thomas Kohlert, Pablo Sala, Frank Pollmann, H. M. Bharath, Immanuel Bloch, Monika Aidelsburger

(2020).

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

##### Origin of Antibunching in Resonance Fluorescence

L. Hanschke, L. Schweickert, J.C.L. Carreno, E. Scholl, K.D. Zeuner, T. Lettner, E.Z. Casalengua, M. Reindl, S.F.C. da Silva, R. Trotta, J.J. Finley, A. Rastelli, E. del Valle, F.P. Laussy, V. Zwiller, K. Muller, K.D. Jons

Physical Review Letters 125 (17), 170402 (2020).

Resonance fluorescence has played a major role in quantum optics with predictions and later experimental confirmation of nonclassical features of its emitted light such as antibunching or squeezing. In the Rayleigh regime where most of the light originates from the scattering of photons with subnatural linewidth, antibunching would appear to coexist with sharp spectral lines. Here, we demonstrate that this simultaneous observation of subnatural linewidth and antibunching is not possible with simple resonant excitation. Using an epitaxial quantum dot for the two-level system, we independently confirm the single-photon character and subnatural linewidth by demonstrating antibunching in a Hanbury Brown and Twiss type setup and using high-resolution spectroscopy, respectively. However, when filtering the coherently scattered photons with filter bandwidths on the order of the homogeneous linewidth of the excited state of the two-level system, the antibunching dip vanishes in the correlation measurement. Our observation is explained by antibunching originating from photon-interferences between the coherent scattering and a weak incoherent signal in a skewed squeezed state. This prefigures schemes to achieve simultaneous subnatural linewidth and antibunched emission.

##### A statistical theory of heavy atoms: energy and excess charge

H. Chen, R.L. Frank, H. Siedentop

The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizsäcker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.

##### Entanglement-Enabled Communication

J. Nötzel

International Conference on Computer, Information and Telecommunication Systems (CITS) 1-6 (2020).

We introduce and analyse a multiple-access channel with two senders and one receiver, in the presence of i.i.d. noise coming from the environment. Partial side information about the environmental states allows the senders to modulate their signals accordingly. An adversarial jammer with its own access to information on environmental states and the modulation signals can jam a fraction of the transmissions. Our results show that for many choices of the system parameters, entanglement shared between the two senders allows them to communicate at non-zero rates with the receiver, while for the same parameters the system forbids any communication without entanglement-assistance, even if the senders have access to common randomness (local correlations).

##### Entanglement-Enabled Communication for the Internet of Things

J. Nötzel, S. DiAdamo

International Conference on Computer, Information and Telecommunication Systems (CITS) 1-6 (2020).

We consider an N-user multiple-access channel (MAC) with a varying channel state. The senders receive partial state information, but cannot communicate amongst reach other. This particular channels rate region vanishes asymptotically with a growing number of users in the sense of an exponential bound on the sum rate. However, when pre-established quantum entanglement is shared between the senders, the sum rate stays at a constant positive number. Thus a beneficial impact of entanglement-modulated coding for multi-access scenarios where many senders attempt to reach one receiver is demonstrated, a scenario with an increased likelihood in the internet of things.

##### Local probes for charge-neutral edge states in two-dimensional quantum magnets

J. Feldmeier, W. Natori, M. Knap, J. Knolle

Physical Review B 102 (13), 134423 (2020).

The bulk-boundary correspondence is a defining feature of topological states of matter. However, for quantum magnets in two dimensions such as spin liquids or topological magnon insulators, a direct observation of topological surface states has proven challenging because of the charge-neutral character of the excitations. Here we propose spin-polarized scanning tunneling microscopy as a spin-sensitive local probe to provide direct information about charge-neutral topological edge states. We show how their signatures, imprinted in the local structure factor, can be extracted by specifically employing the strengths of existing technologies. As our main example, we determine the dynamical spin correlations of the Kitaev honeycomb model with open boundaries. We show that by contrasting conductance measurements of bulk and edge locations, one can extract direct signatures of the existence of fractionalized excitations and nontrivial topology. The broad applicability of this approach is corroborated by a second example of a kagome topological magnon insulator.

##### Quantum simulation of two-dimensional quantum chemistry in optical lattices

J. Argüello-Luengo, A. González-Tudela, T. Shi, P. Zoller, J.I. Cirac

Physical Review Research 2 (4), 042013 (R) (2020).

Benchmarking numerical methods in quantum chemistry is one of the key opportunities that quantum simulators can offer. Here, we propose an analog simulator for discrete two-dimensional quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, such as the discrete versions of H and H+2, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular hydrogen in two dimensions. We extend this approach to larger systems by introducing as many mediating atoms as fermions, and derive the effective repulsion law. In all cases, we analyze how the continuous limit is approached for increasing optical lattice sizes.

##### Disorder-free localization in a simple U (1) lattice gauge theory

I. Papaefstathiou, A. Smith, J. Knolle

Physical Review B 102 (16), 165132 (2020).

Localization due to the presence of disorder has proven crucial for our current understanding of relaxation in isolated quantum systems. The many-body localized phase constitutes a robust alternative to the thermalization of complex interacting systems, but recently the importance of disorder has been brought into question. A number of disorder-free localization mechanisms have been put forward connected to local symmetries of lattice gauge theories. Here, starting from translationally invariant (1 + 1)-dimensional quantum electrodynamics, we modify the dynamics of the gauge field which allows us to construct a lattice model with a U(1) local gauge symmetry revealing a mechanism of disorder-free localization. We consider two different discretizations of the continuum model resulting in a free-fermion soluble model in one case and an interacting model in the other. We diagnose the localization of our translationally invariant model in the far-from-equilibrium dynamics following a global quantum quench.

##### A network-ready random-access qubits memory

S. Langenfeld, O. Morin, M. Körber, G. Rempe

NPJ Quantum Information 6, 86 (2020).

Photonic qubits memories are essential ingredients of numerous quantum networking protocols. The ideal situation features quantum computing nodes that are efficiently connected to quantum communication channels via quantum interfaces. The nodes contain a set of long-lived matter qubits, the channels support the propagation of light qubits, and the interface couples light and matter qubits. Toward this vision, we here demonstrate a random-access multi-qubit write-read memory for photons using two rubidium atoms coupled to the same mode of an optical cavity, a setup that is known to feature quantum computing capabilities. We test the memory with more than ten independent photonic qubits, observe no noticeable cross-talk, and find no need for re-initialization even after ten write-read attempts. The combined write-read efficiency is 26% and the coherence time approaches 1 ms. With these features, the node constitutes a promising building block for a quantum repeater and ultimately a quantum internet.

##### A non-linear adiabatic theorem for the one-dimensional Landau-Pekar equations

R.L. Frank, Z. Gang

Journal of Functional Analysis 279 (7), 108631 (2020).

We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schrodinger equation with time-dependent potential are a key technical ingredient in our proof. (C) 2020 Elsevier Inc. All rights reserved.

##### Sr2MoO4 and Sr2RuO4: Disentangling the Roles of Hund's and van Hove Physics

J. Karp, M. Bramberger, M. Grundner, U. Schollwoeck, A.J. Millis, M. Zingl

Physical Review Letters 125 (16), 166401 (2020).

Sr2MoO4 is isostructural to the unconventional superconductor Sr2RuO4 but with two electrons instead of two holes in the Mo/Ru-t(2g) orbitals. Both materials are Hund's metals, but while Sr2RuO4 has a van Hove singularity in close proximity to the Fermi surface, the van Hove singularity of Sr2MoO4 is far from the Fermi surface. By using density functional plus dynamical mean-field theory, we determine the relative influence of van Hove and Hund's metal physics on the correlation properties. We show that theoretically predicted signatures of Hund's metal physics occur on the occupied side of the electronic spectrum of Sr2MoO4, identifying Sr2MoO4 as an ideal candidate system for a direct experimental confirmation of the theoretical concept of Hund's metals via photoemission spectroscopy.

##### Valley-selective energy transfer between quantum dots in atomically thin semiconductors

A.S. Baimuratov, A. Hoegele

Scientific Reports 10 (1), 16971 (2020).

In monolayers of transition metal dichalcogenides the nonlocal nature of the effective dielectric screening leads to large binding energies of excitons. Additional lateral confinement gives rise to exciton localization in quantum dots. By assuming parabolic confinement for both the electron and the hole, we derive model wave functions for the relative and the center-of-mass motions of electronhole pairs, and investigate theoretically resonant energy transfer among excitons localized in two neighboring quantum dots. We quantify the probability of energy transfer for a direct- gap transition by assuming that the interaction between two quantum dots is described by a Coulomb potential, which allows us to include all relevant multipole terms of the interaction. We demonstrate the structural control of the valley-selective energy transfer between quantum dots.

##### Stability of the Enhanced Area Law of the Entanglement Entropy

P. Müller, R. Schulte

Ann. H. Poincaré 21, 3639 – 3658 (2020).

We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper bound and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

##### Unitarity Entropy Bound: Solitons and Instantons

G. Dvali

Fortsch. Phys. 69, 2000091 (2020).

We show that non-perturbative entities such as solitons and instantons saturate bounds on entropy when the theory saturates unitarity. Simultaneously, the entropy becomes equal to the area of the soliton/instanton. This is strikingly similar to black hole entropy despite absence of gravity. We explain why this similarity is not an accident. We present a formulation that allows to apply the entropy bound to instantons. The new formulation also eliminates apparent violations of the Bekenstein entropy bound by some otherwise-consistent unitary systems. We observe that in QCD, an isolated instanton of fixed size and position violates the entropy bound for strong 't Hooft coupling. At critical 't Hooft coupling the instanton entropy is equal to its area.

##### Geometry of variational methods: dynamics of closed quantum systems

L. Hackl, T. Guaita, T. Shi, J. Haegeman, E. Demler, J.I. Cirac

SciPost Physics 9, 048 (2020).

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: K\"ahler and non-K\"ahler. Traditional variational methods typically require the variational family to be a K\"ahler manifold, where multiplication by the imaginary unit preserves the tangent spaces. This covers the vast majority of cases studied in the literature. However, recently proposed classes of generalized Gaussian states make it necessary to also include the non-K\"ahler case, which has already been encountered occasionally. We illustrate our approach in detail with a range of concrete examples where the geometric structures of the considered manifolds are particularly relevant. These go from Gaussian states and group theoretic coherent states to generalized Gaussian states.

##### Communication under Channel Uncertainty: An Algorithmic Perspective and Effective Construction

H. Boche, R.F. Schaefer, H.V. Poor.

IEEE Transactions on Signal Processing 68, 6224 - 6239 (2020).

The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes have been well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is less understood and closed-form characterizations of optimal schemes remain unknown in many cases. This paper approaches this question from a fundamental, algorithmic point of view by studying whether or not such optimal schemes can be constructed algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the concepts of compound channels and averaged channels are considered as models for channel uncertainty and block fading and it is shown that, although the compound channel and averaged channel themselves are computable channels, the corresponding capacities are not computable in general, i.e., there exists no algorithm (or Turing machine) that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal (i.e., capacity-achieving) signal processing and coding schemes possible. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed. Thus, there is a crucial difference between the existence of optimal schemes and their algorithmic constructability. In addition, it is shown that there is no search algorithm that can find the maximal number of messages that can be reliably transmitted for a fixed blocklength. Finally, the case of partial channel knowledge is studied in which either the transmitter or the receiver have perfect channel knowledge while the other part remains uncertain. It is shown that also in the cases of an informed encoder and informed decoder, the capacity remains non-computable in general and, accordingly, optimal signal processing and coding schemes are not effectively constructible.

##### Communication under Channel Uncertainty: An Algorithmic Perspective and Effective Construction

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Transactions on Signal Processing 68, 6224 - 6239 (2020).

The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes have been well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is less understood and closed-form characterizations of optimal schemes remain unknown in many cases. This paper approaches this question from a fundamental, algorithmic point of view by studying whether or not such optimal schemes can be constructed algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the concepts of compound channels and averaged channels are considered as models for channel uncertainty and block fading and it is shown that, although the compound channel and averaged channel themselves are computable channels, the corresponding capacities are not computable in general, i.e., there exists no algorithm (or Turing machine) that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal (i.e., capacity-achieving) signal processing and coding schemes possible. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed. Thus, there is a crucial difference between the existence of optimal schemes and their algorithmic constructability. In addition, it is shown that there is no search algorithm that can find the maximal number of messages that can be reliably transmitted for a fixed blocklength. Finally, the case of partial channel knowledge is studied in which either the transmitter or the receiver have perfect channel knowledge while the other part remains uncertain. It is shown that also in the cases of an informed encoder and informed decoder, the capacity remains non-computable in general and, accordingly, optimal signal processing and coding schemes are not effectively constructible.

##### On the Alberti-Uhlmann Condition for Unital Channels

S. Chakraborty, D. Chruscinski, G. Sarbick, F. vom Ende

Quantum 4, (2020).

We address the problem of existence of completely positive trace preserving (CPTP) maps between two sets of density matrices. We refine the result of Alberti and Uhlmann and derive a necessary and sufficient condition for the existence of a unital channel between two pairs of qubit states which ultimately boils down to three simple inequalities.

##### Von Neumann Type Trace Inequalities for Schatten-Class Operators

G. Dirr, F. vom Ende

Journal of Operator Theory 84 (2), 323-338 (2020).

We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for Hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some recent results on the C-numerical range of Schatten-class operators. For the readers' convenience, we sketched the proof of these results in the Appendix.

##### Identification Capacity of Channels With Feedback: Discontinuity Behavior, Super-Activation, and Turing Computability

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Transactions on Informational Theory 66 (10), 6184-6199 (2020).

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not, and the identification-feedback (IDF) capacity of channels with feedback is studied. The IDF capacity is shown to be discontinuous and super-additive for both deterministic and randomized encoding. For the deterministic IDF capacity the phenomenon of super-activation occurs, which is the strongest form of super-additivity. This is the first time that super-activation is observed for discrete memoryless channels. On the other hand, for the randomized IDF capacity, super-activation is not possible. Finally, the developed theory is studied from an algorithmic point of view by using the framework of Turing computability. The problem of computing the IDF capacity on a Turing machine is connected to problems in pure mathematics and it is shown that if the IDF capacity would be Turing computable, it would provide solutions to other problems in mathematics including Goldbach's conjecture and the Riemann Hypothesis. However, it is shown that the deterministic and randomized IDF capacities are not Banach-Mazur computable. This is the weakest form of computability implying that the IDF capacity is not computable even for universal Turing machines. On the other hand, the identification capacity without feedback is Turing computable revealing the impact of the feedback: It transforms the identification capacity from being computable to non-computable.

##### Variational Monte Carlo simulation with tensor networks of a pure Z(3) gauge theory in (2+1)D

P. Emonts, M.C. Banuls, I. Cirac, E. Zohar

Physical Review D 102 (7), 074501 (2020).

Variational minimization of tensor network states enables the exploration of low energy states of lattice gauge theories. However, the exact numerical evaluation of high-dimensional tensor network states remains challenging in general. In [E. Zohar and J. I. Cirac, Phys. Rev. D 97, 034510 (2018)] it was shown how, by combining gauged Gaussian projected entangled pair states with a variational Monte Carlo procedure, it is possible to efficiently compute physical observables. In this paper we demonstrate how this approach can be used to investigate numerically the ground state of a lattice gauge theory. More concretely, we explicitly carry out the variational Monte Carlo procedure based on such contraction methods for a pure gauge KogutSusskind Hamiltonian with a Z(3) gauge field in two spatial dimensions. This is a first proof of principle to the method, which provides an inherent way to increase the number of variational parameters and can be readily extended to systems with physical fermions.

##### Realizing a deterministic source of multipartite-entangled photonic qubits

J.-C. Besse, K. Reuer, M. C. Collodo, A. Wulff, L. Wernli, A. Copetudo, D. Malz, P. Magnard, A. Akin, M. Gabureac, G. Norris, J.I. Cirac, A. Wallraff, C. Eichler

Nature Communications 11, 4877 (2020).

Sources of entangled electromagnetic radiation are a cornerstone in quantum information processing and offer unique opportunities for the study of quantum many-body physics in a controlled experimental setting. Generation of multi-mode entangled states of radiation with a large entanglement length, that is neither probabilistic nor restricted to generate specific types of states, remains challenging. Here, we demonstrate the fully deterministic generation of purely photonic entangled states such as the cluster, GHZ, and W state by sequentially emitting microwave photons from a controlled auxiliary system into a waveguide. We tomographically reconstruct the entire quantum many-body state for up to N = 4 photonic modes and infer the quantum state for even larger N from process tomography. We estimate that localizable entanglement persists over a distance of approximately ten photonic qubits.

##### Quasiparticle Lifetime of the Repulsive Fermi Polaron

H.S. Adlong, W.E. Liu, F. Scazza, M. Zaccanti, N.D. Oppong, S. Foelling, M.M. Parish, J. Levinsen

Physical Review Letters 125 (13), 133401 (2020).

We investigate the metastable repulsive branch of a mobile impurity coupled to a degenerate Fermi gas via short-range interactions. We show that the quasiparticle lifetime of this repulsive Fermi polaron can be experimentally probed by driving Rabi oscillations between weakly and strongly interacting impurity states. Using a time-dependent variational approach, we find that we can accurately model the impurity Rabi oscillations that were recently measured for repulsive Fermi polarons in both two and three dimensions. Crucially, our theoretical description does not include relaxation processes to the lower-lying attractive branch. Thus, the theory-experiment agreement demonstrates that the quasiparticle lifetime is dominated by many-body dephasing within the upper repulsive branch rather than by relaxation from the upper branch itself. Our findings shed light on recent experimental observations of persistent repulsive correlations, and have important consequences for the nature and stability of the strongly repulsive Fermi gas.

##### Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

S. Weichselbaumer, M. Zens, C.W. Zollitsch, M.S. Brandt, S. Rotter, R. Gross, H. Huebl.

Physical Review Letters 125, 137701 (2020).

We report on a novel dynamical phenomenon in electron spin resonance experiments of phosphorus donors. When strongly coupling the paramagnetic ensemble to a superconducting lumped element resonator, the coherent exchange between these two subsystems leads to a train of periodic, self-stimulated echoes after a conventional Hahn echo pulse sequence. The presence of these multiecho signatures is explained using a simple model based on spins rotating on the Bloch sphere, backed up by numerical calculations using the inhomogeneous Tavis-Cummings Hamiltonian.

##### Absence of μ-Problem in Grand Unification

G. Dvali, A. Jankowsky

Using properties of Goldstino, we show that in generic grand unified theories with gravity-mediated supersymmetry breaking the μ-problem is non-existent. What happens is that supersymmetry breaking universally induces the shifts of the heavy fields that generate μ and Bμ terms. In the leading order, these are given by the mass of gravitino and are insensitive to the scale of grand unification. The mechanism works regardless whether doublet-triplet splitting is achieved via fine-tuning or not. Moreover, we illustrate this general phenomenon on explicit examples of theories that achieve doublet-triplet splitting dynamically. These include the theories with Higgs doublet as a pseudo-Goldstone boson, as well as, the approach based on spontaneous decoupling of the light color-triplet from quarks and leptons.

##### Cross-polarisation ENDOR for spin-1 deuterium nuclei

I. Bejenke, R. Zeier, R. Rizzato, S.J. Glaser, M. Bennati

Molecular Physics 118 (18), e1763490 (2020).

Efficient transfer of spin polarisation from electron to nuclear spins is emerging as a common target of several advanced spectroscopic experiments, ranging from sensitivity enhancement in nuclear magnetic resonance (NMR) and methods for the detection of single molecules based on optically detected magnetic resonance (ODMR) to hyperfine spectroscopy. Here, we examine the feasibility of electron-nuclear cross-polarisation at a modified Hartmann-Hahn condition (called eNCP) for applications in ENDOR experiments with spin-1 deuterium nuclei, which are important targets in studies of hydrogen bonds in biological systems and materials. We have investigated a two-spin model system of deuterated malonic acid radicals in a single crystal. Energy matching conditions as well as ENDOR signal intensities were determined for a spin Hamiltonian under the effect of microwave and radiofrequency irradiation. The results were compared with numerical simulations and 94-GHz ENDOR experiments. The compelling agreement between theoretical predictions and experimental results demonstrates that spin density operator formalism in conjunction with suitable approximations in regard to spin relaxation provides a satisfactory description of the polarisation transfer effect. The results establish a basis for future numerical optimizations of polarisation transfer experiments using multiple-pulse sequences or shaped pulses and for moving from model systems to real applications in disordered systems.

##### One-particle density matrix of a trapped Lieb–Liniger anyonic gas

S. Scopa, L. Piroli, P. Calabrese

Journal of Statistical Mechanics: Theory and Experiment '093103 (2020).

We provide a thorough characterisation of the zero-temperature one-particle density matrix of trapped interacting anyonic gases in one dimension, exploiting recent advances in the field theory description of spatially inhomogeneous quantum systems. We first revisit homogeneous anyonic gases with point-wise interactions. In the harmonic Luttinger liquid expansion of the one-particle density matrix for finite interaction strength, the non-universal field amplitudes were not yet known. We extract them from the Bethe Ansatz formula for the field form factors, providing an exact asymptotic expansion of this correlation function, thus extending the available results in the Tonks–Girardeau limit. Next, we analyse trapped gases with non-trivial density profiles. By applying recent analytic and numerical techniques for inhomogeneous Luttinger liquids, we provide exact expansions for the one-particle density matrix. We present our results for different confining potentials, highlighting the main differences with respect to bosonic gases.

##### Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

S, Jandura, M. Iqbal, N. Schuch

Physical Review Research 2, 033382 (2020).

We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the resonating valence bond wave functions to a trimer and SU(3) setting. We demonstrate that these models carry a Z3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological ninefold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers—it can display either Z3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior. Our results accordingly hold for the SU(3) model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and SU(3)-singlet ansatzes to model SU(3) topological spin liquids on the kagome lattice.

##### Quantum trimer models and topological SU(3) spin liquids on the kagome lattice

T. Shi, J.I. Cirac, E. Demler

Physical Review Research 2 (3), 033379 (2020).

We construct and study quantum trimer models and resonating SU(3)-singlet models on the kagome lattice, which generalize quantum dimer models and the resonating valence bond wave functions to a trimer and SU(3) setting. We demonstrate that these models carry a Z3 symmetry which originates in the structure of trimers and the SU(3) representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological ninefold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers—it can display either Z3 topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced U(1) symmetry and critical behavior. Our results accordingly hold for the SU(3) model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and SU(3)-singlet ansatzes to model SU(3) topological spin liquids on the kagome lattice.

##### Purity speed limit of open quantum systems from magic subspaces

V.A.A. Diaz, V. Martikyan, S.J. Glaser, D. Sugny

Physical Review A 102 (3), 033104 (2020).

We introduce the concept of magic subspaces for the control of dissipative Nlevel quantum systems whose dynamics are governed by the Lindblad equation. For a given purity, these subspaces can be defined as the set of density matrices for which the rate of purity change is maximum or minimum. Adding fictitious control fields to the system so two density operators with the same purity can be connected in a very short time, we show that magic subspaces allow us to derive a purity speed limit, which only depends on the relaxation rates. We emphasize the superiority of this limit with respect to established bounds and its tightness in the case of a two-level dissipative quantum system. The link between the speed limit and the corresponding time-optimal solution is discussed in the framework of this study. Explicit examples are described for twoand three-level quantum systems.

##### Dark solitons revealed in Lieb-Liniger eigenstates

W. Golletz, W. Górecki, R. Ołdziejewski, K. Pawłowski

Physical Review Research 2 (3), 033368 (2020).

We study how dark solitons, i.e., solutions of one-dimensional, single-particle, nonlinear, time-dependent Schrödinger equation, emerge from eigenstates of a linear many-body model of contact-interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem has been addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the ansatz state. The postmeasurement state turns out to be a wave packet of yrast states of the reduced system.

##### Relativistic Scott conjecture: a short proof

R.L. Frank, K. Merz, H. Siedentop

We consider heavy neutral atoms of atomic number Z modeled with kinetic energy (c^2p^2+c^4)^1/2−c^2 used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale Z−1 in the limit Z,c→∞ keeping Z/c fixed. We give a short proof of a recent result by the authors and Barry Simon showing the convergence of the density to the relativistic hydrogenic density on this scale.

##### Efficient description of many-body systems with Matrix Product Density Operators

J.G. Jarkovský, A. Molnár, N. Schuch, J.I. Cirac

PRX Quantum 1, 010304 (2020).

Matrix product states form a powerful ansatz for the simulation of a wide range of one-dimensional quantum systems that are in a pure state. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the “area law.” However, in order to accurately capture the physics of realistic systems, one generally needs to apply a mixed-state description. In this work, we establish the mixed-state analog of this characterization. We show that one-dimensional mixed states with a low amount of entanglement, quantified by the entanglement of purification, can be efficiently approximated by matrix product density operators.

##### Determinant formula for the field form factor in the anyonic Lieb–Liniger model

L. Piroli, S. Scopa, P. Calabrese

Journal of Physics A 53, 405001 (2020).

We derive an exact formula for the field form factor in the anyonic Lieb–Liniger model, valid for arbitrary values of the interaction c, anyonic parameter κ, and number of particles N. Analogously to the bosonic case, the form factor is expressed in terms of the determinant of an N × N matrix, whose elements are rational functions of the Bethe quasimomenta but explicitly depend on κ. The formula is efficient to evaluate, and provide an essential ingredient for several numerical and analytical calculations. Its derivation consists of three steps. First, we show that the anyonic form factor is equal to the bosonic one between two special off-shell Bethe states, in the standard Lieb–Liniger model. Second, we characterize its analytic properties and provide a set of conditions that uniquely specify it. Finally, we show that our determinant formula satisfies these conditions.

##### Phase Diagram of the Quantum Random Energy Model

C. Manai, S. Warzel

Journal of Statistical Physics 180 (1-6), 654-664 (2020).

We prove Goldschmidt's formula (Goldschmidt in Phys Rev B 47:4858-4861, 1990) for the free energy of the quantum random energy model. In particular, we verify the location of the first order and the freezing transition in the phase diagram. The proof is based on a combination of variational methods on the one hand, and bounds on the size of percolation clusters of large-deviation configurations in combination with simple spectral bounds on the hypercube's adjacency matrix on the other hand.

##### Light-field and spin-orbit-driven currents in van der Waals materials

J. Kiemle, P. Zimmermann, A.W. Holleitner, C. Kastl

Nanophotonics 9 (9), 2693-2708 (2020).

This review aims to provide an overview over recent developments of light-driven currents with a focus on their application to layered van der Waals materials. In topological and spin-orbit dominated van der Waals materials helicity-driven and light-field-driven currents are relevant for nanophotonic applications from ultrafast detectors to onchip current generators. The photon helicity allows addressing chiral and non-trivial surface states in topological systems, but also the valley degree of freedom in two-dimensional van der Waals materials. The underlying spinorbit interactions break the spatiotemporal electrodynamic symmetries, such that directed currents can emerge after an ultrafast laser excitation. Equally, the light-field of few-cycle optical pulses can coherently drive the transport of charge carriers with sub-cycle precision by generating strong and directed electric fields on the atomic scale. Ultrafast light-driven currents may open up novel perspectives at the interface between photonics and ultrafast electronics.

##### Calculating the spectral factorization and outer functions by sampling-based approximations-Fundamental limitations

H. Boche, V. Pohl

Journal of Approximation Theory 257, 105450 (2020).

This paper considers the problem of approximating the spectral factor of continuous spectral densities with finite Dirichlet energy based on finitely many samples of these spectral densities. Although there exists a closed form expression for the spectral factor, this formula shows a very complicated behavior because of the non-linear dependency of the spectral factor from spectral density and because of a singular integral in this expression. Therefore approximation methods are usually applied to calculate the spectral factor.

It is shown that there exists no sampling-based method which depends continuously on the samples and which is able to approximate the spectral factor for all densities in this set. Instead, to any sampling-based approximation method there exists a large set of spectral densities so that the approximation method does not converge to the spectral factor for every spectral density in this set as the number of available sampling points is increased. The paper will also show that the same results hold for sampling-based algorithms for the calculation of the outer function in the theory of Hardy spaces. (C) 2020 Elsevier Inc. All rights reserved.

##### Resonant nanodiffraction x-ray imaging reveals role of magnetic domains in complex oxide spin caloritronics

P.G. Evans, S.D. Marks, S. Gepraegs, M. Dietlein, Y. Joly, M.Y. Dai, J.M. Hu, L. Bouchenoire, P.B.J. Thompson, T.U. Schulli, M.I. Richard, R. Gross, D. Carbone, D. Mannix

Science Advances 6 (40), eaba9351 (2020).

Spin electronic devices based on crystalline oxide layers with nanoscale thicknesses involve complex structural and magnetic phenomena, including magnetic domains and the coupling of the magnetism to elastic and plastic crystallographic distortion. The magnetism of buried nanoscale layers has a substantial impact on spincaloritronic devices incorporating garnets and other oxides exhibiting the spin Seebeck effect (SSE). Synchrotron hard x-ray nanobeam diffraction techniques combine structural, elemental, and magnetic sensitivity and allow the magnetic domain configuration and structural distortion to be probed in buried layers simultaneously. Resonant scattering at the Gd L-2 edge of Gd3Fe5O12 layers yields magnetic contrast with both linear and circular incident x-ray polarization. Domain patterns facet to form low-energy domain wall orientations but also are coupled to elastic features linked to epitaxial growth. Nanobeam magnetic diffraction images reveal diverse magnetic microstructure within emerging SSE materials and a strong coupling of the magnetism to crystallographic distortion.

##### Turing meets circuit theory: Not every continuous-time LTI system can be simulated on a digital computer

H. Boche, V. Pohl.

IEEE Transactions on Circuits and Systems I: Regular Papers 67, 5051 - 5064 (2020).

Solving continuous problems on digital computers gives generally only approximations of the continuous solutions. It is therefore crucial that the error between the continuous solution and the digital approximation can effectively be controlled. This paper investigates the possibility of simulating linear, time-invariant (LTI) systems on Turing machines. It is shown that there exist elementary LTI systems for which an admissible and computable input signal results in a non-computable output signal. For these LTI systems, the paper gives sharp characterizations of input spaces such that the output is guaranteed to be computable. The second part of the paper discusses the computability of the impulse and step response of LTI systems. It is shown that the computability of the step response implies not the computability of the impulse response. Moreover, there exist impulse responses which cannot be computed from the transfer function using the inverse Laplace transform. Finally, the paper gives a stronger version of a classical non-computability result, showing that there exist admissible and computable initial values for the wave equation so that the solution cannot be computed at certain points in space and time.

##### Subsystem symmetry enriched topological order in three dimensions

D.T. Stephen, J. Garre-Rubio, A. Dua, D.J. Williamson

Physical Review Research 2 (3), 033331 (2020).

We introduce a model of three-dimensional (3D) topological order enriched by planar subsystem symmetries. The model is constructed starting from the 3D toric code, whose ground state can be viewed as an equal-weight superposition of two-dimensional (2D) membrane coverings. We then decorate those membranes with 2D cluster states possessing symmetry-protected topological order under linelike subsystem symmetries. This endows the decorated model with planar subsystem symmetries under which the looplike excitations of the toric code fractionalize, resulting in an extensive degeneracy per unit length of the excitation. We also show that the value of the topological entanglement entropy is larger than that of the toric code for certain bipartitions due to the subsystem symmetry enrichment. Our model can be obtained by gauging the global symmetry of a short-range entangled model which has symmetry-protected topological order coming from an interplay of global and subsystem symmetries. We study the nontrivial action of the symmetries on boundary of this model, uncovering a mixed boundary anomaly between global and subsystem symmetries. To further study this interplay, we consider gauging several different subgroups of the total symmetry. The resulting network of models, which includes models with fracton topological order, showcases more of the possible types of subsystem symmetry enrichment that can occur in 3D.

##### Effect of interfacial oxidation layer in spin pumping experiments on Ni80Fe20/SrIrO3 heterostructures

T.S. Suraj, M. Mueller, S. Gelder, S. Gepraegs, M. Opel, M. Weiler, K. Sethupathi, H. Huebl, R. Gross, M.S.R. Rao, M. ALthammer

Journal of Applied Physics 128 (8), 083903 (2020).

SrIrO3 with its large spin-orbit coupling and low charge conductivity has emerged as a potential candidate for efficient spin-orbit torque magnetization control in spintronic devices. Here we report on the influence of an interfacial oxide layer on spin pumping experiments in Ni80Fe20 (NiFe)/SrIrO3 bilayer heterostructures. To investigate this scenario, we have carried out broadband ferromagnetic resonance (BBFMR) measurements, which indicate the presence of an interfacial antiferromagnetic oxide layer. We performed in-plane BBFMR experiments at cryogenic temperatures, which allowed us to simultaneously study dynamic spin pumping properties (Gilbert damping) and static magnetic properties (such as the effective magnetization and magnetic anisotropy). The results for NiFe/SrIrO3 bilayer thin films were analyzed and compared to those from a NiFe/NbN/SrIrO3 trilayer reference sample, where a spin-transparent, ultra-thin NbN layer was inserted to prevent the oxidation of NiFe. At low temperatures, we observe substantial differences in the magnetization dynamics parameters of these samples. In particular, the Gilbert damping in the NiFe/SrIrO3 bilayer sample drastically increases below 50 K, which can be well explained by enhanced spin fluctuations at the antiferromagnetic ordering temperature of the interfacial oxide layer. Our results emphasize that this interfacial oxide layer plays an important role for the spin current transport across the NiFe/SrIrO3 interface.

##### Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

- M.C. Banuls, K. Cichy, H.T. Hung, Y.J. Kao, D. Lin, Y.P. Lin, D.T.L. Tan

Proceedings of Science LATTICE2019, 22 (2020).

We present concluding results from our study for zero-temperature phase structure of the massive Thirring model in 1+1 dimensions with staggered regularisation. Employing the method of matrix product states, several quantities, including two types of correlators, are investigated, leading to numerical evidence of a Berezinskii-Kosterlitz-Thouless phase transition. Exploratory results for real-time dynamics pertaining to this transition, obtained using the approaches of variational uniform matrix product state and time-dependent variational principle, are also discussed.

##### Thermodynamics of two-dimensional bosons in the lowest Landau level

B. Jeevanesan, S. Moroz.

Physics Review Research 2, 33323 (2020).

We study the thermodynamics of short-range-interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.

##### From spin chains to real-time thermal field theory using tensor networks

M.C. Bañuls, M. P. Heller, K. Jansen, J. Knaute, and V. Svensson

Physical Review Research 2, 33301 (2020).

One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded equilibrium correlators governing the linear response theory. In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infrared descriptions of quantum Ising chains.We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of nonintegrable interacting quantum field theories.

##### Resolving Fermi surfaces with tensor networks

Q. Mortier, N. Schuch, F. Verstraete, J. Haegeman

We show that Projected Entangled-Pair States (PEPS) are able to describe critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2d lattice. In the thermodynamic limit, the energy precision as a function of the bond dimension improves as a power law, illustrating that an arbitrary precision can be obtained by increasing the bond dimension in a controlled manner. We also identify a non-trivial obstruction in the Gaussian and fermionic variant of PEPS, rooted in its topology and restricting its efficient applicability to models with a matching parity configuration.

##### Rotor Jackiw-Rebbi Model: A Cold-Atom Approach to Chiral Symmetry Restoration and Charge Confinement

Daniel González-Cuadra, Alexandre Dauphin, Monika Aidelsburger, Maciej Lewenstein, Alejandro Bermudez

PRX Quantum 1, 020321 (2020).

Understanding the nature of confinement, as well as its relation with the spontaneous breaking of chiral symmetry, remains one of the long-standing questions in high-energy physics. The difficulty of this task stems from the limitations of current analytical and numerical techniques to address nonperturbative phenomena in non-Abelian gauge theories. In this work, we show how similar phenomena emerge in simpler models, and how these can be further investigated using state-of-the-art cold-atom quantum simulators. More specifically, we introduce the rotor Jackiw-Rebbi model, a (1+1)-dimensional quantum field theory where interactions between Dirac fermions are mediated by quantum rotors. Starting from a mixture of ultracold atoms in an optical lattice, we show how this quantum field theory emerges in the long-wavelength limit. For a wide and experimentally relevant parameter regime, the Dirac fermions acquire a dynamical mass via the spontaneous breakdown of chiral symmetry. We study the effect of both quantum and thermal fluctuations, and show how they lead to the phenomenon of chiral symmetry restoration. Moreover, we uncover a confinement-deconfinement quantum phase transition, where mesonlike fermions fractionalize into quarklike quasiparticles bound to topological solitons of the rotor field. The proliferation of these solitons at finite chemical potentials again serves to restore the chiral symmetry, yielding a clear analogy with the quark-gluon plasma in quantum chromodynamics, where the restored symmetry coexists with the deconfined fractional charges. Our results indicate how the interplay between these phenomena could be analyzed in more detail in realistic atomic experiments.

##### On the excess charge of a relativistic statistical model of molecules with an inhomogeneity correction

H. Chen, H. Siedentop

Journal of Physics A 53, 395201 (2020).

We show that the molecular relativistic Thomas–Fermi–Weizsäcker functional consisting of atoms of atomic numbers Z1, ..., Zk has a minimizer, if the particle number N is constrained to a number less or equal to the total nuclear charge Z := Z1 + ⋯ + ZK. Moreover, there is no minimizer, if the particle number exceeds 2.56Z. This gives lower and upper bounds on the maximal ionization of heavy atoms.

##### Semantic Security for Quantum Wiretap Channels

H. Boche, M. Cai, M. Wiese, C. Deppe, R. Ferrara

IEEE International Symposium on Information Theory (ISIT) 19910465 (2020).

We determine the semantic security capacity for quantum wiretap channels. We extend methods for classical channels to quantum channels to demonstrate that a strongly secure code guarantees a semantically secure code with the same secrecy rate. Furthermore, we show how to transform a non-secure code into a semantically secure code by means of biregular irreducible functions (BRI functions). We analyze semantic security for classical-quantum channels and for quantum channels.

##### On the Algorithmic Computability of Achievability and Converse: ϵ-Capacity of Compound Channels and Asymptotic Bounds of Error-Correcting Codes

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Symposium on Information Theory (ISIT) 19897049 (2020).

A coding theorem consists of two parts: achievability and converse which establish lower and upper bounds on the capacity. This paper analyzes these bounds from a fundamental, algorithmic point of view by studying whether or not such bounds can be computed algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers. To this end, computable continuous functions are studied and properties of computable sequences of such functions are identified. Subsequently, these findings are exemplarily applied to two different open problems. The first one is the ε-capacity of compound channels which is unknown to date. It is studied whether or not the ε-capacity can be algorithmically computed and it is shown that there is no computable characterization of the difference between computable upper and lower bounds possible. Thus, computable sharp lower and upper bounds on the ε-capacity of computable compound channels cannot exist. The crucial consequence is that the ε-capacity cannot be characterized by a finite-letter entropic expression. The second application involves asymptotic bounds for error-correcting codes which is a long-standing open problem in coding theory. Only lower and upper bounds are known which are not sharp. It is conjectured that the asymptotic bound is indeed a non-computable function which would then imply with the previous findings that it is impossible to find computable lower and upper bounds that are asymptotically tight.

##### Computability of the Zero-Error capacity with Kolmogorov Oracle

H. Boche, C. Deppe

IEEE International Symposium on Information Theory (ISIT) 19910457 (2020).

The zero-error capacity of a discrete classical channel was first defined by Shannon as the least upper bound of rates for which one transmits information with zero probability of error. The problem of finding the zero-error capacity C 0 , which assigns a capacity to each channel as a function, was reformulated in terms of graph theory as a function Θ, which assigns a value to each simple graph. This paper studies the computability of the zero-error capacity. For the computability, the concept of a Turing machine and a Kolmogorov oracle is used. It is unknown if the zero-error capacity is computable in general. We show that in general the zero-error capacity is semi-computable with the help of a Kolmogorov Oracle. Furthermore, we show that C 0 and Θ are computable functions if and only if there is a computable sequence of computable functions of upper bounds, i.e. the converse exist in the sense of information theory, which point-wise converges to C 0 or Θ. Finally, we examine Zuiddam's characterization of C 0 and Θ in terms of algorithmic computability.

##### Computing the renormalization group flow of two-dimensional ϕ4 theory with tensor networks

C. Delcamp, A. Tilloy

Physical Review Research 2 (3), 033278 (2020).

We study the renormalization group flow of ϕ4 theory in two dimensions. Regularizing space into a fine-grained lattice and discretizing the scalar field in a controlled way, we rewrite the partition function of the theory as a tensor network. Combining local truncations and a standard coarse-graining scheme, we obtain the renormalization group flow of the theory as a map in a space of tensors. Aside from qualitative insights, we verify the scaling dimensions at criticality and extrapolate the critical coupling constant fc=λ/μ2 to the continuum to find fcontc=11.0861(90), which favorably compares with alternative methods.

##### Entanglement-Enabled Communication

J. Nötzel

IEEE Journal on Selected Areas in Information Theory 1, 401-415 (2020).

We introduce and analyse a multiple-access channel with two senders and one receiver, in the presence of i.i.d. noise coming from the environment. Partial side information about the environmental states allows the senders to modulate their signals accordingly. An adversarial jammer with its own access to information on environmental states and the modulation signals can jam a fraction of the transmissions. Our results show that for many choices of the system parameters, entanglement shared between the two senders allows them to communicate at non-zero rates with the receiver, while for the same parameters the system forbids any communication without entanglement-assistance, even if the senders have access to common randomness (local correlations). A simplified model displaying a similar behaviour but with a compound channel instead of a jammer is outlined to introduce basic aspects of the modeling. We complement these results by demonstrating that there even exist model parameters for which entanglement-assisted communication is no longer possible, but a hypothetical use of nonlocal no-signalling correlations between Alice and Bob could enable them to communicate to Charlie again.

##### Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders

L. Stenzel, A.L.C. Hayward, U. Schollwoeck, F. Heidrich-Meisner

Physical Review A 102 (2), 023315 (2020).

In recent experiments with ultracold atoms, both two-dimensional (2D) Chern insulators and one-dimensional topological charge pumps have been realized. Without interactions, both systems can be described by the same Hamiltonian, when some variables are being reinterpreted. In this paper, we study the relation of both models when Hubbard interactions are added, using the density-matrix renormalization-group algorithm. To this end, we express the fermionic Hofstadter model in a hybrid-space representation, and define a family of interactions, which connects 1D Hubbard charge pumps to 2D Hubbard Chern insulators. We study a three-band model at particle density rho = 2/3, where the topological quantization of the 1D charge pump changes from Chern number C = 2 to C = -1 as the interaction strength increases. We find that the C = -1 phase is robust when varying the interaction terms on narrow-width cylinders. However, this phase does not extend to the limit of the 2D Hofstadter-Hubbard model, which remains in the C = 2 phase. We discuss the existence of both topological phases for the largest cylinder circumferences that we can access numerically. We note the appearance of a ferromagnetic ground state between the strongly interacting 1D and 2D models. For this ferromagnetic state, one can understand the C = -1 phase from a band structure argument. Our method for measuring the Hall conductivity could similarly be realized in experiments: We compute the current response to a weak, linear potential, which is applied adiabatically. The Hall conductivity converges to integer-quantized values for large system sizes, corresponding to the system's Chern number.

##### Atomistic defects as single-photon emitters in atomically thin MoS2

K. Barthelmi, J. Klein, A. Hoetger, L. Sigl, F. Sigger, E. Mitterreiter, S. Rey, S. Gyger, M. Lorke, M. Florian, F. Jahnke, T: Taniguchi, K. Watanabe, V. Zwiller, K.D. Jons, U. Wurstbauer, C. Kastl, A. Weber-Bargioni, J.J. Finley, K. Mueller, A.W. Holleitner

Applied Physics Letters 117 (7), 070501 (2020).

Precisely positioned and scalable single-photon emitters (SPEs) are highly desirable for applications in quantum technology. This Perspective discusses single-photon-emitting atomistic defects in monolayers of MoS2 that can be generated by focused He-ion irradiation with few nanometers positioning accuracy. We present the optical properties of the emitters and the possibilities to implement them into photonic and optoelectronic devices. We showcase the advantages of the presented emitters with respect to atomistic positioning, scalability, long (microsecond) lifetime, and a homogeneous emission energy within ensembles of the emitters. Moreover, we demonstrate that the emitters are stable in energy on a timescale exceeding several weeks and that temperature cycling narrows the ensembles' emission energy distribution.

##### Experimental probes of Stark many-body localization

S.R. Taylor, M. Schulz, F. Pollmann, R. Moessner

Physical Review B 102 (5), 054206 (2020).

Recent work has focused on exploring many-body localization (MBL) in systems without quenched disorder: one such proposal is Stark MBL in which small perturbations to a strong linear potential yield localization. However, as with conventional MBL, it is challenging to experimentally distinguish between noninteracting localization and true MBL. In this paper, we show that several existing experimental probes, designed specifically to differentiate between these scenarios, work similarly in the Stark MBL setting. In particular, we show that a modified spin-echo response shows clear signs of a power-law decay for Stark MBL while quickly saturating for disorder-free Wannier-Stark localization. Furthermore, we observe the characteristic logarithmic-in-time spreading of quantum mutual information in the Stark MBL regime, and an absence of spreading in a noninteracting Stark-localized system. We also show that there are no significant differences in several existing MBL measures for a system consisting of soft-core bosons with repulsive on-site interactions. Lastly, we discuss why curvature or small disorder are needed for an accurate reproduction of MBL phenomenology and how this may be illustrated in experiment. This also connects with recent progress on Hilbert space fragmentation in "fractonic" models with a conserved dipole moment, and we suggest this as an auspicious platform for experimental investigations of these phenomena.

##### Skyrmion Ground States of Rapidly Rotating Few-Fermion Systems

L. Palm, F. Grusdt, P. M. Preiss

New Journal of Physics 22, 83037 (2020).

We show that ultracold fermions in an artificial magnetic field open up a new window to the physics of the spinful fractional quantum Hall (FQH) effect. We numerically study the lowest energy states of strongly interacting few-fermion systems in rapidly rotating optical microtraps. We find that skyrmion-like ground states with locally ferromagnetic, long-range spin textures emerge. To realize such states experimentally, rotating microtraps with higher-order angular momentum components may be used to prepare fermionic particles in a lowest Landau level. We find parameter regimes in which skyrmion-like ground states should be accessible in current experiments and demonstrate an adiabatic pathway for their preparation in a rapidly rotating harmonic trap. The addition of long range interactions will lead to an even richer interplay between spin textures and FQH physics.

##### Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

H. Dreyer, L. Vanderstraeten, J.Y. Chen, R. Verresen, N. Schuch

We study the response of critical Resonating Valence Bond (RVB) spin liquids to doping with longer-range singlets, and more generally of U(1)-symmetric tensor networks to non-symmetric perturbations. Using a field theory description, we find that in the RVB, doping constitutes a relevant perturbation which immediately opens up a gap, contrary to previous observations. Our analysis predicts a very large correlation length even at significant doping, which we verify using high-accuracy numerical simulations. This emphasizes the need for careful analysis, but also justifies the use of such states as a variational ansatz for critical systems. Finally, we give an example of a PEPS where non-symmetric perturbations do not open up a gap and the U(1) symmetry re-emerges.

##### Scrambling in random unitary circuits: Exact results

- B. Bertini, L. Piroli

Physical Review B 102 (6), 064305 (2020).

We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged Rényi-2 tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a “maximally chaotic” subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, rederiving known formulas for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.

##### Arbitrarily Varying Wiretap Channels with and without Non-Causal Side Information at the Jammer

C.R. Janda, E.A. Jorswieck, M. Wiese, H. Boche

IEEE Conference on Communications and Network Security (CNS) 19876201 (2020).

We investigate the Arbitrarily Varying Wiretap Channel (AVWC) with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that codewords are known at an active adversary before they are transmitted. By considering the maximum error criterion, we allow also messages to be known at the jammer before the corresponding codeword is transmitted. A multi letter formula for the common randomness secrecy capacity is derived. Furthermore, we compare our results to the random code secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer, maximum error criterion with non-causal side information of the messages at the jammer, and the case of average error criterion without non-causal side information at the jammer.

##### Entanglement dynamics of a many-body localized system coupled to a bath

E. Wybo, M. Knap, F. Pollmann

Physical Review B 102 (6), 064303 (2020).

The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However, this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third Renyi negativity R-3, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of R-3 follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.

##### Can surface-transfer doping and UV irradiation during annealing improve shallow implanted nitrogen-vacancy centers in diamond?

N. J. Glaser, G. Braunbeck, O. Bienek, I. D. Sharp, F. Reinhard

Applied Physics Letters 117, 54003 (2020).

It has been reported that the conversion yield and coherence time of ion-implanted NV centers improve if the Fermi level is raised or lowered during the annealing step following implantation. Here, we investigate whether surface transfer doping and surface charging, by UV light, can be harnessed to induce this effect. We analyze the coherence times and the yield of NV centers created by ion implantation and annealing, applying various conditions during annealing. Specifically, we study coating diamond with nickel, palladium, or aluminum oxide, to induce positive surface transfer doping, as well as annealing under UV illumination to trigger vacancy charging. The metal-coated diamonds display a two times higher formation yield than the other samples. The coherence time T2 varies by less than a factor of two between the investigated samples. Both effects are weaker than previous reports, suggesting that stronger modifications of the band structure are necessary to find a pronounced effect. UV irradiation has no effect on the yield and T2 times.

##### Dynamics of a Two-Dimensional Quantum Spin-Orbital Liquid: Spectroscopic Signatures of Fermionic Magnons

W.M.H. Natori, J. Knolle

Physical Review Letters 125 (6), 067201 (2020).

We provide an exact study of dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. We show that the spin dynamics in this Kugel-Khomskii type model is exactly the density-density correlation function of S = 1 fermionic magnons, which could be probed in resonant inelastic x-ray scattering experiments. We predict the characteristic signatures of spin-orbital fractionalization in inelastic scattering experiments and compare them to the ones of the spin-anisotropic Kitaev honeycomb spin liquid. In particular, the resonant inelastic x-ray scattering response shows a characteristic momentum dependence directly related to the dispersion of fermionic excitations. The neutron scattering cross section displays a mixed response of fermionic magnons as well as spin-orbital excitations. The latter has a bandwidth of broad excitations and a vison gap that is three times larger than that of the spin-1 = 2 Kitaev model.

##### Simulating lattice gauge theories within quantum technologies

M.C. Banuls, R. Blatt, J. Catani, A. Celi, J.I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S: Montangero, C.A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.J. Wiese, M. Wingate, K. Zakrzewski, P. Zoller

European Physical Journal D 47 (8), 165 (2020).

Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.

##### Higher-order entanglement and many-body invariants for higher-order topological phases

Y. You, J. Bibo, F. Pollmann

Physical Review Research 2, 33192 (2020).

We discuss how strongly interacting higher-order symmetry protected topological (HOSPT) phases can be characterized from the entanglement perspective: First, we introduce a topological many-body invariant which reveals the noncommutative algebra between a flux operator and Cn rotations. We argue that this invariant denotes the angular momentum carried by the instanton which is closely related to the discrete Wen-Zee response and the fractional corner charge. Second, we define a new entanglement property, dubbed “higher-order entanglement,” to scrutinize and differentiate various higher-order topological phases from a hierarchical sequence of the entanglement structure. We support our claims by numerically studying a super-lattice Bose-Hubbard model that exhibits different HOSPT phases.

##### Lattice modulation spectroscopy of one-dimensional quantum gases: Universal scaling of the absorbed energy

R. Citro, E. Demler, T. Giamarchi, M. Knap, and E. Orignac

Physical Review Research 2 (3), 33187 (2020).

Lattice modulation spectroscopy is a powerful tool for probing low-energy excitations of interacting many-body systems. By means of bosonization we analyze the absorbed power in a one-dimensional interacting quantum gas of bosons or fermions, subjected to a periodic drive of the optical lattice. For these Tomonaga-Luttinger liquids we find a universal ω3 scaling of the absorbed power, which at very low-frequency turns into an ω2 scaling when scattering processes at the boundary of the system are taken into account. We confirm this behavior numerically by simulations based on time-dependent matrix product states. Furthermore, in the presence of impurities, the theory predicts an ω2 bulk scaling. While typical response functions of Tomonaga-Luttinger liquids are characterized by exponents that depend on the interaction strength, modulation spectroscopy of cold atoms leads to a universal power-law exponent of the absorbed power. Our findings can be readily demonstrated in ultracold atoms in optical lattices with current experimental technology.

##### Entanglement Hamiltonian of the 1+1-dimensional free, compactified boson conformal field theory

A. Roy, F. Pollmann, H, Saleur

Journal of Statistical Mechanics - Theory and Experiment 2020 (8), 083104 (2020).

Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1 + 1 space-time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson CFT over a finite spatial interval. We compare the analytical results obtained for the continuum theory with numerical simulations of a lattice-regularized model for the CFT using density matrix renormalization group technique. To that end, we use a lattice regularization provided by superconducting quantum electronic circuits, built out of Josephson junctions and capacitors. Up to non-universal effects arising due to the lattice regularization, the numerical results are compatible with the predictions of the exact computations.

##### Prethermalization of quantum systems interacting with non-equilibrium environments

A. Angles-Castillo, M.C. Banuls, A. Perez, I. De Vega

New Journal of Physics 22 (8), 083067 (2020).

The usual paradigm of open quantum systems falls short when the environment is actually coupled to additional fields or components that drive it out of equilibrium. Here we explore the simplest such scenario, by considering a two level system coupled to a first thermal reservoir that in turn couples to a second thermal bath at a different temperature. We derive a master equation description for the system and show that, in this situation, the dynamics can be especially rich. In particular, we observe prethermalization, a transitory phenomenon in which the system initially approaches thermal equilibrium with respect to the first reservoir, but after a longer time converges to the thermal state dictated by the temperature of the second environment. Using analytical arguments and numerical simulations, we analyze the occurrence of this phenomenon, and how it depends on temperatures and coupling strengths. The phenomenology gets even richer if the system is placed between two such non-equilibrium environments. In this case, the energy current through the system may exhibit transient features and even switch direction, before the system eventually reaches a non-equilibrium steady state.

##### Inaccessible entanglement in symmetry protected topological phases

C. de Groot, D.T. Stephen, A. Molnar, N. Schuch

Journal of Physics A 53, 335302 (2020).

We study the entanglement structure of symmetry-protected topological (SPT) phases from an operational point of view by considering entanglement distillation in the presence of symmetries. We demonstrate that non-trivial SPT phases in one-dimension necessarily contain some entanglement which is inaccessible if the symmetry is enforced. More precisely, we consider the setting of local operations and classical communication (LOCC) where the local operations commute with a global onsite symmetry group G, which we call G-LOCC, and we define the inaccessible entanglement Einacc as the entanglement that cannot be used for distillation under G-LOCC. We derive a tight bound on Einacc which demonstrates a direct relation between inaccessible entanglement and the SPT phase, namely $\mathrm{log}\left({D}_{\omega }^{2}\right){\leqslant}{E}_{\mathrm{i}\mathrm{n}\mathrm{a}\mathrm{c}\mathrm{c}}{\leqslant}\mathrm{log}\left(\vert G\vert \right)$, where Dω is the topologically protected edge mode degeneracy of the SPT phase ω with symmetry G. For particular phases such as the Haldane phase, ${D}_{\omega }=\sqrt{\vert G\vert }$ so the bound becomes an equality. We numerically investigate the distribution of states throughout the bound, and show that typically the region near the upper bound is highly populated, and also determine the nature of those states lying on the upper and lower bounds. We then discuss the relation of Einacc to string order parameters, and also the extent to which it can be used to distinguish different SPT phases of matter.

##### Fractional corner charges in a 2D super-lattice Bose-Hubbard model

J. Bibo, I. Lovas, Y. You, F. Grusdt, F. Pollmann

Physical Review B 102, 041126 (R) (2020).

We study higher order topology in the presence of strong interactions in a two-dimensional, experimentally accessible superlattice Bose-Hubbard model with alternating hoppings and strong on-site repulsion. We evaluate the phase diagram of the model around half-filling using the density renormalization group ansatz and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and C4 lattice symmetry. The phases are distinguished in terms of a many-body topological invariant and a quantized, experimentally accessible fractional corner charge that is robust against arbitrary, symmetry preserving edge manipulations. We support our claims by numerically studying the full counting statistics of the corner charge, finding a sharp distribution peaked around the quantized values. Our results allow for a direct comparison with experiments and represent a confirmation of theoretically predicted higher order topology in a strongly interacting system. Experimentally, the fractional corner charge can be observed in ultracold atomic settings using state of the art quantum gas microscopy.

##### Out-of-horizon correlations following a quench in a relativistic quantum field theory

I. Kukuljan, S. Sotiriadis, G. Takács

Journal of High Energy Physics 7, 224 (2020).

One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the “horizon effect” a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the “horizon effect”. We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench.

##### Constrained random phase approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene

T.I. Vanhala, L. Pollet

Physical Review B 102 (3), 035154 (2020).

Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models, taking into account screening from the moire bands left outside the model space. Based on an atomic-scale tight-binding model, we numerically compute the polarization function and study its behavior for different twist angles. We discuss an approximation scheme which allows us to compute the screened interaction, in spite of the very large number of atoms in the unit cell. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a two-dimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediate-momentum regime, the dependence on the twist angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of 1/(4 nm), attaining values of 18-25, depending on the exact model, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the on-site and extended interaction terms for the recently developed hexagonal-lattice model. For freestanding twisted bilayer graphene, the effective interaction decays slower than 1/r at intermediate distances r, while it remains essentially unscreened at large enough r.

##### Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model

M.P. Qin, C.M. Chung, H. Shi, E. Vitali, C. Hubig, U. Schollwoeck, S.R. White, S.W. Zhang

Physical Review X 10 (3), 031016 (2020).

We study the superconducting pairing correlations in the ground state of the doped Hubbard model-in its original form without hopping beyond nearest neighbor or other perturbing parameters-in two dimensions at intermediate to strong coupling and near optimal doping. The nature of such correlations has been a central question ever since the discovery of cuprate high-temperature superconductors. Despite unprecedented effort and tremendous progress in understanding the properties of this fundamental model, a definitive answer to whether the ground state is superconducting in the parameter regime most relevant to cuprates has proved exceedingly difficult to establish. In this work, we employ two complementary, state-of-the-art, many-body computational methods-constrained-path (CP) auxiliary-field quantum Monte Carlo (AFQMC) and density matrix renormalization group (DMRG) methods-deploying the most recent algorithmic advances in each. Systematic and detailed comparisons between the two methods are performed. The DMRG is extremely reliable on small width cylinders, where we use it to validate the AFQMC. The AFQMC is then used to study wide systems as well as fully periodic systems, to establish that we have reached the thermodynamic limit. The ground state is found to be nonsuperconducting in the moderate to strong coupling regime in the vicinity of optimal hole doping.

##### Parton theory of angle-resolved photoemission spectroscopy spectra in antiferromagnetic Mott insulators

A. Bohrdt, E: Demler, F. Pollmann, M. Knap, F. Grusdt

Physical Review B 102 (3), 035139 (2020).

Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the t-J model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.

##### Ramsey interferometry of non-Hermitian quantum impurities.

F. Tonielli, N. Chakraborty, F. Grusdt, J. Marino

Physical Review Research 2, 032003 (R) (2020).

We introduce a Ramsey pulse scheme which extracts the non-Hermitian Hamiltonian associated with an arbitrary Lindblad dynamics. We propose a related protocol to measure via interferometry a generalized Loschmidt echo of a generic state evolving in time with the non-Hermitian Hamiltonian itself, and we apply the scheme to a one-dimensional weakly interacting Bose gas coupled to a stochastic atomic impurity. The Loschmidt echo is mapped into a functional integral from which we calculate the long-time decohering dynamics at arbitrary impurity strengths. For strong dissipation we uncover the phenomenology of a quantum many-body Zeno effect: Corrections to the decoherence exponent resulting from the impurity self-energy become purely imaginary, in contrast to the regime of small dissipation where they instead enhance the decay of quantum coherences. Our results illustrate the prospects for experiments employing Ramsey interferometry to study dissipative quantum impurities in condensed matter and cold-atom systems.

##### Nondestructive photon counting in waveguide QED

D. Malz, J.I. Cirac

Physical Review Research 2, 033091 (2020).

Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, but despite significant efforts, state-of-the-art devices are limited to few photons. In contrast, state-dependent atom counting in arrays can be done with extremely high fidelity up to hundreds of atoms. We show that in waveguide QED, the problem of photon counting can be reduced to atom counting, by entangling the photonic state with an atomic array in the collective number basis. This is possible as the incoming photons couple to collective atomic states and can be achieved by engineering a second decay channel of an excited atom to a metastable state. Our scheme is robust to disorder and finite Purcell factors, and its fidelity increases with the atom number. Analyzing the state of the re-emitted photons, we further show that if the initial atomic state is a symmetric Dicke state, dissipation engineering can be used to implement a nondestructive photon-number measurement, in which the incident state is scattered into the waveguide unchanged. Our results generalize to related platforms, including superconducting qubits.

##### Field-induced reorientation of helimagnetic order in Cu2OSeO3 probed by magnetic force microscopy

P. Milde, L. Koehler, E. Neuber, P. Ritzinger, M. Garst, A. Bauer, C. Pfleiderer, H. Berger, L.M. Eng

Physical Review B 102 (2), 024426 (2020).

Cu2OSeO3 is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic-field (H) over right arrow. We report a magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of Cu2OSeO3. In the presence of a magnetic field, the helimagnetic order, in general, reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10 K for fields close to the crystallographic < 110 > direction that involves a phase transition at H-c1. Experimental evidence is presented for the formation of magnetic domains in real space as well as for the microscopic origin of relaxation events that accompany the reorientation process. In addition, the electric polarization is measured by means of Kelvin-probe force microscopy. We show that the characteristic field dependency of the electric polarization originates in this helimagnetic reorientation process. Our experimental results are well described by an effective Landau theory previously invoked for MnSi, that captures the competition between magnetocrystalline anisotropies and Zeeman energy.

##### A subradiant optical mirror formed by a single structured atomic layer

J. Rui, D.V. Wei, A. Rubio-Abadal, S. Hollerith, J. Zeiher, D.M. Stamper-Kurn, C. Gross, I. Bloch

Nature 583 (7816), 369–374 (2020).

Versatile interfaces with strong and tunable light-matter interactions are essential for quantum science(1)because they enable mapping of quantum properties between light and matter(1). Recent studies(2-10)have proposed a method of controlling light-matter interactions using the rich interplay of photon-mediated dipole-dipole interactions in structured subwavelength arrays of quantum emitters. However, a key aspect of this approach-the cooperative enhancement of the light-matter coupling strength and the directional mirror reflection of the incoming light using an array of quantum emitters-has not yet been experimentally demonstrated. Here we report the direct observation of the cooperative subradiant response of a two-dimensional square array of atoms in an optical lattice. We observe a spectral narrowing of the collective atomic response well below the quantum-limited decay of individual atoms into free space. Through spatially resolved spectroscopic measurements, we show that the array acts as an efficient mirror formed by a single monolayer of a few hundred atoms. By tuning the atom density in the array and changing the ordering of the particles, we are able to control the cooperative response of the array and elucidate the effect of the interplay of spatial order and dipolar interactions on the collective properties of the ensemble. Bloch oscillations of the atoms outside the array enable us to dynamically control the reflectivity of the atomic mirror. Our work demonstrates efficient optical metamaterial engineering based on structured ensembles of atoms(4,8,9)and paves the way towards controlling many-body physics with light(5,6,11)and light-matter interfaces at the single-quantum level(7,10).

A single two-dimensional array of atoms trapped in an optical lattice shows a tunable cooperative subradiant optical response, acting as a single-monolayer optical mirror with controllable reflectivity.

##### On the Algorithmic Solvability of Spectral Factorization and Applications

H. Boche, V. Pohl.

IEEE Transactions on Information Theory 66, 4574-4592 (2020).

Spectral factorization is an operation which appears in many different engineering applications. This paper studies whether spectral factorization can be algorithmically computed on an abstract machine (a Turing machine). It is shown that there exist computable spectral densities with very good analytic properties (i.e. smooth with finite energy) such that the corresponding spectral factor cannot be determined on a Turing machine. Further, it will be proved that it is impossible to decide algorithmically whether or not a given computable density possesses a computable spectral factor. This negative result has consequences for applications of spectral factorization in computer-aided design, because there it is necessary that this problem be decidable. Conversely, this paper will show that if the logarithm of a computable spectral density belongs to certain Sobolev space of sufficiently smooth functions, then the spectral factor is always computable. As an application, the paper discusses the possibility of calculating the optimal causal Wiener filter on an abstract machine.

##### Vibrational Dressing in Kinetically Constrained Rydberg Spin Systems

P.P Mazza, R. Schmidt, I. Lesanovsky

Physical Review Letters 125 (3), 033602 (2020).

Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behavior in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We investigate in detail the properties of these quasiparticles, such as their dispersion relation, effective mass, and the quasiparticle weight. Rydberg lattice quantum simulators are particularly suited for studying this phonon-dressed kinetically constrained dynamics as their exaggerated length scales permit the site-resolved monitoring of spin and phonon degrees of freedom.

##### Proof of the Strong Scott Conjecture for Heavy Atoms: the Furry Picture

K. Merz, H. Siedentop

We prove the convergence of the density on the scale Z−1 to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.

##### Tune-out and magic wavelengths for ground-state 23Na40K molecules

R. Bause, M. Li, A. Schindewolf, X.-Y. Chen, M. Duda, S. Kotochigova, I. Bloch, X.-Y. Luo

Physical Review Letters 125, 23201 (2020).

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of 23Na40K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

##### Quantum advantage with noisy shallow circuits

S. Bravyi, D. Gosset, R. König, M. Tomamichel

Nature Physics (2020).

As increasingly sophisticated prototypes of quantum computers are being developed, a pressing challenge is to find computational problems that can be solved by an intermediate-scale quantum computer, but are beyond the capabilities of existing classical computers. Previous work in this direction has introduced computational problems that can be solved with certainty by quantum circuits of depth independent of the input size (so-called ‘shallow’ circuits) but cannot be solved with high probability by any shallow classical circuit. Here we show that such a separation in computational power persists even when the shallow quantum circuits are restricted to geometrically local gates in three dimensions and corrupted by noise. We also present a streamlined quantum algorithm that is shown to achieve a quantum advantage in a one-dimensional geometry. The latter may be amenable to experimental implementation with the current generation of quantum computers.

##### Plaquette versus ordinary d-wave pairing in the t '-Hubbard model on a width-4 cylinder

C.M. Chung, M.P. Qin, S.W. Zhang, U. Schollwoeck, S.R. White

Physical Review B 102 (4), 041106 (2020).

The Hubbard model and its extensions are important microscopic models for understanding high-Tc superconductivity in cuprates. In the model with next-nearest-neighbor hopping t' (the t'-Hubbard model), pairing is strongly influenced by t'. In particular, a recent study on a width-4 cylinder observed quasi-long-range superconducting order, associated with a negative t', which was taken to imply superconductivity in the two-dimensional (2D) limit. In this work we study more carefully pairing in the width-4 t'-Hubbard model. We show that in this specific system, the pairing symmetry with t' < 0 is not the ordinary d-wave one would expect in the 2D limit. Instead we observe a so-called plaquette d-wave pairing. We show that the plaquette d-wave or its extension is difficult to generalize in other geometries, for example a 4-leg ladder with open boundaries or a width-6 cylinder. We find that a negative t' suppresses the conventional d-wave, leading to plaquette pairing. In contrast, a different t '' coupling acting diagonally on the plaquettes suppresses plaquette pairing, leading to conventional d-wave pairing.

##### Robust Bilayer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy

J. Koepsell, S. Hirthe, D. Bourgund, P. Sompet, J. Vijayan, G. Salomon, C. Gross, I. Bloch

Physical Review Letters 125 (1), 010403 (2020).

Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly stable vertical superlattice and subsequent charge pumping to separate the layers by 21 mu m. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods, or the realization of tunable bilayer systems.

##### Locally-triggered hydrophobic collapse induces global interface self-cleaning in van-der-Waals heterostructures at room-temperature

S. Wakolbinger, F.R. Geisenhof, F. Winterer, S. Palmer, J.G. Crimmann, K. Watanabe, T. Taniguchi, F. Trixler, R.T. Weitz

2D Materials 7 (3), 035002 (2020).

Mutual relative orientation and well defined, uncontaminated interfaces are the key to obtain van-der-Waals heterostacks with defined properties. Even though the van-der-Waals forces are known to promote the 'self-cleaning' of interfaces, residue from the stamping process, which is often found to be trapped between the heterostructure constituents, can interrupt the interlayer interaction and therefore the coupling. Established interfacial cleaning methods usually involve high-temperature steps, which are in turn known to lead to uncontrolled rotations of layers within fragile heterostructures. Here, we present an alternative method feasible at room temperature. Using the tip of an atomic force microscope (AFM), we locally control the activation of interlayer attractive forces, resulting in the global removal of contaminants from the interface (i.e. the contaminants are also removed in regions several mu m away from the line touched by the AFM tip). By testing combinations of various hydrophobic van-der-Waals materials, mild temperature treatments, and by observing the temporal evolution of the contaminant removal process, we identify that the AFM tip triggers a dewetting-induced hydrophobic collapse and the van-der-Waals interaction is driving the cleaning process. We anticipate that this process is at the heart of the known 'self-cleaning' mechanism. Our technique can be utilized to controllably establish interlayer close coupling between a stack of van-der-Waals layers, and additionally allows to pattern and manipulate heterostructures locally for example to confine material into nanoscopic pockets between two van-der-Waals materials.

##### Hall viscosity and conductivity of two-dimensional chiral superconductors

F. Rose, O. Golan, S. Moroz

Scipost Physics 9 (1), 006 (2020).

We compute the Hall viscosity and conductivity of non-relativistic two-dimensional chi-ral superconductors, where fermions pair due to a short-range attractive potential, e.g. p + ip pairing, and interact via a long-range repulsive Coulomb force. For a logarithmic Coulomb potential, the Hall viscosity tensor contains a contribution that is singular at low momentum, which encodes corrections to pressure induced by an external shear strain. Due to this contribution, the Hall viscosity cannot be extracted from the Hall conductivity in spite of Galilean symmetry. For mixed-dimensional chiral superconductors, where the Coulomb potential decays as inverse distance, we find an intermediate behavior between intrinsic two-dimensional superconductors and superfluids. These results are obtained by means of both effective and microscopic field theory.

##### Realization of an anomalous Floquet topological system with ultracold atoms

K. Wintersperger, C. Braun, F. Nur Ünal, A. Eckardt, M. Di Liberto, N. Goldman, I. Bloch, M. Aidelsburger

Nature Physics (2020).

Coherent control via periodic modulation, also known as Floquet engineering, has emerged as a powerful experimental method for the realization of novel quantum systems with exotic properties. In particular, it has been employed to study topological phenomena in a variety of different platforms. In driven systems, the topological properties of the quasienergy bands can often be determined by standard topological invariants, such as Chern numbers, which are commonly used in static systems. However, due to the periodic nature of the quasienergy spectrum, this topological description is incomplete and new invariants are required to fully capture the topological properties of these driven settings. Most prominently, there are two-dimensional anomalous Floquet systems that exhibit robust chiral edge modes, despite all Chern numbers being equal to zero. Here we realize such a system with bosonic atoms in a periodically driven honeycomb lattice and infer the complete set of topological invariants from energy gap measurements and local Hall deflections.

##### Identification Capacity of Channels with Feedback: Discontinuity Behavior, Super-Activation, and Turing Computability

R.F. Schaefer, H. Boche, H.V. Poor.

IEEE Transactions on Information Theory (2020).

The problem of identification is considered, in which it is of interest for the receiver to decide only whether a certain message has been sent or not, and the identification-feedback (IDF) capacity of channels with feedback is studied. The IDF capacity is shown to be discontinuous and super-additive for both deterministic and randomized encoding. For the deterministic IDF capacity the phenomenon of super-activation occurs, which is the strongest form of super-additivity. This is the first time that super-activation is observed for discrete memoryless channels. On the other hand, for the randomized IDF capacity, super-activation is not possible. Finally, the developed theory is studied from an algorithmic point of view by using the framework of Turing computability. The problem of computing the IDF capacity on a Turing machine is connected to problems in pure mathematics and it is shown that if the IDF capacity would be Turing computable, it would provide solutions to other problems in mathematics including Goldbach’s conjecture and the Riemann Hypothesis. However, it is shown that the deterministic and randomized IDF capacities are not Banach-Mazur computable. This is the weakest form of computability implying that the IDF capacity is not computable even for universal Turing machines. On the other hand, the identification capacity without feedback is Turing computable revealing the impact of the feedback: It transforms the identification capacity from being computable to non-computable.

##### SU(3)_1 Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS

J.Y. Chen, S. Capponi, A. Wietek, M. Mambrini, N. Schuch, D. Poilblanc

Physical Review Letters 125, 017201 (2020).

Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of projected entangled pair states (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU(3)1 chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. In all three Z3 sectors, the level counting of the linear dispersing modes is in full agreement with SU(3)1 Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU(N)k chiral PEPS are discussed.

##### SU(3)_1 Chiral Spin Liquid on the Square Lattice: A View from Symmetric Projected Entangled Pair States

J.-Y. Chen, S. Capponi, A. Wietek, M. Mambrini, N. Schuch, D. Poilblanc

Physical Review Letters 125 (1), 017201 (2020).

Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of projected entangled pair states (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU(3)1 chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. In all three Z3 sectors, the level counting of the linear dispersing modes is in full agreement with SU(3)1 Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU(N)k chiral PEPS are discussed.

##### Spin Hall magnetoresistance in antiferromagnetic insulators

S. Gepraegs, M. Opel, J. Fischer, O. Gomonay, P. Schwenke, M. Althammer, H. Huebl, R. Gross

Journal of Applied Physics 127 (24), (2020).

Antiferromagnetic materials promise improved performance for spintronic applications as they are robust against external magnetic field perturbations and allow for faster magnetization dynamics compared to ferromagnets. The direct observation of the antiferromagnetic state, however, is challenging due to the absence of a macroscopic magnetization. Here, we show that the spin Hall magnetoresistance (SMR) is a versatile tool to probe the antiferromagnetic spin structure via simple electrical transport experiments by investigating the easy-plane antiferromagnetic insulators

alpha -

Fe 2

O 3 (hematite) and NiO in bilayer heterostructures with a Pt heavy-metal top electrode. While rotating an external magnetic field in three orthogonal planes, we record the longitudinal and the transverse resistivities of Pt and observe characteristic resistivity modulations consistent with the SMR effect. We analyze both their amplitude and phase and compare the data to the results from a prototypical collinear ferrimagnetic

Y 3

Fe 5

O 12/Pt bilayer. The observed magnetic field dependence is explained in a comprehensive model, based on two magnetic sublattices and taking into account magnetic field-induced modifications of the domain structure. Our results show that the SMR allows us to understand the spin configuration and to investigate magnetoelastic effects in antiferromagnetic multi-domain materials. Furthermore, in

alpha

- Fe 2

O 3/Pt bilayers, we find an unexpectedly large SMR amplitude of

2.5 x

10

- 3, twice as high as for prototype

Y 3

Fe 5

O 12/Pt bilayers, making the system particularly interesting for room-temperature antiferromagnetic spintronic applications.

##### The 2020 Skyrmionics roadmap

C.H. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, Tianping Ma, S. Mankovsky, T. L. Monchesky, M. Mostovoy, N. Nagaosa, S.S.P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y. Taguchi, Y. Tokura, K. von Bergmann, J. Zang

Journal of Physics D: Applied Physics 53, 363001 (2020).

The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics Roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purpose-design broad-band spin dynamic and logic devices.

##### Thermal Control of Spin Excitations in the Coupled Ising-Chain Material RbCoCl3

M. Mena, N. Hänni, S. Ward, E. Hirtenlechner, R. Bewley, C. Hubig, U. Schollwöck, B. Normand, K.W. Krämer, D.F. McMorrow, C. Rüegg

Physical Review Letters 124, 257201 (2020).

We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S=1/2) antiferromagnetic Ising chains in RbCoCl3. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the “Zeeman-ladder” bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to interpret the magnetic order, and finite-temperature density-matrix renormalization-group calculations to fit the spectral features of all three phases.

##### Dimerization and Néel Order in Different Quantum Spin Chains Through a Shared Loop Representation

M. Aizenman, H. Duminil-Copin, S. Warzel

Annales Henri Poincaré 21, 2737–2774 (2020).

The ground-states of the spin-S antiferromagnetic chain HAF with a projection-based interaction and the spin-1/2 XXZ-chain HXXZ at anisotropy parameter Δ=cosh(λ) share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar Q-state Potts model at Q−−√=2S+1=2cosh(λ). The multifaceted relation is used here to directly relate the distinct forms of translation symmetry breaking which are manifested in the ground-states of these two models: dimerization for HAF at all S>1/2, and Néel order for HXXZ at λ>0. The results presented include: (i) a translation to the above quantum spin systems of the results which were recently proven by Duminil–Copin–Li–Manolescu for a broad class of two-dimensional random-cluster models, and (ii) a short proof of the symmetry breaking in a manner similar to the recent structural proof by Ray–Spinka of the discontinuity of the phase transition for Q>4. Altogether, the quantum manifestation of the change between Q=4 and Q>4 is a transition from a gapless ground-state to a pair of gapped and extensively distinct ground-states.

##### Buffer-gas cooling of molecules in the low-density regime: comparison between simulation and experiment

T. Gantner, M. Koller, X. Wu, G. Rempe, M. Zeppenfeld

Journal of Physics B 53, 14 (2020).

Cryogenic buffer gas cells have been a workhorse for the cooling of molecules in the last few decades. The straightforward sympathetic cooling principle makes them applicable to a huge variety of different species. Notwithstanding this success, detailed simulations of buffer gas cells are rare, and have never been compared to experimental data in the regime of low to intermediate buffer gas densities. Here, we present a numerical approach based on a trajectory analysis, with molecules performing a random walk in the cell due to collisions with a homogeneous buffer gas. This method can reproduce experimental flux and velocity distributions of molecules emerging from the buffer gas cell for varying buffer gas densities. This includes the strong decrease in molecule output from the cell for increasing buffer gas density and the so-called boosting effect, when molecules are accelerated by buffer-gas atoms after leaving the cell. The simulations provide various insights which could substantially improve buffer-gas cell design.

##### Atomistic Positioning of Defects in Helium Ion Treated Single-Layer MoS2

E. Mitterreiter, B. Schuler, K.A. Cochrane, U. Wurstbauer, A: Weber-Bargioni, C. Kastl, A.W. Holleitner

Nano Letters 20 (6), 4437-4444 (2020).

Structuring materials with atomic precision is the ultimate goal of nanotechnology and is becoming increasingly relevant as an enabling technology for quantum electronics/spintronics and quantum photonics. Here, we create atomic defects in monolayer MoS2 by helium ion (He-ion) beam lithography with a spatial fidelity approaching the single-atom limit in all three dimensions. Using low-temperature scanning tunneling microscopy (STM), we confirm the formation of individual point defects in MoS2 upon He-ion bombardment and show that defects are generated within 9 nm of the incident helium ions. Atom-specific sputtering yields are determined by analyzing the type and occurrence of defects observed in high-resolution STM images and compared with with Monte Carlo simulations. Both theory and experiment indicate that the He-ion bombardment predominantly generates sulfur vacancies.

##### Multipartite entanglement analysis from random correlations

L. Knips, J. Dziewior, W. Klobus, W. Laskowski, T. Paterek, P.J. Shadbolt, H. Weinfurter, J.D.A. Meinecke

NPJ Quantum Information 6 (1), 51 (2020).

Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here, we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state. We analytically derive an entanglement criterion for two-qubit states and provide strong numerical evidence for witnessing genuine multipartite entanglement of three and four qubits. Our methods take the purity of the states into account and are based on only the second moments of measured correlations. Extended features of this theory are demonstrated experimentally with four photonic qubits. As long as the rate of entanglement generation is sufficiently high compared to the speed of the fluctuations, this method overcomes any type and strength of localized unitary noise.

##### Quantum East Model: Localization, Nonthermal Eigenstates, and Slow Dynamics

N. Pancotti, G. Giudice, J.I. Cirac, J.P. Garrahan, M.C. Banuls

Physical Review X 10 (2), 021051 (2020).

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization, and tensor-network methods, we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of nonthennal states that become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition. A "superspin" generalization allows us to fmd a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the nonthermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and nonergodicity more generally in disorder-free systems with constraints, and we give numerical evidence that these results may be extended to two-dimensional systems.

##### Quantum East Model: Localization, Nonthermal Eigenstates, and Slow Dynamics

Pancotti N., Giudice G., Cirac J.I., Garrahan J.P., Banuls M.C.

Physical Review X 10 (2), 021051 (2020).

We study in detail the properties of the quantum East model, an interacting quantum spin chain inspired by simple kinetically constrained models of classical glasses. Through a combination of analytics, exact diagonalization, and tensor-network methods, we show the existence of a transition, from a fast to a slow thermalization regime, which manifests itself throughout the spectrum. On the slow side, by exploiting the localization of the ground state and the form of the Hamiltonian, we explicitly construct a large (exponential in size) number of nonthennal states that become exact finite-energy-density eigenstates in the large size limit, as expected for a true phase transition. A "superspin" generalization allows us to fmd a further large class of area-law states proved to display very slow relaxation. These states retain memory of their initial conditions for extremely long times. Our numerical analysis reveals that the localization properties are not limited to the ground state and that many eigenstates have large overlap with product states and can be approximated well by matrix product states at arbitrary energy densities. The mechanism that induces localization to the ground state, and hence the nonthermal behavior of the system, can be extended to a wide range of models including a number of simple spin chains. We discuss implications of our results for slow thermalization and nonergodicity more generally in disorder-free systems with constraints, and we give numerical evidence that these results may be extended to two-dimensional systems.

##### Message transmission over classical quantum channels with a jammer with side information: Correlation as resource, common randomness generation

H. Boche, M. Cai, N. Cai

Journal of Mathematical Physics 61 (6), 062201 (2020).

In this paper, we analyze the capacity of a general model for arbitrarily varying classical-quantum channels (AVCQCs) when the sender and the receiver use correlation as a resource. In this general model, a jammer has side information about the channel input. We determine a single letter formula for the correlation assisted capacity. As an application of our main result, we determine the correlation assisted common randomness generation capacity. In this scenario, the two channel users have access to correlation as a resource and further use an AVCQC with an informed jammer for additional discussion. The goal is to create common randomness between the two channel users. We also analyze these capacity formulas when only a small number of signals from the correlation are available. For the correlation assisted common randomness generation capacity, we show an additional interesting property: For a sufficient amount of "public communication," common randomness generation capacity is Turing computable; however, without this public communication constraint, the correlation assisted common randomness generation capacity is, in general, not Turing computable. Furthermore, we show that even without knowing the capacity formula of the deterministic capacity using the maximal error criterion, we can show that it is impossible to evaluate the performance algorithmically on any current or future digital computer.

##### Dynamical Variational Approach to Bose Polarons at Finite Temperatures

D. Dzsotjan, R. Schmidt, M. Fleischhauer

Physical Review Letters 124 (22), 223401 (2020).

We discuss the interaction of a mobile quantum impurity with a Bose-Einstein condensate of atoms at finite temperature. To describe the resulting Bose polaron formation we develop a dynamical variational approach applicable to an initial thermal gas of Bogoliubov phonons. We study the polaron formation after switching on the interaction, e.g., by a radio-frequency (rf) pulse from a noninteracting to an interacting state. To treat also the strongly interacting regime, interaction terms beyond the Frohlich model are taken into account. We calculate the real-time impurity Green's function and discuss its temperature dependence. Furthermore we determine the rf absorption spectrum and find good agreement with recent experimental observations. We predict temperature-induced shifts and a substantial broadening of spectral lines. The analysis of the real-time Green's function reveals a crossover to a linear temperature dependence of the thermal decay rate of Bose polarons as unitary interactions are approached.

##### On-chip quantum opticsand integrated optomechanics

D. Hoch, T. Sommer, S. Müller, M. Poot

Turkish Journal of Physics 44, 239 – 246 (2020).

Recent developmentsin quantum computing and the growing interest in optomechanics and quantum opticsneed platforms that enable rapid prototyping and scalability. This can be fulfilled by on-chip integration, as we presenthere. The different nanofabrication steps are explained, and our automated measurement setup is discussed. We presentan opto-electromechanical device, the H-resonator, which enables optomechanical experiments such as electrostaticsprings and nonlinearities and thermomechanical squeezing. Moreover, it also functions as an optomechanical phaseshifter, an essential element for our integrated quantum optics efforts. Besides this, the equivalent of a beam splitter inphotonics-the directional coupler-is shown. Its coupling ratio can be reliably controlled, as we show with experimentaldata. Several directional couplers combined can realize the CNOT operation with almost ideal fidelity.

##### Resource-Aware Control via Dynamic Pricing for Congestion Game with Finite-Time Guarantees

E. Tampubolon, H. Ceribasic, H. Boche

IEEE International Workshop on Signal Processing Advances in Wireless Communications (2020).

Congestion game is a widely used model for modern networked applications. A central issue in such applications is that the selfish behavior of the participants may result in resource overloading and negative externalities for the system participants. In this work, we propose a pricing mechanism that guarantees the sub-linear increase of the time-cumulative violation of the resource load constraints. The feature of our method is that it is resource-centric in the sense that it depends on the congestion state of the resources and not on specific characteristics of the system participants. This feature makes our mechanism scalable, flexible, and privacy-preserving. Moreover, we show by numerical simulations that our pricing mechanism has no significant effect on the agents' welfare in contrast to the improvement of the capacity violation.

##### Floquet Prethermalization in a Bose-Hubbard System

A. Rubio-Abadal, M. Ippoliti, S. Hollerith, D. Wei, J, Rui, S.L. Sondhi, V. Khemani, C. Gross, I. Bloch

Physical Review X 10 (2), 021044 (2020).

Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system-leading to long-lived "prethermal" regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.

##### Orientation dependence of the magnetic phase diagram of Yb2Ti2O7

S. Säubert, A. Scheie, C. Duvinage, J. Kindervater, S. Zhang, H.J. Changlani, G. Xu, S.M. Kohpayeh, O. Tchernyshyov, C.L. Broholm, C. Pfleiderer

Physical Review B 101, 174434 (2020).

In the quest to realize a quantum spin liquid (QSL), magnetic long-range order is hardly welcome. Yet it can offer deep insights into a complex world of strong correlations and fluctuations. Much hope was placed in the cubic pyrochlore Yb2Ti2O7 as a putative U(1) QSL but a new class of ultrapure single crystals make it abundantly clear that the stoichiometric compound is a ferromagnet. Here we present a detailed experimental and theoretical study of the corresponding field-temperature phase diagram. We find it to be richly anisotropic with a critical endpoint for B∥⟨100⟩, while a field parallel to ⟨110⟩ or ⟨111⟩ enhances the critical temperature by up to a factor of two and shifts the onset of the field-polarized state to finite fields. Landau theory shows that Yb2Ti2O7 in some ways is remarkably similar to pure iron. However, it also pinpoints anomalies that cannot be accounted for at the classical mean-field level including a dramatic enhancement of TC and a reentrant phase boundary under applied magnetic fields with a component transverse to the easy axes, as well as the anisotropy of the upper critical field in the quantum limit.

##### How much delocalisation is needed for an enhanced area law of the entanglement entropy?

Peter Müller, Leonid Pastur, Ruth Schulte

Commun. Math. Phys. 376 (1), 649 - 679 (2020).

We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.

##### State-Dependent Optical Lattices for the Strontium Optical Qubit

A. Heinz, A. J. Park, N. Šantić, J. Trautmann, S. G. Porsev, M. S. Safronova, I. Bloch, and S. Blatt

Physical Review Letters 124, 203201 (2020).

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than four orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

##### Effective Approximation of Bandlimited Signals and Their Samples

H. Boche, U.J. Moenich

International Conference on Acoustics Speech and Signal Processing ICASSP 19787677 (2020).

Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.

##### Computing Hilbert Transform and Spectral Factorization for Signal Spaces of Smooth Functions

H. Boche, V. Pohl

International Conference on Acoustics Speech and Signal Processing (ICASSP) 19787218 (2020).

Although the Hilbert transform and the spectral factorization are of central importance in signal processing, both operations can generally not be calculated in closed form. Therefore, algorithmic solutions are prevalent which provide an approximation of the true solution. Then it is important to effectively control the approximation error of these approximate solutions. This paper characterizes for both operations precisely those signal spaces of differentiable functions for which such an effective control of the approximation error is possible. In other words, the paper provides a precise characterization of signal spaces of smooth functions on which these two operations are computable on Turing machines.

##### Can every analog system be simulated on a digital computer?

H. Boche, V. Pohl

International Conference on Acoustics Speech and Signal Processing (ICASSP) 19788661 (2020).

A Turing machine is a model describing the fundamental limits of any realizable computer, digital signal processor (DSP), or field programmable gate array (FPGA). This paper shows that there exist very simple linear time-invariant (LTI) systems which can not be simulated on a Turing machine. In particular, this paper considers the linear system described by the voltage-current relation of an ideal capacitor. For this system, it is shown that there exist continuously differentiable and computable input signals such that the output signal is a continuous function which is not computable. Moreover, for this particular system, we present sharp results characterizing computable input signals which guarantee that the output signal is computable. Additionally, it is shown that the computability of the step response of an LTI system does not necessarily imply that the impulse response is computable.

##### Computability of the Peak Value of Bandlimited Signals

H. Boche, U.J. Moenich

International Conference on Acoustics Speech and Signal Processing ICASSP 19788259 (2020).

In this paper we study the peak value problem, i.e., the task of computing the peak value of a bandlimited signal from its samples. The peak value problem is important, for example, in communications, where the peak value of the transmit signal has to be controlled in order that the amplifier is not overloaded, which would generate out-of-band radiation. We prove that the peak value of a computable bandlimited signal is computable on digital hardware if oversampling is used. The computability ensures that the approximation error can be effectively controlled. Further, we provide an algorithm that can be used to perform this computation and prove that oversampling is indeed necessary, because there exist signals for which the peak value problem cannot be algorithmically solved without oversampling. Hence, without oversampling the peak value of such signals cannot be computed on any digital hardware, including DSPs, FPGAs, and CPUs.

##### Robust Transmission over Channels with Channel Uncertainty: An Algorithmic Perspective

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 19788103 (2020).

The availability and quality of channel state information heavily influences the performance of wireless communication systems. For perfect channel knowledge, optimal signal processing and coding schemes are well studied and often closed-form solutions are known. On the other hand, the case of imperfect channel information is much less understood and closed-form solutions remain unknown in general. This paper approaches this question from a fundamental, algorithmic point of view to study whether or not such optimal schemes can be found algorithmically in principle (without putting any constraints on the computational complexity of such algorithms). To this end, the compound channel is considered as a model for channel uncertainty and it is shown that although the compound channel itself is a computable channel, the corresponding capacity is not computable in general, i.e., there exists no algorithm or Turing machine that takes the channel as an input and computes the corresponding capacity. As an implication of this, it is then shown that for such compound channels, there are no effectively constructible optimal signal processing and coding schemes that achieve the capacity. This is particularly noteworthy as such schemes must exist (since the capacity is known), but they cannot be effectively, i.e., algorithmically, constructed.

##### Optimal Sampling Rate and Bandwidth of Bandlimited Signals - An Algorithmic Perspective

H. Boche, U.J. Mönich

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 19788543 (2020).

The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the actual bandwidth of a bandlimited signal. We prove that this is not possible in general, because there exist bandlimited computable signals, which have a bandwidth that is not computable. To this end we employ the concept of Turing computability, which provides a theoretical model that describes the fundamental limits of any practically realizable digital hardware, such as CPUs, DSPs, or FPGAs. Further, we answer the weaker question if it can be algorithmically answered whether the bandwidth of a given signal is larger than a predefined value.

##### Anisotropic Magnetic Resonance in Random Nanocrystal Quantum Dot Ensembles

A.J.S. Almeida, A. Sahu, D.J. Norris, G.N. Kakazei, M.S. Brandt, M. Stutzmann, R.N. Pereira

ACS Omega 5, 11333 (2020).

Magnetic anisotropy critically determines the utility of magnetic nanocrystals (NCs) in new nanomagnetism technologies. Using angular-dependent electron magnetic resonance (EMR), we observe magnetic anisotropy in isotropically arranged NCs of a nonmagnetic material. We show that the shape of the EMR angular variation can be well described by a simple model that considers magnetic dipole–dipole interactions between dipoles randomly located in the NCs, most likely due to surface dangling bonds. The magnetic anisotropy results from the fact that the energy term arising from the magnetic dipole–dipole interactions between all magnetic moments in the system is dominated by only a few dipole pairs, which always have an anisotropic geometric arrangement. Our work shows that magnetic anisotropy may be a general feature of NC systems containing randomly distributed magnetic dipoles.

##### Discrete interactions between a few interlayer excitons trapped at a MoSe2-WSe2 heterointerface

M. Kremser, M. Brotons-Gisbert, J. Knoerzer, J. Gueckelhorn, M. Meyer, M. Barbone, A.V. Stier, B.D. Gerardot, K. Mueller, J.J. Finley

NPJ 2D Materials and Applications 4 (1), 8 (2020).

Inter-layer excitons (IXs) in hetero-bilayers of transition metal dichalcogenides (TMDs) represent an exciting emergent class of long-lived dipolar composite bosons in an atomically thin, near-ideal two-dimensional (2D) system. The long-range interactions that arise from the spatial separation of electrons and holes can give rise to novel quantum, as well as classical multi-particle correlation effects. Indeed, first indications of exciton condensation have been reported recently. In order to acquire a detailed understanding of the possible many-body effects, the fundamental interactions between individual IXs have to be studied. Here, we trap a tunable number of dipolar IXs (N-IX 1-5) within a nanoscale confinement potential induced by placing a MoSe2-WSe2 hetero-bilayer (HBL) onto an array of SiO2 nanopillars. We control the mean occupation of the IX trap via the optical excitation level and observe discrete sharp-line emission from different configurations of interacting IXs. The intensities of these features exhibit characteristic near linear, quadratic, cubic, quartic and quintic power dependencies, which allows us to identify them as different multiparticle configurations with N-IX 1-5. We directly measure the hierarchy of dipolar and exchange interactions as N-IX increases. The interlayer biexciton (N-IX = 2) is found to be an emission doublet that is blue-shifted from the single exciton by Delta E = (8.4 +/- 0.6) meV and split by 2J = (1.2 +/- 0.5) meV. The blueshift is even more pronounced for triexcitons ((12.4 +/- 0.4) meV), quadexcitons ((15.5 +/- 0.6) meV) and quintexcitons ((18.2 +/- 0.8) meV). These values are shown to be mutually consistent with numerical modelling of dipolar excitons confined to a harmonic trapping potential having a confinement lengthscale in the range l approximate to 3 nm. Our results contribute to the understanding of interactions between IXs in TMD hetero-bilayers at the discrete limit of only a few excitations and represent a key step towards exploring quantum correlations between IXs in TMD hetero-bilayers.

##### Range-Separated Density-Functional Theory in Combination with the Random Phase Approximation: An Accuracy Benchmark

A. Kreppel, D. Graf, H. Laqua, C. Ochsenfeld

Journal of Chemical Theory and Computation 16 (5), 2985-2994 (2020).

A formulation of range-separated random phase approximation (RPA) based on our efficient omega-CDGD-RI-RPA [J. Chem. Theory Comput. 2018, 14, 2505] method and a large scale benchmark study are presented. By application to the GMTKN55 data set, we obtain a comprehensive picture of the performance of range-separated RPA in general main group thermochemistry, kinetics, and noncovalent interactions. The results show that range-separated RPA performs stably over the broad range of molecular chemistry included in the GMTKN55 set. It improves significantly over semilocal DFT but it is still less accurate than modern dispersion corrected double-hybrid functionals. Furthermore, range-separated RPA shows a faster basis set convergence compared to standard full-range RPA making it a promising applicable approach with only one empirical parameter.

##### Inflation and Decoupling

G. Dvali, A. Kehagias, A. Riotto

Decoupling of heavy modes in effective low energy theory is one of the most fundamental concepts in physics. It tells us that modes must have a negligible effect on the physics of gravitational backgrounds with curvature radius larger than their wavelengths. Despite this, there exist claims that trans-Planckian modes put severe bound on the duration of inflation even when the Hubble parameter is negligible as compared to the Planck mass. If true, this would mean that inflation violates the principle of decoupling or at least requires its reformulation. We clarify the fundamental misconception on which these bounds are based and respectively refute them. Our conclusion is that inflation fully falls within the validity of a reliable effective field theory treatment and does not suffer from any spurious trans-Planckian problem.

##### Theory of exciton-electron scattering in atomically thin semiconductors

C. Fey, P. Schmelcher, A. Imamoglu, R. Schmidt

Physical Review B 101 (19), 195417 (2020).

The realization of mixtures of excitons and charge carriers in van der Waals materials presents a frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy model for such systems, we develop an exact diagonalization approach based on a discrete variable representation that predicts the scattering and bound state properties of three charges in two-dimensional transition metal dichalcogenides. From the solution of the quantum mechanical three-body problem we thus obtain the bound state energies of excitons and trions within an effective mass model which are in excellent agreement with quantum Monte Carlo predictions. The diagonalization approach also gives access to excited states of the three-body system. This allows us to predict the scattering phase shifts of electrons and excitons that serve as input for a low-energy theory of interacting mixtures of excitons and charge carriers at finite density. To this end we derive an effective exciton-electron scattering potential that is directly applicable for quantum Monte Carlo or diagrammatic many-body techniques. As an example, we demonstrate the approach by studying the many-body physics of exciton Fermi polarons in transition-metal dichalcogenides, and we show that finite-range corrections have a substantial impact on the optical absorption spectrum. Our approach can be applied to a plethora of many-body phenomena realizable in atomically thin semiconductors ranging from exciton localization to induced superconductivity.

##### Robust Pricing Mechanism for Resource Sustainability under Privacy Constraint in Competitive Online Learning Multi-Agent Systems

E. Tampubolon, H. Boche

International Conference on Acoustics Speech and Signal Processing ICASSP 8733-8737 (2020).

We consider the problem of resource congestion control for competing online learning agents under privacy and security constraints. Based on the non-cooperative game as the model for agents' interaction and the noisy online mirror ascent as the model for the rationality of the agents, we propose a novel pricing mechanism that gives the agents incentives for sustainable use of the resources. An advantage of our method is that it is privacy-preserving in the sense that mainly the resource congestion serves as an orientation for our pricing mechanism, in place of the agents' preference and state. Moreover, our method is robust against adversary agents' feedback in the form of the noisy gradient. We present the following result of our theoretical investigation: In case that the feedback noise is persistent, and for several choices of the intrinsic parameter (the learning rate) of the agents and of the mechanism parameters (the learning rate of the price-setters, their progressivity, and the extrinsic price sensitivity of the agents), we show that the accumulative violation of the resource constraints of the resulted iterates is sub-linear w.r.t the time horizon. To support our theoretical findings, we provide some numerical simulations.

##### Optimal Sampling Rate and Bandwidth of Bandlimited Signals - An Algorithmic Perspective

H. Boche, U.J. Moenich

International Conference on Acoustics Speech and Signal Processing ICASSP 5905-5909 (2020).

The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the actual bandwidth of a bandlimited signal. We prove that this is not possible in general, because there exist bandlimited computable signals, which have a bandwidth that is not computable. To this end we employ the concept of Turing computability, which provides a theoretical model that describes the fundamental limits of any practically realizable digital hardware, such as CPUs, DSPs, or FPGAs. Further, we answer the weaker question if it can be algorithmically answered whether the bandwidth of a given signal is larger than a predefined value.

##### Robust Online Mirror Saddle-Point Method for Constrained Resource Allocation

E. Tampubolon, H. Boche

International Conference on Acoustics Speech and Signal Processing ICASSP 4970-4974 (2020).

Online-learning literature has focused on designing algorithms that ensure sub-linear growth of the cumulative long-term constraint violations. The drawback of this guarantee is that strictly feasible actions may cancel out constraint violations on other time slots. For this reason, we introduce a new performance measure, whose particular instance is the cumulative positive part of the constraint violations. We propose a class of non-causal algorithms for online-decision making, which guarantees, in slowly changing environments, sub-linear growth of this quantity despite noisy first-order feedback. Furthermore, we demonstrate by numerical experiments the performance gain of our method relative to state of the art.

##### Denial-of-Service Attacks on Communication Systems: Detectability and Jammer Knowledge

H. Boche, R.F. Schaefer, H.V. Poor.

IEEE Transactions on Signal Processing 68, 3754-3768 (2020).

Wireless communication systems are inherently vulnerable to intentional jamming. In this paper, two classes of such jammers are considered: those with partial and full knowledge. While the first class accounts for those jammers that know the encoding and decoding function, the latter accounts for those that are further aware of the actual transmitted message. Of particular interest are so-called denial-of-service (DoS) attacks in which the jammer is able to completely disrupt any transmission. Accordingly, it is of crucial interest for the legitimate users to detect such adversarial DoS attacks. This paper develops a detection framework based on Turing machines. Turing machines have no limitations on computational complexity and computing capacity and storage and can simulate any given algorithm. For both scenarios of a jammer with partial and full knowledge, it is shown that there exists no Turing machine which can decide whether or not a DoS attack is possible for a given channel and the corresponding decision problem is undecidable. On the other hand, it is shown for both scenarios that it is possible to algorithmically characterize those channels for which a DoS attack is not possible. This means that it is possible to detect those scenarios in which the jammer is not able to disrupt the communication. For all other channels, the Turing machine does not stop and runs forever making this decision problem semidecidable. Finally, it is shown that additional coordination resources such as common randomness make the communication robust against such attacks.

##### On the ε-Capacity of Finite Compound Channels with Applications to the Strong Converse and Second Order Coding Rate

H. Boche, R.F. Schaefer, H.V. Poor

54th Annual Conference on Information Sciences and Systems (CISS) 19592800 (2020).

This paper considers the compound channel where the actual channel realization is unknown. It is only known that it comes from a given uncertainty set and that it remains constant throughout the entire duration of transmission. The capacity has been established providing a complete characterization and a simple formula for the computation of the maximal transmission rate. This is no longer the case for the ε-capacity of a compound channel, which characterizes the maximum transmission rate when a non-vanishing average error ε is tolerated. In this case, the compound channel is known to have no strong converse under the average error criterion and, therewith, the ε-capacity may be larger than the capacity for a vanishing error. As the capacity of compound channels is unknown, Ahlswede raised the question of whether or not there exists a (simple) recursive formula for it. This paper approaches this question from a fundamental, algorithmic point of view by studying whether or not such formulas can be found algorithmically in principle (without putting any constraints on the computational complexity of the algorithms). To this end, it is shown that there exists no algorithm or Turing machine that takes the compound channel and error as inputs and computes the corresponding ε-capacity. Accordingly, there is also no recursive formula for the ε-capacity providing a negative answer to Ahlswede's initial question. The developed framework is subsequently applied to the question of the existence of a strong converse, the existence of an optimal second order coding rate, and whether or not the pessimistic and optimistic definitions of the ε-capacity coincide. Cast as decision problems, it is shown that these questions are undecidable and therewith impossible to be answered algorithmically.

##### Quantum Reverse Hypercontractivity: Its Tensorization and Application to Strong Converses

S. Beigi, N. Datta, C. Rouzé

Communications in Mathematical Physics 376, 753–794 (2020).

In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock–Varopoulos inequality in the non-commutative setting which allows us to derive quantum hypercontractivity and reverse hypercontractivity inequalities solely from 2-log-Sobolev and 1-log-Sobolev inequalities respectively. We then prove some tensorization-type results providing us with tools to prove hypercontractivity and reverse hypercontractivity not only for certain quantum superoperators but also for their tensor powers. Finally as an application of these results, we generalize a recent technique for proving strong converse bounds in information theory via reverse hypercontractivity inequalities to the quantum setting. We prove strong converse bounds for the problems of quantum hypothesis testing and classical-quantum channel coding based on the quantum reverse hypercontractivity inequalities that we derive.

##### Spin structure relation to phase contrast imaging of isolated magnetic Bloch and Neel skyrmions

S. Poellath, T. Lin, N. Lei, W. Zhao, J. Zweck, C.H. Back

Ultramicroscopy 212, 112973 (2020).

Magnetic skyrmions are promising candidates for future storage devices with a large data density. A great variety of materials have been found that host skyrmions up to the room-temperature regime. Lorentz microscopy, usually performed in a transmission electron microscope (TEM), is one of the most important tools for characterizing skyrmion samples in real space. Using numerical calculations, this work relates the phase contrast in a TEM to the actual magnetization profile of an isolated Neel or Bloch skyrmion, the two most common skyrmion types. Within the framework of the used skyrmion model, the results are independent of skyrmion size and wall width and scale with sample thickness for purely magnetic specimens. Simple rules are provided to extract the actual skyrmion configuration of pure Bloch or Neel skyrmions without the need of simulations. Furthermore, first differential phase contrast (DPC) measurements on Neel skyrmions that meet experimental expectations are presented and showcase the described principles. The work is relevant for material sciences where it enables the engineering of skyrmion profiles via convenient characterization.

##### Flexible low-voltage high-frequency organic thin-film transistors

J.W. Borchert, U. Zschieschang, F. Letzkus, M. Giorgio, R.T. Weitz, M. Caironi, J.N. Burghartz, S. Ludwigs, H. Klauk

Science Advances 6 (21), eaaz5156 (2020).

The primary driver for the development of organic thin-film transistors (TFTs) over the past few decades has been the prospect of electronics applications on unconventional substrates requiring low-temperature processing. A key requirement for many such applications is high-frequency switching or amplification at the low operating voltages provided by lithium-ion batteries (similar to 3 V). To date, however, most organic-TFT technologies show limited dynamic performance unless high operating voltages are applied to mitigate high contact resistances and large parasitic capacitances. Here, we present flexible low-voltage organic TFTs with record static and dynamic performance, including contact resistance as small as 10 Omega.cm, on/off current ratios as large as 10(10), subthreshold swing as small as 59 mV/decade, signal delays below 80 ns in inverters and ring oscillators, and transit frequencies as high as 21 MHz, all while using an inverted coplanar TFT structure that can be readily adapted to industry-standard lithographic techniques.

##### Intermolecular forces and correlations mediated by a phonon bath

X. Li, E. Yakaboylu, G. Bighin, R. Schmidt, M. Lemeshko, A. Deuchert

Journal of Chemical Physics 152 (16), 164302 (2020).

Inspired by the possibility to experimentally manipulate and enhance chemical reactivity in helium nanodroplets, we investigate the effective interaction and the resulting correlations between two diatomic molecules immersed in a bath of bosons. By analogy with the bipolaron, we introduce the biangulon quasiparticle describing two rotating molecules that align with respect to each other due to the effective attractive interaction mediated by the excitations of the bath. We study this system in different parameter regimes and apply several theoretical approaches to describe its properties. Using a Born-Oppenheimer approximation, we investigate the dependence of the effective intermolecular interaction on the rotational state of the two molecules. In the strong-coupling regime, a product-state ansatz shows that the molecules tend to have a strong alignment in the ground state. To investigate the system in the weak-coupling regime, we apply a one-phonon excitation variational ansatz, which allows us to access the energy spectrum. In comparison to the angulon quasiparticle, the biangulon shows shifted angulon instabilities and an additional spectral instability, where resonant angular momentum transfer between the molecules and the bath takes place. These features are proposed as an experimentally observable signature for the formation of the biangulon quasiparticle. Finally, by using products of single angulon and bare impurity wave functions as basis states, we introduce a diagonalization scheme that allows us to describe the transition from two separated angulons to a biangulon as a function of the distance between the two molecules.

##### Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

M. Iqbal, D. Poilblanc, N. Schuch

Physical Review B 101, 155141 (2020).

We investigate the spin-1/2 Heisenberg antiferromagnet on a kagome lattice with breathing anisotropy (i.e., with weak and strong triangular units), constructing an improved simplex resonating valence bond (RVB) ansatz by successive applications (up to three times) of local quantum gates, which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting projected entangled pair state involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries Z2 topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.

##### Entanglement and its relation to energy variance for local one-dimensional Hamiltonians

M.C. Banuls, D.A. Huse, J.I. Cirac

Physical Review B 101 (14), 144305 (2020).

We explore the relation between the entanglement of a pure state and its energy variance for a local one-dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance delta(2) for N spins, with bond dimension scaling as root ND01/delta, where D-0 > 1 is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the construction on two different models and compare the local reduced density matrices of the resulting states to the corresponding thermal equilibrium. Our results suggest that the spatially homogeneous states with logarithmically decreasing variance, which can be constructed efficiently, do converge to the thermal equilibrium in the thermodynamic limit, while the same is not true if the variance remains constant.

##### Quantum Many-Body Scars in Optical Lattices

H.Z. Zhao, J. Vovrosh, F. Mintert, J. Knolle

Physical Review Letters 124 (16), 160604 (2020).

The concept of quantum many-body scars has recently been put forward as a route to describe weak ergodicity breaking and violation of the eigenstate thermalization hypothesis. We propose a simple setup to generate quantum many-body scars in a doubly modulated Bose-Hubbard system which can be readily implemented in cold atomic gases. The dynamics are shown to be governed by kinetic constraints which appear via density-assisted tunneling in a high-frequency expansion. We find the optimal driving parameters for the kinetically constrained hopping which leads to small isolated subspaces of scared eigenstates. The experimental signatures and the transition to fully thermalizing behavior as a function of driving frequency are analyzed.

##### Compact Dark Matter Objects via N Dark Sectors

G. Dvali, E. Koutsangelas, F. Kühnel

Phys. Rev. D 101, 83533 (2020).

We propose a novel class of compact dark matter objects in theories where the dark matter consists of multiple sectors. We call these objects N-MACHOs. In such theories neither the existence of dark matter species nor their extremely weak coupling to the observable sector represent additional hypotheses but instead are imposed by the solution to the Hierarchy Problem and unitarity. The crucial point is that particles from the same sector have non-trivial interactions but interact only gravitationally otherwise. As a consequence, the pressure that counteracts the gravitational collapse is reduced while the gravitational force remains the same. This results in collapsed structures much lighter and smaller as compared to the ordinary single-sector case. We apply this phenomenon to a dark matter theory that consists of N dilute copies of the Standard Model. The solutions do not rely on an exotic stabilization mechanism, but rather use the same well-understood properties as known stellar structures. This framework also gives rise to new microscopic superheavy structures, for example with mass 108g and size 10−13cm. By confronting the resulting objects with observational constraints, we find that, due to a huge suppression factor entering the mass spectrum, these objects evade the strongest constrained region of the parameter space. Finally, we discuss possible formation scenarios of N-MACHOs. We argue that, due to the efficient dissipation of energy on small scales, high-density regions such as ultra-compact mini-halos could serve as formation sites of N-MACHOs.

##### Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

H. Boche, G. Janssen, S. Saeedinaeeni.

Journal of Mathematical Physics 61, 042204 (2020).

We derive universal codes for transmission of broadcast and confidential messages over classical-quantum–quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes, we generalize random codes for transmission of public messages to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

##### Capacity Regions for Compound Quantum Broadcast Channels with Confidential Messages

H. Boche, G. Janßen, S. Saeedinaeeni

Journal of Mathematical Physics 61, 042204 (2020).

We derive universal codes for transmission of broadcast and confidential messages over classical-quantum–quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes, we generalize random codes for transmission of public messages to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

##### Interacting Polaron-Polaritons

L.B. Tan, O. Cotlet, A. Bergschneider, R. Schmidt, P. Back, Y. Shimazaki, M. Kroner, A. Imamoglu

Physical Review X 10, 21011 (2020).

Two-dimensional semiconductors provide an ideal platform for exploration of linear exciton and polariton physics, primarily due to large exciton binding energy and strong light-matter coupling. These features, however, generically imply reduced exciton-exciton interactions, hindering the realization of active optical devices such as lasers or parametric oscillators. Here, we show that electrical injection of itinerant electrons into monolayer molybdenum diselenide allows us to overcome this limitation: dynamical screening of exciton-polaritons by electrons leads to the formation of new quasiparticles termed polaron-polaritons that exhibit unexpectedly strong interactions as well as optical amplification by Bose-enhanced polaron-electron scattering. To measure the nonlinear optical response, we carry out time-resolved pump-probe measurements and observe polaron-polariton interaction enhancement by a factor of 50 (0.5 μeV μm2) as compared to exciton-polaritons. Concurrently, we measure a spectrally integrated transmission gain of the probe field of ≳2 stemming from stimulated scattering of polaron-polaritons. We show theoretically that the nonequilibrium nature of optically excited quasiparticles favors a previously unexplored interaction mechanism stemming from a phase-space filling in the screening cloud, which provides an accurate explanation of the strong repulsive interactions observed experimentally. Our findings show that itinerant electron-exciton interactions provide an invaluable tool for electronic manipulation of optical properties, demonstrate a new mechanism for dramatically enhancing polariton-polariton interactions, and pave the way for realization of nonequilibrium polariton condensates.

##### Markovianity of an emitter coupled to a structured spin-chain bath

J. Roos, J.I. Cirac, M.C. Banuls

Physical Review A 101 (4), 042114 (2020).

We analyze the dynamics of a spin-1/2 subsystem coupled to a spin chain. We simulate numerically the full quantum many-body system for various sets of parameters and initial states of the chain, and characterize the divisibility of the subsystem dynamics, i.e., whether it is Markovian and can be described by a (time-dependent) master equation. We identify regimes in which the subsystem admits such Markovian description, despite the many-body setting, and provide insight about why the same is not possible in other regimes. Interestingly, coupling the subsystem at the edge, instead of the center, of the chain gives rise to qualitatively distinct behavior.

##### A quantum network node with crossed optical fibre cavities

M. Brekenfeld, D. Niemietz, J.D. Christesen, G. Rempe

Nature Physics 16, 647-651 (2020).

Quantum networks provide unique possibilities for resolving open questions on entanglement and promise innovative applications ranging from secure communication to scalable computation. Although two quantum nodes coupled by a single channel are adequate for basic quantum communication tasks between two parties, fully functional large-scale quantum networks require a web-like architecture with multiply connected nodes. Efficient interfaces between network nodes and channels can be implemented with optical cavities. Using two optical fibre cavities coupled to one atom, we here realize a quantum network node that connects to two quantum channels, one provided by each cavity. It functions as a passive, heralded and high-fidelity quantum memory that requires neither amplitude- and phase-critical control fields nor error-prone feedback loops. Our node is robust, fits naturally into larger fibre-based networks and has prospects for extensions including qubit-controlled quantum switches, routers and repeaters.

##### Many-body topological invariants from randomized measurements in synthetic quantum matter

A. Elben, J. Yu; G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, B. Vermesch

Science Advances 6, eaaz3666 (2020).

Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

##### Rydberg impurity in a Fermi gas: Quantum statistics and rotational blockade

J. Sous, H.R. Sadeghpour, T.C. Killian, E. Demler, R. Schmidt

Physical Review Research 2, 23021 (2020).

We consider the quench of an atomic impurity via a single Rydberg excitation in a degenerate Fermi gas. The Rydberg interaction with the background gas particles induces an ultralong-range potential that binds particles to form dimers, trimers, tetramers, etc. Such oligomeric molecules were recently observed in atomic Bose-Einstein condensates. Understanding the effects of a correlated background on molecule formation, absent in bosonic baths, is crucial to explain ongoing experiments with Fermi gases. In this work we demonstrate with a functional determinant approach that quantum statistics and fluctuations have clear observable consequences. We show that the occupation of molecular states is predicated on the Fermi statistics, which suppresses molecular formation in an emergent molecular shell structure. At high gas densities this leads to spectral narrowing, which can serve as a probe of the quantum gas thermodynamic properties. Rydberg excitations in Fermi gases go beyond traditional impurity problems, creating an opportunity for studies of mesoscopic interactions in synthetic quantum matter.

##### A random unitary circuit model for black hole evaporation

- L. Piroli, C. Sünderhauf, X.-L. Qi

Journal of High Energy Physics 4, 063 (2020).

Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is driven by the continuous limit of certain 2-local random unitary circuits. We study both cases where the unitaries are chosen with and without a conserved U(1) charge and focus on two aspects of the dynamics. First, we study analytically and numerically the growth of the entanglement entropy of the system, showing that two different time scales appear: one is intrinsic to the internal dynamics (the scrambling time), while the other depends on the system-environment coupling. In the presence of a U(1) conserved charge, we show that the entanglement follows a Page-like behavior in time: it begins to decrease in the middle stage of the “evaporation”, and decreases monotonically afterwards. Second, we study the time needed to retrieve information initially injected in the system from measurements on the environment qudits. Based on explicit numerical computations, we characterize such time both when the retriever has control over the initial configuration or not, showing that different scales appear in the two cases.

##### The C-numerical range in infinite dimensions

G. Dirr, F. vom Ende

Linear & Multilinear Algebra 68 (4), 867-868 (2020).

##### Universal superposition codes: Capacity regions of compound quantum broadcast channel with confidential messages

H. Boche, G. Janssen, S. Saeedinaeeni

Journal of Mathematical Physics 61 (4), (2020).

We derive universal codes for transmission of broadcast and confidential messages over classical-quantum-quantum and fully quantum channels. These codes are robust to channel uncertainties considered in the compound model. To construct these codes, we generalize random codes for transmission of public messages to derive a universal superposition coding for the compound quantum broadcast channel. As an application, we give a multi-letter characterization of regions corresponding to the capacity of the compound quantum broadcast channel for transmitting broadcast and confidential messages simultaneously. This is done for two types of broadcast messages, one called public and the other common.

##### Confined Phases of One-Dimensional Spinless Fermions Coupled to Z(2) Gauge Theory

U. Borla, R. Verresen, F. Grusdt, S. Moroz

Physical Review Letters 124 (12), 120503 (2020).

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z(2) gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

##### Statistical localization: From strong fragmentation to strong edge modes

T. Rakovszky, P. Sala, R. Verresen, M. Knap, F. Pollmann

Physical Review B 101 (12), 125126 (2020).

Certain disorder-free Hamiltonians can be nonergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of "statistically localized integrals of motion" (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to subextensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a nonintegrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.

##### Thermodynamics of a hierarchical mixture of cubes

S. Jansen.

Journal of Statistical Physics (2020).

We investigate a toy model for phase transitions in mixtures of incompressible droplets. The model consists of non-overlapping hypercubes in Zd of sidelengths 2j, j?N0. Cubes belong to an admissible set B such that if two cubes overlap, then one is contained in the other. Cubes of sidelength 2j have activity zj and density ?j. We prove explicit formulas for the pressure and entropy, prove a van-der-Waals type equation of state, and invert the density-activity relations. In addition we explore phase transitions for parameter-dependent activities zj(?)=exp(2dj??Ej). We prove a sufficient criterion for absence of phase transition, show that constant energies Ej?? lead to a continuous phase transition, and prove a necessary and sufficient condition for the existence of a first-order phase transition.

##### Fermionic tensor networks for higher order topological insulators from charge pumping

A. Hackenbroich, B.A. Bernevig, N. Schuch, N. Regnault

Physical Review B 101, 115134 (2020).

We apply the charge-pumping argument to fermionic tensor network representations of d-dimensional topological insulators (TIs) to obtain tensor network states (TNSs) for (d+1)-dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair state (PEPS) for a Chern insulator starting from a matrix product state (MPS) in d=1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second-order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d=2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d+1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest-neighbor Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.

##### Resource Allocation for Secure Communication Systems: Algorithmic Solvability

H. Boche, R.F. Schaefer, H.V. Poor

IEEE International Workshop on Information Forensics and Security (WIFS) 19456004 (2019).

Medium access control and in particular resource allocation is one of the most important tasks when designing wireless communication systems as it determines the overall performance of a system. For the particular allocation of the available resources it is of crucial importance to know whether or not a channel supports a certain quality-of-service (QoS) requirement. This paper develops a decision framework based on Turing machines and studies the algorithmic decidability of whether or not a QoS requirement is met. Turing machines have no limitations on computational complexity, computing capacity, and storage. They can simulate any given algorithm and therewith characterize the fundamental performance limits for today's digital computers. In this paper, secure communication and identification systems are considered both under channel uncertainty and adversarial attacks. While for perfect channel state information, the question is decidable since the corresponding capacity function is computable, it is shown that the corresponding questions become semidecidable in the case of channel uncertainty and adversarial attacks. This means there exist Turing machines that stop and output the correct answer if and only if a channel supports the given QoS requirement. Interestingly, the opposite question of whether a channel capacity is below a certain threshold is not semidecidable.

##### Localisation for Delone operators via Bernoulli randomisation

P. Müller, C. Rojas-Molina

Delone operators are Schrödinger operators in multi-dimensional Euclidean space with a potential given by the sum of all translates of a given "single-site potential" centred at the points of a Delone set. In this paper, we use randomisation to study dynamical localisation for families of Delone operators. We do this by suitably adding more points to a Delone set and by introducing i.i.d. Bernoulli random variables as coupling constants at the additional points. The resulting non-ergodic continuum Anderson model with Bernoulli disorder is accessible to the latest version of the multiscale analysis. The novel ingredient here is the initial length-scale estimate whose proof is hampered due to the non-periodic background potential. It is obtained by the use of a quantitative unique continuation principle. As applications we obtain both probabilistic and topological statements about dynamical localisation. Among others, we show that Delone sets for which the associated Delone operators exhibit dynamical localisation at the bottom of the spectrum are dense in the space of Delone sets.

##### Classification of Matrix-Product Unitaries with Symmetries

- Z.P. Gong, C. Sünderhauf, N. Schuch, J.I. Cirac

Physical Review Letters 124 (10), 100402 (2020).

We prove that matrix-product unitaries with on-site unitary symmetries are completely classified by the (chiral) index and the cohomology class of the symmetry group G, provided that we can add trivial and symmetric ancillas with arbitrary on-site representations of G. If the representations in both system and ancillas are fixed to be the same, we can define symmetry-protected indices (SPIs) which quantify the imbalance in the transport associated to each group element and greatly refines the classification. These SPIs are stable against disorder and measurable in interferometric experiments. Our results lead to a systematic construction of two-dimensional Floquet symmetry-protected topological phases beyond the standard classification, and thus shed new light on understanding nonequilibrium phases of quantum matter.

##### Reachable Sets from Toy Models to Controlled Markovian Quantum Systems

G. Dirr, F. vom Ende, T. Schulte-Herbrüggen

Proc. IEEE Conf. Decision Control 58, 2322 (2020).

In the framework of bilinear control systems, we present reachable sets of coherently controllable open quantum systems with switchable coupling to a thermal bath of arbitrary temperature T ≥ 0. The core problem boils down to studying points in the standard simplex amenable to two types of controls that can be used interleaved:(i)permutations within the simplex,(ii)contractions by a dissipative one-parameter semigroup. Our work illustrates how the solutions of the core problem pertain to the reachable set of the original controlled Markovian quantum system. We completely characterize the case T = 0 and present inclusions for T > 0.

##### The Solvability Complexity Index of Sampling-based Hilbert Transform Approximations

H. Boche, V. Pohl

13th International Conference on Sampling Theory and Applications (SampTA) 19451267 (2019).

This paper determines the solvability complexity index (SCI) and a corresponding tower of algorithms for the computational problem of calculating the Hilbert transform of a continuous function with finite energy from its samples. It is shown that the SCI of these algorithms is equal to 2 and that the SCI is independent on whether the calculation is done by linear or by general (i.e. linear and/or non-linear) algorithms.

##### Computability of the Fourier Transform and ZFC

H. Boche, U.J. Mönich

13th International conference on Sampling Theory and Applications (SampTA) 19451289 (2019).

In this paper we study the Fourier transform and the possibility to determine the binary expansion of the values of the Fourier transform in the Zermelo-Fraenkel set theory with the axiom of choice included (ZFC). We construct a computable absolutely integrable bandlimited function with continuous Fourier transform such that ZFC (if arithmetically sound) cannot determine a single binary digit of the binary expansion of the Fourier transform at zero. This result implies that ZFC cannot determine for every precision goal a rational number that approximates the Fourier transform at zero. Further, we discuss connections to Turing computability.

##### Periodically Driven Sachdev-Ye-Kitaev Models

C. Kuhlenkamp, M.Knap

Physical Review Letters 124 (10), 106401 (2020).

Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.

##### Z2 characterization for three-dimensional multiband Hubbard models

B. Irsigler, J. Zheng, F. Grusdt, W. Hofstetter

Physical Review Research 2, 13299 (2020).

We introduce three numerical methods for characterizing the topological phases of three-dimensional multiband Hubbard models based on twisted boundary conditions, Wilson loops, as well as the local topological marker. We focus on the half-filled, three-dimensional time-reversal-invariant Hofstadter model with finite spin-orbit coupling. Besides the weak and strong topological insulator phases we find a nodal line semimetal in the parameter regime between the two three-dimensional topological insulator phases. Using dynamical mean-field theory combined with the topological Hamiltonian approach we find stabilization of these three-dimensional topological states due to the Hubbard interaction. We study surface states which exhibit an asymmetry between left and right surfaces originating from the broken parity symmetry of the system. Our results set the stage for further research on inhomogeneous three-dimensional topological systems, proximity effects, topological Mott insulators, nontrivially linked nodal line semimetals, and circuit-based quantum simulators.

##### Probing Thermalization through Spectral Analysis with Matrix Product Operators

Y.L. Yang, S. Iblisdir, J.I. Cirac, M.C. Banuls

Physical Review Letters 124 (10), 100602 (2020).

We combine matrix product operator techniques with Chebyshev polynomial expansions and present a method that is able to explore spectral properties of quantum many-body Hamiltonians. In particular, we show how this method can be used to probe thermalization of large spin chains without explicitly simulating their time evolution, as well as to compute full and local densities of states. The performance is illustrated with the examples of the Ising and PXP spin chains. For the nonintegrable Ising chain, our findings corroborate the presence of thermalization for several initial states, well beyond what direct time-dependent simulations have been able to achieve so far.

##### Exploring the Limits of Open Quantum Dynamics II: Gibbs-Preserving Maps from the Perspective of Majorization

F. vom Ende

Motivated by reachability questions in coherently controlled open quantum systems coupled to a thermal bath, as well as recent progress in the field of thermo-/vector-d-majorization we generalize classical majorization from unital quantum channels to channels with an arbitrary fixed point D of full rank. Such channels preserve some Gibbs-state and thus play an important role in the resource theory of quantum thermodynamics, in particular in thermo-majorization.

Based on this we investigate D-majorization on matrices in terms of its topological and order properties, such as existence of unique maximal and minimal elements, etc. Moreover we characterize D-majorization in the qubit case via the trace norm and elaborate on why this is a challenging task when going beyond two dimensions.

##### Exploring the Limits of Open Quantum Dynamics I: Motivation, New Results from Toy Models to Applications

T. Schulte-Herbrüggen, F. vom Ende, G. Dirr

Which quantum states can be reached by controlling open Markovian n-level quantum systems? Here, we address reachable sets of coherently controllable quantum systems with switchable coupling to a thermal bath of temperature T. The core problem reduces to a toy model of studying points in the standard simplex allowing for two types of controls: (i) permutations within the simplex, (ii) contractions by a dissipative semigroup. By illustration, we put the problem into context and show how toy-model solutions pertain to the reachable set of the original controlled Markovian quantum system. Beyond the case T=0 (amplitude damping) we present new results for 0<T<∞ using methods of d-majorisation.

##### Exact dynamics in dual-unitary quantum circuits

L. Piroli, B. Bertini, J.I. Cirac, T. Prosen

Physical Review B 101 (9), 094304 (2020).

We consider the class of dual-unitary quantum circuits in 1+1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size ℓ reaches infinite temperature after a time t∝ℓ, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

##### Continuous Generation of Quantum Light from a Single Ground-State Atom in an Optical Cavity

C.J. Villas-Boas, K.N. Tolazzi, B. Wang, C. Ianzano, G. Rempe

Physical Review Letters 124 (9), 93603 (2020).

We show an optical wave-mixing scheme that generates quantum light by means of a single three-level atom. The atom couples to an optical cavity and two laser fields that together drive a cycling current within the atom. Weak driving in combination with strong atom-cavity coupling induces transitions in a harmonic ladder of dark states, accompanied by single-photon emission via a quantum Zeno effect and suppression of atomic excitation via quantum interference. For strong driving, the system can generate coherent or Schrödinger cat-like fields with frequencies distinct from those of the applied lasers.

##### Evolution of magnetocrystalline anisotropies in Mn1-xFexSi and Mn1-xCoxSi as inferred from small-angle neutron scattering and bulk properties

J. Kindervater, T. Adams, A. Bauer, F.X. Haslbeck, A. Chacon, S. Muehlbauer, F. Jonietz, A: Neubauer, U. Gasser, G. Nagy, N. Martin, W. Haeussler, R. Georgii, M. Garst, C. Pfleiderer

Physical Review B 101 (10), 104406 (2020).

We report a comprehensive small-angle neutron scattering (SANS) study of magnetic correlations in Mn1-xFexSi at zero magnetic field. To delineate changes of magnetocrystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and high-resolution specific heat data and investigated selected compositions of Mn1-xCoxSi. For all systems studied, the helimagnetic transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS intensity patterns of the spontaneous magnetic order recorded under zero-field cooling, which were systematically tracked over forty angular positions, display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing x the character of the MCAs shifts from terms that are fourth order to terms that are sixth order in spin-orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe- or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of well-defined thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn1-xCoxSi establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, which are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn1-xFexSi and Mn1-xCoxSi offers a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.

##### Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout

J. Knörzer, M. J. A. Schuetz, G. Giedke, D. S. Wild, K. De Greve, R. Schmidt, M. D. Lukin, and I.Cirac.

Physical Review B 101, 125101 (2020).

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.

##### Wigner crystals in two-dimensional transition-metal dichalcogenides: Spin physics and readout

J. Knoerzer, M.J.A. Schuetz, G. Giedke, D.S. Wild, K. De Greve, R. Schmidt, M.D. Lukin, J.I. Cirac

Physical Review B 101 (12), 125101 (2020).

Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.

##### Topological Spin Liquids: Robustness under perturbations

M. Iqbal, H. Casademunt, N. Schuch

Physical Review B 101, 115101 (2020).

We study the robustness of the paradigmatic kagome resonating valence bond (RVB) spin liquid and its orthogonal version, the quantum dimer model. The nonorthogonality of singlets in the RVB model and the induced finite length scale not only makes it difficult to analyze, but can also significantly affect its physics, such as how much noise resilience it exhibits. Surprisingly, we find that this is not the case: The amount of perturbations which the RVB spin liquid can tolerate is not affected by the finite correlation length, making the dimer model a viable model for studying RVB physics under perturbations. Remarkably, we find that this is a universal phenomenon protected by symmetries: First, the dominant correlations in the RVB are spinon correlations, making the state robust against doping with visons. Second, reflection symmetry stabilizes the spin liquid against doping with spinons, by forbidding mixing of the initially dominant correlations with those which lead to the breakdown of topological order.

##### Multimode Fock states with large photon number: effective descriptions and applications in quantum metrology

M. Perarnau-Llobet, A. Gonzalez-Tudela, J.I. Cirac

Quantum Science and Technology 5 (2), 025003 (2020).

We develop general tools to characterise and efficiently compute relevant observables of multimode N-photon states generated in nonlinear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a d-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the quantum Fisher information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different d modes.

##### Highly Efficient, Linear-Scaling Seminumerical Exact-Exchange Method for Graphic Processing Units

H. Laqua, T.H. Thompson, J. Kussmann, C. Ochsenfeld

Journal of Chemical Theory and Computation 16 (3), 1456-1468 (2020).

We present a highly efficient and asymptotically linear-scaling graphic processing unit accelerated seminumerical exact-exchange method (snLinK). We go beyond our previous central processing unit-based method (Laqua, H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Theory Comput. 2018, 14, 3451-3458) by employing our recently developed integral bounds (Thompson, T. H.; Ochsenfeld, C. J. Chem. Phys. 2019, 1.50, 044101) and high-accuracy numerical integration grid (Laqua, H.; Kussmann, J.; Ochsenfeld, C. J. Chem. Phys. 2018, 149, 204111). The accuracy is assessed for several established test sets, providing errors significantly below 1mE(h) for the smallest grid. Moreover, a comprehensive performance analysis for large molecules between 62 and 1347 atoms is provided, revealing the outstanding performance of our method, in particular, for large basis sets such as the polarized quadruple-zeta level with diffuse functions.

##### Improved stability for 2D attractive Bose gases

P.T. Nam, N. Rougerie

Journal of Mathematical Physics 61, 21901 (2020).

We study the ground-state energy of N attractive bosons in the plane. The interaction is scaled for the gas to be dilute so that the corresponding mean-field problem is a local non-linear Schrödinger (NLS) equation. We improve the conditions under which one can prove that the many-body problem is stable (of the second kind). This implies, using previous results, that the many-body ground states and dynamics converge to the NLS ones for an extended range of diluteness parameters.

##### Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

P. Sala, T. Rakovszky, R. Verresen, M. Knap, F. Pollmann

Physical Review X 10 (1), 011047 (2020).

We show that the combination of charge and dipole conservation-characteristic of fracton systems-leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total S-z) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature autocorrelation saturates to a finite value-showcasing nonthermal behavior. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local S-z basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: The system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits nonthermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment-conserving random unitary circuit models for which we reach identical conclusions.

##### Higher Order Corrections to the Mean-Field Description ofthe Dynamics of Interacting Bosons

L. Boßmann, N. Pavovic, P. Pickl, A. Soffer

Journal of Statistical Physics 178 (6), 1362–1396 (2020).

In this paper, we introduce a novel method for deriving higher order corrections to the mean-field description of the dynamics of interacting bosons. More precisely, we consider thedynamics ofNd-dimensional bosons for largeN. The bosons initially form a Bose–Einsteincondensate and interact with each other via a pair potential of the form(N−1)−1Ndβv(Nβ·)forβ∈[0,14d).WederiveasequenceofN-body functions which approximate the true many-body dynamics inL2(RdN)-norm to arbitrary precision in powers ofN−1. The approximatingfunctions are constructed as Duhamel expansions of finite order in terms of the first quantisedanalogue of a Bogoliubov time evolution.

##### Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms

A. Bohrdt, A. Omran, E. Demler, S. Gazit, F. Grusdt

Physical Review Letters 124, 73601 (2020).

Dominant multiparticle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this Letter, we propose a protocol showing how SU(N)-invariant multibody interactions can be implemented in optical tweezer arrays. We utilize the flexibility to rearrange the tweezer configuration on short timescales compared to the typical lifetimes, in combination with strong nonlocal Rydberg interactions. As a specific example, we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using density-matrix renormalization group simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated J–Q model, a candidate for hosting a deconfined quantum critical point.

##### On-site tuning of the carrier lifetime in silicon for on-chip THz circuits using a focused beam of helium ions

P. Zimmermann, A.W. Holleitner

Applied Physics Letters 116 (7), 073501 (2020).

In this study, we demonstrate that a focused helium ion beam allows the local adjustment and optimization of the carrier lifetime in silicon-based photoswitches integrated in ultrafast on-chip terahertz-circuits. Starting with a carrier lifetime of 5.3 ps for as-grown silicon on sapphire, we monotonously reduce the carrier lifetime in integrated switches to a minimum of similar to 0.55 ps for a helium ion fluence of 20x10(15) ions/cm(2). By introducing an analytical model for the carrier lifetimes in the photoswitches, we particularly demonstrate that the carrier lifetime can be adjusted locally even within single photoswitches. In turn, the demonstrated on-site tuning allows optimizing ultrafast high-frequency circuits, into which radiation-sensitive nanoscale materials, such as two-dimensional materials, are embedded. Published under license by AIP Publishing.

##### Continuous Phase-Space Representations for Finite-Dimensional Quantum States and their Tomography

B. Koczor, R. Zeier, S.J. Glaser

Physical Review A 101 (2), 22318 (2020).

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough understanding of their relations was still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The infinite-dimensional case from quantum optics is then recovered in the large-spin limit.

##### Quantum phases of a one-dimensional Majorana-Bose-Hubbard model

A. Roy, J. Hauschild, F. Pollmann

Physical Review B 101, 75419 (2020).

Majorana zero modes (MZM-s) occurring at the edges of a one-dimensional (1D), p-wave, spinless superconductor, in the absence of fluctuations of the phase of the superconducting order parameter, are quintessential examples of topologically protected zero-energy modes occurring at the edges of 1D symmetry-protected topological phases. In this work, we numerically investigate the fate of the topological phase in the presence of phase fluctuations using the density matrix renormalization group (DMRG) technique. To that end, we consider a one-dimensional array of MZM-s on mesoscopic superconducting islands at zero temperature. Cooper-pair and MZM-assisted single-electron tunneling, together with finite charging energy of the mesoscopic islands, give rise to a rich phase diagram of this model. We show that the system can be in either a Mott-insulating phase, a Luttinger liquid (LL) phase of Cooper pairs, or a second gapless phase. In contrast to the LL of Cooper pairs, this second phase is characterized by nonlocal string correlation functions which decay algebraically due to gapless charge-e excitations. The three phases are separated from each other by phase transitions of either Kosterlitz-Thouless or Ising type. Using a Jordan-Wigner transformation, we map the system to a generalized Bose-Hubbard model with two types of hopping and use DMRG to analyze the different phases and the phase transitions.

##### Secure Storage Capacity Under Rate Constraints—Continuity and Super Activation

S. Baur, H. Boche, R.F. Schaefer, H.V. Poor.

IEEE Transactions on Information Forensics and Security 15, 959-970 (2020).

The source model for secret key generation with one way public communication refers to a setting in which a secret key should be agreed upon at two terminals. At both terminals correlated components of a common source are available. In addition, a message can be sent from one terminal to the other via a public channel. In this paper, a related scenario is considered where instead of secret key generation, the goal is to securely store data in a public database. The database allows for error-free storing of the data, but is constrained in its size which imposes a rate constraint on storing. The corresponding capacity for secure storage is known and it has been shown that the capacity-achieving strategy satisfies the strong secrecy criterion. Here, the case when the storage in the public database is subject to errors is considered and the corresponding capacity is characterized. In addition, the continuity properties of the two capacity functions are analyzed. These capacity functions are continuous as opposed to the discontinuous secret key capacity with rate constraint. It is shown that for secure storage the phenomenon of super activation can occur. Finally, it is discussed how the results in this paper differ from previous results on super activation.

##### Isometric tensor network representation of string-net liquids

T. Soejima, K. Siva, N. Bultinck, S. Chatterjee, F. Pollmann, M.P. Zaletel

Physical Review B 101 (8), 085117 (2020).

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite-depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.

##### Parametric Instabilities of Interacting Bosons in Periodically Driven 1D Optical Lattices

K. Wintersperger, M. Bukov, J. Näger, S. Lellouch, E. Demler, U. Schneider, I. Bloch, N. Goldman, M. Aidelsburger

Physical Review X 10, 011030 (2020).

Periodically driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and interparticle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabilities in weakly interacting Bose-Einstein condensates in strongly driven optical lattices through momentum-resolved measurements, in line with theoretical predictions. Parametric instabilities can trigger the destruction of weakly interacting Bose-Einstein condensates through the rapid growth of collective excitations, in particular in systems with weak harmonic confinement transverse to the lattice axis. Understanding the onset of parametric instabilities in driven quantum matter is crucial for determining optimal conditions for the engineering of modulation-induced many-body systems.

##### On the correlation energy of interacting fermionic systems in the mean-field regime

C. Hainzl, M. Porta, F. Rexze

Communications in Mathematical Physics 374, 485–524 (2020).

We consider a system of N\gg 1 interacting fermionic particles in three dimensions, confined in a periodic box of volume 1, in the mean-field scaling. We assume that the interaction potential is bounded and small enough. We prove upper and lower bounds for the correlation energy, which are optimal in their N-dependence. Moreover, we compute the correlation energy at leading order in the interaction potential, recovering the prediction of second order perturbation theory. The proof is based on the combination of methods recently introduced for the study of fermionic many-body quantum dynamics together with a rigorous version of second-order perturbation theory, developed in the context of non-relativistic QED.

##### Differential Power Analysis Attacks from an Information-Theoretic Perspective

A. Grigorescu, H. Boche

IEEE Information Theory Workshop (ITW) 19352987 (2019).

Differential power analysis (DPA) attacks exploit the variance in power measurements of cryptographic devices to recover secret keys. What can an adversary achieve with power measurements? In this work, information-theoretic tools are used to quantify the amount of sensitive information revealed by a power measurement. It is shown that in order to find a secret key, an adversary needs to try a number of different keys. The number is exponential to the key size and the exponent is given by the key's entropy, conditioned on the power measurement.

##### On the Structure of the Capacity Formula for General Finite State Channels with Applications

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Information Theory Workshop (ITW) 19352971 (2019).

Finite state channels (FSCs) model discrete channels with memory where the channel output depends on the channel input and the actual channel state. The capacity of general FSCs has been established as the limit of a sequence of multi-letter expressions; a corresponding finite-letter characterization is not known to date. In this paper, it is shown that it is indeed not possible to find such a finite-letter entropic characterization for FSCs whose input, output, and state alphabets satisfy |X| ≥2, |Y| ≥2, and |S| ≥q2. Further, the algorithmic computability of the capacity of FSCs is studied. To account for this, the concept of a Turing machine is adopted as it provides fundamental performance limits for today's digital computers. It is shown that the capacity of a FSC is not Banach-Mazur computable and therewith not Turing computable for |X| ≥2, |Y| ≥2, |S| ≥2.

##### Coding for Non-IID Sources and Channels: Entropic Approximations and a Question of Ahlswede

H. Boche, R.F. Schaefer, H.V. Poor

2019 IEEE Information Theory Workshop (ITW) 19352964 (2019).

The theory of Verdú and Han provides a powerful framework to analyze and study general non-independent and identically distributed (non-i.i. d.) sources and channels. Already for simple non-i.i. d. sources and channels, this framework can result in complicated general capacity formulas. Ahlswede asked in his Shannon lecture if these general capacity formulas can be effectively, i.e., algorithmically, computed. In this paper, it is shown that there exist computable non-i.i. d. sources and channels, for which the capacity is a non-computable number. Even worse, it is shown that there are non-i.i. d. sources and channels for which the capacity is a computable number, i.e., the limit of the corresponding sequence of multi-letter capacity expressions is computable, but the convergence of this sequence is not effective. This answers Ahlswede's question in a strong form, since in this case, the multi-letter capacity expressions for these sources and channels cannot be used to approximate the optimal performance algorithmically.

##### Confined phases of one-dimensional spinless fermions coupled to Z2 gauge theory

U. Borla, R. Verresen, F. Grusdt, S. Moroz.

Physics Review Letters 124, 120503 (2020).

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z2 gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the Density Matrix Renormalization Group the system is shown to form a Luttinger liquid, indicating the emergence of fermionic fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

##### Secure Communication and Identification Systems — Effective Performance Evaluation on Turing Machines

H. Boche, R.F. Schaefer, H.V. Poor.

IEEE Transactions on Information Forensics and Security 15, 1013 - 1025 (2020).

Modern communication systems need to satisfy pre-specified requirements on spectral efficiency and security. Physical layer security is a concept that unifies both and connects them with entropic quantities. In this paper, a framework based on Turing machines is developed to address the question of deciding whether or not a communication system meets these requirements. It is known that the class of Turing solvable problems coincides with the class of algorithmically solvable problems so that this framework provides the theoretical basis for effective verification of such performance requirements. A key issue here is to decide whether or not the performance functions, i.e., capacities, of relevant communication scenarios, particularly those with secrecy requirements and active adversaries, are Turing computable. This is a necessary condition for the corresponding communication protocols to be effectively verifiable. Within this framework, it is then shown that for certain scenarios including the wiretap channel the corresponding capacities are Turing computable. Next, a general necessary condition on the performance function for Turing computability is established. With this, it is shown that for certain scenarios, including the wiretap channel with an active jammer, the performance functions are not computable when deterministic codes are used. As a consequence, such performance functions are also not computable on all other computer architectures such as the von Neumann-architecture or the register machines.

##### Review on novel methods for lattice gauge theories

M.C. Banuls, K. Cichy

Reports on Progress in Physics 83 (2), 024401 (2020).

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

##### A stable quantum Darmois-Skitovich theorem

J. Cuesta

Journal of Mathematical Physics 61 (2), 022201 (2020).

The Darmois-Skitovich theorem is a simple characterization of the normal distribution in terms of the independence of linear forms. We present here a non-commutative version of this theorem in the context of Gaussian bosonic states and show that this theorem is strongly stable under small errors in its underlying conditions. An explicit estimate of the stability constants which depend on the physical parameters of the problem is given.

##### Evaluation of time-dependent correlators after a local quench in iPEPS: hole motion in the t - J model

C. Hubig, A: Bohrdt, M. Knap, F. Grusdt, J.I. Cirac

Scipost Physics 8 (2), 021 (2020).

Infinite projected entangled pair states (iPEPS) provide a convenient variational description of infinite, translationally-invariant two-dimensional quantum states. However, the simulation of local excitations is not directly possible due to the translationally-invariant ansatz. Furthermore, as iPEPS are either identical or orthogonal, expectation values between different states as required during the evaluation of non-equal-time correlators are ill-defined. Here, we show that by introducing auxiliary states on each site, it becomes possible to simulate both local excitations and evaluate non-equal-time correlators in an iPEPS setting under real-time evolution. We showcase the method by simulating the t - J model after a single hole has been placed in the half-filled antiferromagnetic background and evaluating both return probabilities and spin correlation functions, as accessible in quantum gas microscopes.

##### Nonlocal emergent hydrodynamics in a long-range quantum spin system

A. Schuckert, I. Lovas, M. Knap

Physical Review B 101 (2), 020416 (2020).

Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ nonequilibrium quantum field theory and semiclassical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as r(-alpha). While diffusion is recovered for alpha > 1.5, longer-ranged couplings with 0.5 < alpha <= 1.5 give rise to effective classical Levy flights, a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time-dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for 0.5 < alpha <= 1.5, autocorrelations show hydrodynamic tails decaying in time as t(-1/(2 alpha-1)) and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.

##### Isometric Tensor Network States in Two Dimensions

M.P. Zaletel, F. Pollmann

Physical Review Letters 124, 37201 (2020).

Tensor-network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm for approximating of the ground state of a Hamiltonian as an isometric TNS—which we demonstrate for the 2D transverse field Ising model.

##### Review on novel methods for lattice gauge theories

M.C. Bañuls, K. Cichy

Reports on Progress in Physics 83 (2), 024401 (2020).

Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem.

In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.

##### Excitations in strict 2-group higher gauge models of topological phases

A. Bullivant, C. Delcamp

Journal of High Energy Physics 1, 107 (2020).

We consider an exactly solvable model for topological phases in (3+1)d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.

##### Dark-time decay of the retrieval efficiency of light stored as a Rydberg excitation in a noninteracting ultracold gas

S. Schmidt-Eberle, T. Stolz, G. Rempe, S.Dürr.

Physical Review A 101, 013421 (2020).

We study the dark-time decay of the retrieval efficiency for light stored in a Rydberg state in an ultracold gas of 87Rb atoms based on electromagnetically induced transparency (EIT). Using low atomic density to avoid dephasing caused by atom-atom interactions, we measure a 1/*e* time of 30µs for the 80*S* state in free expansion. One of the dominant limitations is the combination of photon recoil and thermal atomic motion at 0.2µK. If the 1064-nm dipole trap is left on, then the 1/*e* time is reduced to 13 µs, in agreement with a model taking differential light shifts and gravitational sag into account. To characterize how coherent the retrieved light is, we overlap it with reference light and measure the visibility V of the resulting interference pattern, obtaining V>90% for short dark time. Our experimental work is accompanied by a detailed model for the dark-time decay of the retrieval efficiency of light stored in atomic ensembles. The model is generally applicable for photon storage in Dicke states, such as in EIT with $\lamda$-type or ladder-type level schemes and in Duan-Lukin-Cirac-Zoller single-photon sources. The model includes a treatment of the dephasing caused by thermal atomic motion combined with net photon recoil, as well as the influence of trapping potentials. It takes into account that the signal light field is typically not a plane wave. The model maps the retrieval efficiency to single-atom properties and shows that the retrieval efficiency is related to the decay of fringe visibility in Ramsey spectroscopy and to the spatial first-order coherence function of the gas.

##### Dark-time decay of the retrieval efficiency of light stored as a Rydberg excitation in a noninteracting ultracold gas

S. Schmidt-Eberle, T. Stolz, G. Rempe, and S.Dürr.

Physical Review A 101, 13421 (2020).

We study the dark-time decay of the retrieval efficiency for light stored in a Rydberg state in an ultracold gas of 87Rb atoms based on electromagnetically induced transparency (EIT). Using low atomic density to avoid dephasing caused by atom-atom interactions, we measure a 1/e time of 30 μs for the 80S state in free expansion. One of the dominant limitations is the combination of photon recoil and thermal atomic motion at 0.2 μK. If the 1064-nm dipole trap is left on, then the 1/e time is reduced to 13 μs, in agreement with a model taking differential light shifts and gravitational sag into account. To characterize how coherent the retrieved light is, we overlap it with reference light and measure the visibility V of the resulting interference pattern, obtaining V>90% for short dark time. Our experimental work is accompanied by a detailed model for the dark-time decay of the retrieval efficiency of light stored in atomic ensembles. The model is generally applicable for photon storage in Dicke states, such as in EIT with Λ-type or ladder-type level schemes and in Duan-Lukin-Cirac-Zoller single-photon sources. The model includes a treatment of the dephasing caused by thermal atomic motion combined with net photon recoil, as well as the influence of trapping potentials. It takes into account that the signal light field is typically not a plane wave. The model maps the retrieval efficiency to single-atom properties and shows that the retrieval efficiency is related to the decay of fringe visibility in Ramsey spectroscopy and to the spatial first-order coherence function of the gas.

##### Large Spin Hall Magnetoresistance in Antiferromagnetic alpha-Fe2O3/Pt Heterostructures

J. Fischer, M. Althammer, N. Vlietstra, H. Huebl, S.T.B. Goennenwein, R. Gross, S. Gepraegs, M. Opel

Physical Review Applied 13 (1), 014019 (2020).

We investigate the spin Hall magnetoresistance (SMR) at room temperature in thin-film heterostructures of antiferromagnetic insulating (0001)-oriented alpha-Fe2O3 (hematite) and Pt. We measure their longitudinal and transverse resistivities while rotating an applied magnetic field of up to 17 T in three orthogonal planes. For out-of-plane magnetotransport measurements, we find indications for a multidomain antiferromagnetic configuration whenever the field is aligned along the film normal. For in-plane field rotations, we clearly observe a sinusoidal resistivity oscillation characteristic for the SMR due to a coherent rotation of the Neel vector. The maximum SMR amplitude of 0.25% is, surprisingly, twice as high as for prototypical ferrimagnetic Y3Fe5O12/Pt heterostructures. The SMR effect saturates at much smaller magnetic fields than in comparable antiferromagnets, making the alpha-Fe2O3/Pt system particularly interesting for roomtemperature antiferromagnetic spintronic applications.

##### Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains

J. Vijayan, P. Sompet, G. Salomon, J. Koepsell, S. Hirthe, A. Bohrdt, F. Grusdt, I. Bloch, and C. Gross

Science 10, 186-189 (2020).

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

##### Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime

P.T. Nam, M. Napiórkowski, J. Ricaud, A. Triay

We study the Bose-Einstein condensates of trapped Bose gases in the Gross-Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross-Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Our work extends the previous results of Lieb, Seiringer and Yngvason on the leading order convergence, and of Boccato, Brennecke, Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of 'completing the square', inspired by recent works of Brietzke, Fournais and Solovej on the Lee-Huang-Yang formula, and a general estimate for Bogoliubov quadratic Hamiltonians on Fock space.

##### Long-Distance Distribution of Atom-Photon Entanglement at Telecom Wavelength

T. van Leent, M. Bock, R. Garthoff, K. Redeker, W. Zhang, T. Bauer, W. Rosenfeld, C. Becher, and H. Weinfurter.

Physical Review Letters 124, 010510 (2020).

Entanglement between stationary quantum memories and photonic channels is the essential resource for future quantum networks. Together with entanglement distillation, it will enable efficient distribution of quantum states. We report on the generation and observation of entanglement between a 87Rb atom and a photon at telecom wavelength transmitted through up to 20 km of optical fiber. For this purpose, we use polarization-preserving quantum frequency conversion to transform the wavelength of a photon entangled with the atomic spin state from 780 nm to the telecom *S* band at 1522 nm. We achieve an unprecedented external device conversion efficiency of 57% and observe an entanglement fidelity between the atom and telecom photon of ?78.5±0.9% after transmission through 20 km of optical fiber, mainly limited by decoherence of the atomic state. This result is an important milestone on the road to distribute quantum information on a large scale.

##### Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

N.O. Linden, M. Zingl, C. Hubig, O. Parcollet, U. Schollwoeck

Physical Review B 101 (4), 041101 (2020).

Using an imaginary-time matrix-product state (MPS) based quantum impurity solver we perform a realistic dynamical mean-field theory (DMFT) calculation combined with density functional theory (DFT) for Sr2RuO4. We take the full Hubbard-Kanamori interactions and spin-orbit coupling (SOC) into account. The MPS impurity solver works at essentially zero temperature in the presence of SOC, a regime of parameters currently inaccessible to continuous-time quantum Monte Carlo methods, due to a severe sign problem. We show that earlier results obtained at high temperature, namely, that the diagonal self-energies are nearly unaffected by SOC and that interactions lead to an effective enhancement of the SOC, hold even at low temperature. We observe that realism makes the numerical solution of the impurity model with MPS much more demanding in comparison to earlier works on Bethe lattice models, requiring several algorithmic improvements.

##### Turing Computability of Fourier Transforms of Bandlimited and Discrete Signals

H. Boche, U.J. Mönich.

IEEE Transactions on Signal Processing 68, 532-547 (2020).

The Fourier transform is an important operation in signal processing. However, its exact computation on digital computers can be problematic. In this paper we consider the computability of the Fourier transform and the discrete-time Fourier transform (DTFT). We construct a computable bandlimited absolutely integrable signal that has a continuous Fourier transform, which is, however, not Turing computable. Further, we also construct a computable sequence such that the DTFT is not Turing computable. Turing computability models what is theoretically implementable on a digital computer. Hence, our result shows that the Fourier transform of certain signals cannot be computed on digital hardware of any kind, including CPUs, FPGAs, and DSPs. This also implies that there is no symmetry between the time and frequency domain with respect to computability. Therefore, numerical approaches which employ the frequency domain representation of a signal (like calculating the convolution by performing a multiplication in the frequency domain) can be problematic. Interestingly, an idealized analog machine can compute the Fourier transform. However, it is unclear whether and how this theoretical superiority of the analog machine can be translated into practice. Further, we show that it is not possible to find an algorithm that can always decide for a given signal whether the Fourier transform is computable or not.

##### Accurate photonic temporal mode analysis with reduced resources

O. Morin, S. Langenfeld, M. Körber, G. Rempe

Physical Review A 101, 13801 (2020).

The knowledge and thus characterization of the temporal modes of quantum light fields is important in many areas of quantum physics ranging from experimental setup diagnosis to fundamental-physics investigations. Recent results showed how the autocorrelation function computed from continuous-wave homodyne measurements can be a powerful way to access the temporal mode structure. Here, we push forward this method by providing a deeper understanding and by showing how to extract the amplitude and phase of the temporal mode function with reduced experimental resources. Moreover, a quantitative analysis allows us to identify a regime of parameters where the method provides a trustworthy reconstruction, which we illustrate experimentally.

##### Secure Communication and Identification Systems - Effective Performance Evaluation on Turing Machines

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Transactions on Information Forensics and Security 15, 1013-1025 (2020).

Modern communication systems need to satisfy pre-specified requirements on spectral efficiency and security. Physical layer security is a concept that unifies both and connects them with entropic quantities. In this paper, a framework based on Turing machines is developed to address the question of deciding whether or not a communication system meets these requirements. It is known that the class of Turing solvable problems coincides with the class of algorithmically solvable problems so that this framework provides the theoretical basis for effective verification of such performance requirements. A key issue here is to decide whether or not the performance functions, i.e., capacities, of relevant communication scenarios, particularly those with secrecy requirements and active adversaries, are Turing computable. This is a necessary condition for the corresponding communication protocols to be effectively verifiable. Within this framework, it is then shown that for certain scenarios including the wiretap channel the corresponding capacities are Turing computable. Next, a general necessary condition on the performance function for Turing computability is established. With this, it is shown that for certain scenarios, including the wiretap channel with an active jammer, the performance functions are not computable when deterministic codes are used. As a consequence, such performance functions are also not computable on all other computer architectures such as the von Neumann-architecture or the register machines.

##### Turing Computability of Fourier Transforms of Bandlimited and Discrete Signals

H. Boche, U.J. Moenich

IEEE Transactions on Signal Processing 68, 532-547 (2020).

The Fourier transform is an important operation in signal processing. However, its exact computation on digital computers can be problematic. In this paper we consider the computability of the Fourier transform and the discrete-time Fourier transform (DTFT). We construct a computable bandlimited absolutely integrable signal that has a continuous Fourier transform, which is, however, not Turing computable. Further, we also construct a computable sequence such that the DTFT is not Turing computable. Turing computability models what is theoretically implementable on a digital computer. Hence, our result shows that the Fourier transform of certain signals cannot be computed on digital hardware of any kind, including CPUs, FPGAs, and DSPs. This also implies that there is no symmetry between the time and frequency domain with respect to computability. Therefore, numerical approaches which employ the frequency domain representation of a signal (like calculating the convolution by performing a multiplication in the frequency domain) can be problematic. Interestingly, an idealized analog machine can compute the Fourier transform. However, it is unclear whether and how this theoretical superiority of the analog machine can be translated into practice. Further, we show that it is not possible to find an algorithm that can always decide for a given signal whether the Fourier transform is computable or not.

##### From Probabilistic Graphical Models to Generalized Tensor Networks for Supervised Learning

I. Glasser, N. Pancotti, J.I. Cirac

IEEE ACCESS 8, 68169-68182 (2020).

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as string-bond states, and architectures commonly used in machine learning. We provide an algorithm to train these networks in a supervised-learning context and show that they overcome the limitations of regular tensor networks in higher dimensions, while keeping the computation efficient. A method to combine neural networks and tensor networks as part of a common deep learning architecture is also introduced. We benchmark our algorithm for several generalized tensor network architectures on the task of classifying images and sounds, and show that they outperform previously introduced tensor-network algorithms. The models we consider also have a natural implementation on a quantum computer and may guide the development of near-term quantum machine learning architectures.

##### Denial-of-Service Attacks on Communication Systems: Detectability and Jammer Knowledge

H. Boche, R.F. Schaefer, H.V. Poor

IEEE Transactions on Signal Processing 68, 3754-3768 (2020).

Wireless communication systems are inherently vulnerable to intentional jamming. In this paper, two classes of such jammers are considered: those with partial and full knowledge. While the first class accounts for those jammers that know the encoding and decoding function, the latter accounts for those that are further aware of the actual transmitted message. Of particular interest are so-called denial-of-service (DoS) attacks in which the jammer is able to completely disrupt any transmission. Accordingly, it is of crucial interest for the legitimate users to detect such adversarial DoS attacks. This paper develops a detection framework based on Turing machines. Turing machines have no limitations on computational complexity and computing capacity and storage and can simulate any given algorithm. For both scenarios of a jammer with partial and full knowledge, it is shown that there exists no Turing machine which can decide whether or not a DoS attack is possible for a given channel and the corresponding decision problem is undecidable. On the other hand, it is shown for both scenarios that it is possible to algorithmically characterize those channels for which a DoS attack is not possible. This means that it is possible to detect those scenarios in which the jammer is not able to disrupt the communication. For all other channels, the Turing machine does not stop and runs forever making this decision problem semidecidable. Finally, it is shown that additional coordination resources such as common randomness make the communication robust against such attacks.

##### Random characteristics for Wigner matrices

Soosten, S. Warzel

Electronic Communications in Probability 24, 75 (2020).

We extend the random characteristics approach to Wigner matrices whose entries are not required to have a normal distribution. As an application, we give a simple and fully dynamical proof of the weak local semicircle law in the bulk.

##### Proof of the strong Scott conjecture for Chandrasekhar atoms

R.L. Frank, K. Merz, H. Siedentop, B. Simon

Pure and Applied Functional Analysis 5 (6), 1319 - 1356 (2020).

We consider a large neutral atom of atomic number Z, taking relativistic effects into account by assuming the dispersion relation √(c^2p^2+c^4). We study the behavior of the one-particle ground state density on the length scale Z−1 in the limit Z,c→∞ keeping Z/c fixed and find that the spherically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the generalization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density.

##### Cluster Expansions with Renormalized Activities and Applications to Colloids

S. Jansen, D. Tsagkarogiannis

Annales Henri Poincare