##### Quantum Communication Networks. Band 23. Foundations in Signal Processing

R. Bassoli, H. Boche, C. Deppe, R. Ferrara, F.H.P. Fitzek, G. Janssen, S. Saeedinaeeni

Communications and Networking, Springer Verlag (2021).

##### Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase

L.Physical Review A Rammelmüller, Y. Hou, J.E. Drut, J. Braun

Physical Review A 103, 043330 (2021).

We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized unitary Fermi gas are discussed in the context of the state of the art.

##### Computability of the Channel Reliability Function and Related Bounds

H. Boche, C. Deppe

2022 IEEE International Symposium on Information Theory (ISIT) (2022).

##### Spectral multiplexing of telecom emitters with stable transition frequency

A. Ulanowski, B.Merkel, A. Reiserer.

Science Advances 8, Issue 43 (2022).

In a quantum network, coherent emitters can be entangled over large distances using photonic channels. In solid-state devices, the required efficient light-emitter interface can be implemented by confining the light in nanophotonic structures. However, fluctuating charges and magnetic moments at the nearby interface then lead to spectral instability of the emitters. Here, we avoid this limitation when enhancing the photon emission up to 70(12)-fold using a Fabry-Perot resonator with an embedded 19-micrometer-thin crystalline membrane, in which we observe around 100 individual erbium emitters. In long-term measurements, they exhibit an exceptional spectral stability of <0.2 megahertz that is limited by the coupling to surrounding nuclear spins. We further implement spectrally multiplexed coherent control and find an optical coherence time of 0.11(1) milliseconds, approaching the lifetime limit of 0.3 milliseconds for the strongest-coupled emitters. Our results constitute an important step toward frequency-multiplexed quantum-network nodes operating directly at a telecommunication wavelength.

##### Narrow optical transitions in erbium-implanted silicon waveguides

A. Gritsch, L. Weiss, J. Früh, S. Rinner, A. Reiserer

Physical Review X 12, 041009 (2022).

The realization of a scalable architecture for quantum information processing is a major challenge of quantum science. A promising approach is based on emitters in nanostructures that are coupled by light. Here, we show that erbium dopants in high-purity silicon-on-insulator chips combine the ease of low-loss waveguide fabrication with < 1 GHz inhomogeneous broadening, strong optical transitions, and an outstanding optical coherence even at temperatures of 8 K, with an upper bound to the homogeneous linewidth of 20 kHz. Our study thus introduces a promising materials platform for the implementation of on-chip quantum memories, microwave-to-optical conversion, and distributed quantum information processing.

##### Semantic Security for Quantum Wiretap Channels

H. Boche, M. Cai, C. Deppe, R. Ferrara, M. Wiese

Journal of Mathematical Physics 63, 092204 (2022).

We consider the problem of semantic security via classical-quantum and quantum wiretap channels and use explicit constructions to transform a non-secure code into a semantically secure code, achieving capacity by means of biregular irreducible functions. Explicit parameters in finite regimes can be extracted from theorems. We also generalize the semantic security capacity theorem, which shows that a strongly secure code guarantees a semantically secure code with the same secrecy rate, to any quantum channel, including the infinite-dimensional and non-Gaussian ones.

##### Implementation and Experimental Evaluation of Reed-Solomon Identification

R. Ferrara, L. Torres,-Figueroa, H. Boche, C. Deppe, W. Labidi. U.J. Mönich, V.-C. Andrei

European Wireless 2022, Dresden, Germany (2022).

##### On the Arithmetic Complexity of the Bandwidth of Bandlimited Signals

H. Boche; Y.N. Böck; U.J. Mönich

IEEE Transactions on Information Theory (Early Access) (2022).

The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable bandlimited signals. To this end we employ the concept of Turing computability, which exactly describes what is theoretically feasible and can be computed on a digital computer. Recently, it has been shown that there exist computable bandlimited signals with finite energy, the actual bandwidth of which is not a computable number, and hence cannot be computed on a digital computer. In this work, we consider the most general class of band-limited signals, together with different computable descriptions thereof. Among other things, our analysis includes a characterization of the arithmetic complexity of the bandwidth of such signals and yields a negative answer to the question of whether it is at least possible to compute non-trivial upper or lower bounds for the bandwidth of a bandlimited signal. Furthermore, we relate the problem of bandwidth computation to the theory of oracle machines. In particular, we consider halting and totality oracles, which belong to the most frequently investigated oracle machines in the theory of computation.

##### Evaporation of microwave-shielded polar molecules to quantum degeneracy

A. Schindewolf, R.Bause, X.-Y. Chen, M. Duda, T. Karman, I. Bloch & X.-Y. Luo

Nature 607, 677–681 (2022).

Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter1,2,3,4,5,6,7,8,9, implement quantum information schemes10,11,12 and test the fundamental symmetries of nature13. Realizing their full potential requires cooling interacting molecular gases deeply into the quantum-degenerate regime. However, the intrinsically unstable collisions between molecules at short range have so far prevented direct cooling through elastic collisions to quantum degeneracy in three dimensions. Here we demonstrate evaporative cooling of a three-dimensional gas of fermionic sodium–potassium molecules to well below the Fermi temperature using microwave shielding. The molecules are protected from reaching short range with a repulsive barrier engineered by coupling rotational states with a blue-detuned circularly polarized microwave. The microwave dressing induces strong tunable dipolar interactions between the molecules, leading to high elastic collision rates that can exceed the inelastic ones by at least a factor of 460. This large elastic-to-inelastic collision ratio allows us to cool the molecular gas to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such cold and dense samples of polar molecules open the path to the exploration of many-body phenomena with strong dipolar interactions.

##### A device-independent quantum key distribution system for distant users

W. Zhang, T. van Leent, K. Redeker, R. Garthoff, R. Schwonnek, F. Fertig, S. Eppelt, V. Scarani, C. C.-W. Lim, H. Weinfurter.

Nature 604, 687–691 (2022).

Device-independent quantum key distribution (DIQKD) enables the generation of secret keys over an untrusted channel using uncharacterized and potentially untrusted devices1,2,3,4,5,6,7,8,9. The proper and secure functioning of the devices can be certified by a statistical test using a Bell inequality10,11,12. This test originates from the foundations of quantum physics and also ensures robustness against implementation loopholes13, thereby leaving only the integrity of the users’ locations to be guaranteed by other means. The realization of DIQKD, however, is extremely challenging—mainly because it is difficult to establish high-quality entangled states between two remote locations with high detection efficiency. Here we present an experimental system that enables for DIQKD between two distant users. The experiment is based on the generation and analysis of event-ready entanglement between two independently trapped single rubidium atoms located in buildings 400 metre apart14. By achieving an entanglement fidelity of F≥0.892(23) and implementing a DIQKD protocol with random key basis15, we observe a significant violation of a Bell inequality of S = 2.578(75)—above the classical limit of 2—and a quantum bit error rate of only 0.078(9). For the protocol, this results in a secret key rate of 0.07 bits per entanglement generation event in the asymptotic limit, and thus demonstrates the system’s capability to generate secret keys. Our results of secure key exchange with potentially untrusted devices pave the way to the ultimate form of quantum secure communications in future quantum networks.

##### Practical quantum advantage in quantum simulation

A. J. Daley, I.Bloch, C. Kokail, S. Flannigan, N. Pearson, M.Troyer & P. Zoller .

Nature 607, 667–676 (2022).

The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as ‘quantum advantage’. As a next step along the development of this technology, it is now important to discuss ‘practical quantum advantage’, the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital–analogue devices that exist today already promise substantial flexibility in near-term applications.

##### Entangling single atoms over 33 km telecom fibre

T. van Leent, M. Bock, F. Fertig, R. Garthoff, S. Eppelt, Y. Zhou, P. Malik, M. Seubert, T. Bauer, W. Rosenfeld, W.Zhang, C. Becher, H. Weinfurter.

Nature 607, 69–73 (2022).

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell’s inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom–photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11,12,13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

##### Computing Upper and Lower Bounds for the Bandwidth of Bandlimited Signals

H. Boche, U.J. Mönich, Y.N. Böck

2022 IEEE International Symposium on Information Theory (2022).

##### Communication With Unreliable Entanglement Assistance

U. Pereg, C. Deppe, H. Boche.

2022 IEEE International Symposium on Information Theory (ISIT) (2022).

Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter first prepares an entangled photon pair locally, and then transmits one of the photons to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance.

##### The Quantum MAC with Cribbing Encoders

U. Pereg, C. Deppe, H. Boche

2022 IEEE International Symposium on Information Theory (ISIT) (2022).

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.

##### Cavity-enhanced quantum network nodes

A. Reiserer

arXiv:2205.15380 (2022).

A future quantum network will consist of quantum processors that are connected by quantum channels, just like conventional computers are wired up to form the Internet. In contrast to classical devices, however, the entanglement and non-local correlations available in a quantum-controlled system facilitate novel fundamental tests of quantum theory. In addition, they enable numerous applications in distributed quantum information processing, quantum communication, and precision measurement.

While pioneering experiments have demonstrated the entanglement of two quantum nodes separated by up to 1.3 km, and three nodes in the same laboratory, accessing the full potential of quantum networks requires scaling of these prototypes to many more nodes and global distances. This is an outstanding challenge, posing high demands on qubit control fidelity, qubit coherence time, and coupling efficiency between stationary and flying qubits.

In this work, I will describe how optical resonators facilitate quantum network nodes that achieve the above-mentioned prerequisites in different physical systems -- trapped atoms, defect centers in wide-bandgap semiconductors, and rare-earth dopants -- by enabling high-fidelity qubit initialization and readout, efficient generation of qubit-photon and remote qubit-qubit entanglement, as well as quantum gates between stationary and flying qubits. These advances open a realistic perspective towards the implementation of global-scale quantum networks in the near future.

##### Trustworthiness Verification and Integrity Testing for Wireless Communication Systems

H. Boche, R.F. Schaefer, H.V. Poor and G.P. Fettweis

IEEE International Conference on Communications (2022).

##### Deciding the Problem of Remote State Estimation via Noisy Communication Channels on Real Number Signal Processing Hardware

H. Boche, Y. Böck, C. Deppe

IEEE International Conference on Communications

##### On non-detectability of non-computability and the degree of non-computability of solutions of circuit and wave equations on digital computers

H. Boche, V. Pohl

IEEE Transactions on Information Theory (2022).

##### Turing Meets Shannon: On the Algorithmic Construction of Channel-Aware Codes

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

IEEE Transactions on Communications 70 (4), 2256 - 2267 (2022).

A capacity result involves two parts: achievability and converse. The achievability proof is usually non-constructive and only the existence of capacity-achieving codes is shown invoking probabilistic techniques. Recently, capacity-achieving codes have been found for several channels demonstrating that such codes can actually be constructed algorithmically. To this end, each construction is designed for a pre-specified channel so that the corresponding algorithm is specifically tailored to it. This paper addresses the general question of whether or not it is possible to find algorithms that can construct capacity-achieving codes for a whole class of channels. To do so, the concept of Turing machines is used which provides the fundamental performance limits of digital computers and therewith fully specifies which tasks are algorithmically feasible in principle. It is shown that there exists no Turing machine that is able to construct capacity-achieving codes for a whole class of channels, where the channel realization from this class is given as an input to the Turing machine. It is further shown that such an algorithmic construction remains impossible when the optimality condition is dropped and codes only need to achieve a fraction of the capacity. Finally, implications on channel-aware transmission, link adaptation, and cross-layer optimization are discussed.

##### On 6G and trustworthiness

G.P. Fettweis, H. Boche

Communications of the ACM 65 (4), 48–49 (2022).

##### An Information-Theoretic Perspective on Quantum Repeaters

U. Pereg, C. Deppe, H. Boche

25th Annual Conference on Quantum Information Processing (2022).

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing, where Receiver 1 can send classical messages to Receiver 2. Another cooperation setting involves quantum conferencing, where Receiver 1 can teleport a quantum state to Receiver 2. When Receiver 1 is not required to recover information and its sole purpose is to help the transmission to Receiver 2, the model reduces to the quantum primitive relay channel. The quantum conferencing setting is intimately related to quantum repeaters, as the sender, Receiver 1, and Receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. In particular, the cutset upper bound and the decode-forward lower bound are derived for the primitive relay channel. Furthermore, we present an entanglement-formation lower bound, where a virtual channel is simulated through the conference link. At last, we show that as opposed to the multiple access channel with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.

##### Light-Induced Quantum Droplet Phases of Lattice Bosons in Multimode Cavities

P. Karpov, F. Piazza

Physical Review Letters 128, 103201 (2022).

Multimode optical cavities can be used to implement interatomic interactions which are highly tunable in strength and range. For bosonic atoms trapped in an optical lattice we show that, for any finite range of the cavity-mediated interaction, quantum self-bound droplets dominate the ground state phase diagram. Their size and in turn density is not externally fixed but rather emerges from the competition between local repulsion and finite-range cavity-mediated attraction. We identify two different regimes of the phase diagram. In the strongly glued regime, the interaction range exceeds the droplet size and the physics resembles the one of the standard Bose-Hubbard model in a (self-consistent) external potential, where in the phase diagram two incompressible droplet phases with different filling are separated by one with a superfluid core. In the opposite weakly glued regime, we find instead direct first order transitions between the two incompressible phases, as well as pronounced metastability. The cavity field leaking out of the mirrors can be measured to distinguish between the various types of droplets.

##### On the Semi-Decidability of the Remote State Estimation Problem

H. Boche, Y. Bock, C. Deppe

IEEE Transactions on Automatic Control (2022).

We consider the decision problem associated with the task of remotely estimating the state of a dynamic plant via a noisy communication channel. Given a machine-readable description of the plants and channels characteristics, does there exist an algorithm that decides whether remote state estimation is possible From an analytic point of view, this problem has been shown to involve the zero-error capacity of the communication channel. By applying results from Turing machine theory and zero-error coding, we analyze several related variants of the decision problem above. Our analysis also incorporates a weakened form of the state estimation objective, which has been shown to depend on the classical Shannon Capacity instead. In the broadest sense, our results yield a fundamental limit to the capabilities of computer-aided design tools and adaptive autonomous systems, assuming they are based on digital hardware.

##### Classical state masking over a quantum channel

U. Pereg, C. Deppe, H. Boche

Physical Review A 105, 022442 (2022).

Transmission of classical information over a quantum state-dependent channel is considered, when the encoder can measure channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. In this quantum setting, it is essential to conceal the CSI measurement as well. A regularized formula is derived for the masking equivocation region, and a full characterization is established for a class of measurement channels.

##### The Quantum Multiple-Access Channel with Cribbing Encoders

U. Pereg, C. Deppe, H. Boche

IEEE Transactions on Information Theory (2022).

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2’s cribbing may inflict a “state collapse” for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.

##### Complexity Blowup if Continuous-Time LTI Systems are Implemented on Digital Hardware

H. Boche, V. Pohl

2021 60th IEEE Conference on Decision and Control (CDC) (2021).

This paper shows that every simple but non-trivial continuous-time, linear time-invariant (LTI) system shows a complexity blowup if its output is simulated on a digital computer. This means that for a given LTI system, a Turing machine can compute a low-complexity input signal in polynomial-time but which yields a corresponding output signal which has high complexity in the sense that the computation time for determining an approximation up to n significant digits grows faster than any polynomial in n. A similar complexity blowup is observed for the calculation of Fourier series approximations and the Fourier transform.

##### Mosaics of combinatorial designs for information-theoretic security

M. Wiese, H. Boche

Designs, Codes and Cryptography 1630-1635 (2022).

We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and privacy amplification for secret key generation. The security functions are functional forms of mosaics of combinatorial designs, more precisely, of group divisible designs and balanced incomplete block designs. Every member of a mosaic is associated with a unique color, and each color corresponds to a unique message or key value. Every block index of the mosaic corresponds to a public seed shared between the two trusted communicating parties. The seed set should be as small as possible. We give explicit examples which have an optimal or nearly optimal trade-off of seed length versus color (i.e., message or key) rate. We also derive bounds for the security performance of security functions given by functional forms of mosaics of designs.

##### Logarithmic estimates for mean-field models in dimension two and the Schrodinger-Poisson system

J. Dolbeault, R.L. Frank, L. Jeanjean

Comptes Rendus Mathematique 359, 1279-1293 (2021).

In dimension two, we investigate a free energy and the ground state energy of the Schrodinger-Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of the problem. Such a system can be considered as a nonlinear Schrodinger equation with a cubic but nonlocal Poisson nonlinearity, and a local logarithmic nonlinearity. Both cases of repulsive and attractive forces are considered. We also assume that there is an external potential with minimal growth at infinity, which turns out to have a logarithmic growth. Our estimates rely on new logarithmic interpolation inequalities which combine logarithmic Hardy-Littlewood-Sobolev and logarithmic Sobolev inequalities. The two-dimensional model appears as a limit case of more classical problems in higher dimensions.

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

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

Physical Review B 104, 235151 (2021).

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.

##### Distinguishing an Anderson insulator from a many-body localized phase through space-time snapshots with neural networks

F. Kotthoff, F. Pollmann, G. De Tomasi

Physical Review B 104, 224307 (2021).

Distinguishing the dynamics of an Anderson insulator from a many-body localized (MBL) phase is an experimentally challenging task. In this work we propose a method based on machine learning techniques to analyze experimental snapshot data to separate the two phases. We show how to train three-dimensional convolutional neural networks (CNNs) using space-time Fock-state snapshots, allowing us to obtain dynamic information about the system. We benchmark our method on a paradigmatic model showing MBL (t-V model with quenched disorder), where we obtain a classification accuracy of approximate to 80% between an Anderson insulator and an MBL phase. We underline the importance of providing temporal information to the CNNs and we show that CNNs learn the crucial difference between an Anderson localized and an MBL phase, namely the difference in the propagation of quantum correlations. Particularly, we show that the misclassified MBL samples are characterized by an unusually slow propagation of quantum correlations, and thus the CNNs label them wrongly as Anderson localized. Finally, we apply our method to the case with quasiperiodic potential, known as the Aubry-Andre model (AA model). We find that the CNNs have more difficulties in separating the two phases. We show that these difficulties are due to the fact that the MBL phase of the AA model is characterized by a slower information propagation for numerically accessible system sizes.

##### Gapless Topological Phases and Symmetry-Enriched Quantum Criticality

R. Verresen, R. Thorngren, N.G. Jones, F. Pollmann

Physical Review X 11, 041059 (2021).

We introduce topological invariants for gapless systems and study the associated boundary phenomena. More generally, the symmetry properties of the low-energy conformal field theory (CFT) provide discrete invariants establishing the notion of symmetry-enriched quantum criticality. The charges of nonlocal scaling operators, or more generally, of symmetry defects, are topological and imply the presence of localized edge modes. We primarily focus on the 1 + 1d case where the edge has a topological degeneracy, whose finite-size splitting can be exponential or algebraic in system size depending on the involvement of additional gapped sectors. An example of the exponential case is given by tuning the spin-1 Heisenberg chain to a symmetry-breaking Ising phase. An example of the algebraic case arises between the gapped Ising and cluster phases: This symmetry-enriched Ising CFT has an edge mode with finite-size splitting scaling as 1/L14. In addition to such new cases, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer-including a complete characterization of symmetry-enriched 1 + 1d Ising CFTs. Nontrivial topological invariants can also be constructed in higher dimensions, which we illustrate for a symmetry-enriched 2 + 1d CFT without gapped sectors.

##### Foundation of One-Particle Reduced Density Matrix Functional Theory for Excited States

J. Liebert, F. Castillo, J.-P. Labbé, C. Schilling

Journal of Chemical Theory and Computation 18 (1), 124-140 (2022).

In Phys. Rev. Lett. 2021, 127, 023001 a reduced density matrix functional theory (RDMFT) was proposed for calculating energies of selected eigenstates of interacting many-Fermion systems. Here, we develop a solid foundation for this so-called w-RDMFT and present the details of various derivations. First, we explain how a generalization of the Ritz variational principle to ensemble states with fixed weights w in combination with the constrained search would lead to a universal functional of the one-particle reduced density matrix. To turn this into a viable functional theory, however, we also need to implement an exact convex relaxation. This general procedure includes Valone's pioneering work on ground state RDMFT as the special case w = (1,0, ...) Then, we work out in a comprehensive manner a methodology for deriving a compact description of the functional's domain. This leads to a hierarchy of generalized exclusion principle constraints which we illustrate in great detail. By anticipating their future pivotal role in functional theories and to keep our work self-contained, several required concepts from convex analysis are introduced and discussed.

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

C. Delcamp, N. Schuch

Quantum 5, 604 (2021).

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.

##### Benchmarking the Accuracy of the Direct Random Phase Approximation and sigma-Functionals for NMR Shieldings

M. Glasbrenner, D. Graf, C. Ochsenfeld

Journal of Chemical Theory and Computation 18, 192–205 (2021).

A method for computing NMR shieldings with the direct random phase approximation (RPA) and the closely related σ-functionals [Trushin, E.; Thierbach, A.; Görling, A. Toward chemical accuracy at low computational cost: density functional theory with σ-functionals for the correlation energy. J. Chem. Phys.2021,154, 014104] is presented, which is based on a finite-difference approach. The accuracy is evaluated in benchmark calculations using high-quality coupled cluster values as a reference. Our results show that the accuracy of the computed NMR shieldings using direct RPA is strongly dependent on the density functional theory reference orbitals and improves with increasing amounts of exact Hartree–Fock exchange in the functional. NMR shieldings computed with direct RPA using a Hartree–Fock reference are significantly more accurate than MP2 shieldings and comparable to CCSD shieldings. Also, the basis set convergence is analyzed and it is shown that at least triple-zeta basis sets are required for reliable results.

##### Atomic waveguide QED with atomic dimers

D. Castells-Graells, D. Malz, C.C. Rusconi, J.I. Cirac

Physical Review A 104, 063707 (2021).

Quantum emitters coupled to a waveguide are a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use antisymmetric states of atomic dimers—a pair of closely spaced atoms—as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide-mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.

##### Efficient low-scaling computation of NMR shieldings at the second-order Moller-Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric

M. Glasbrenner, S. Vogler, C.Ochsenfeld

Journal of Chemical Physics 155, 224107 (2021).

A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller–Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller–Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.

##### Visualizing spinon Fermi surfaces with time-dependent spectroscopy

A. Schuckert, A. Bohrdt, E. Crane, F. Grusdt

Physical Review B 104, 235107 (2021).

Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. To probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid-state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photoemission spectroscopy, an established tool in solid-state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional t-J model with a single hole that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing us to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground-state energy at momentum q = (pi, pi), where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route toward solving the mystery of the Fermi arcs in the cuprate materials.

##### Optomechanics for quantum technologies

S. Barzanjeh, A. Xuereb, S. Gröblacher, M. Paternostro, C.A. Regal, E.M. Weig

Nature Physics 18, 15-24 (2022).

Interaction with light can be used to precisely control motional states. This Review surveys recent progress in the preparation of non-classical mechanical states and in the application of optomechanical platforms to specific tasks in quantum technology. The ability to control the motion of mechanical systems through interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the focus has now turned towards creating and exploiting interesting non-classical states of motion and entanglement in optomechanical systems. Quantumness has also shifted from being the very reason why experiments are constructed to becoming a resource for the investigation of fundamental physics and the creation of quantum technologies. Here, by focusing on opto- and electromechanical platforms we review recent progress in quantum state preparation and entanglement of mechanical systems, together with applications to signal processing and transduction, quantum sensing and topological physics, as well as small-scale thermodynamics.

##### Abelian SU(N)(1) chiral spin liquids on the square lattice

J.-Y. Chen, J.-W. Li, P. Nataf, S. Capponi, M. Mambrini, K. Totsuka, H.-H. Tu, A. Weichselbaum, J. von Delft, D. Poilblanc

Physical Review B 104, 235104 (2021).

In the physics of the fractional quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin like systems, we propose a family of SU(N)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for arbitrary N of an SU(3) model studied previously where time-reversal symmetry is broken explicitly. Guided by the recent discovery of SU(2)1 and SU(3)1 chiral spin liquids (CSL) on similar models we search for topological SU(N)1 CSL in some range of the Hamiltonian parameters via a combination of complementary numerical methods such as exact diagonalizations (ED), infinite density matrix renormalization group (iDMRG) and infinite Projected Entangled Pair State (iPEPS). Extensive ED on small (periodic and open) clusters up to N=10 and an innovative SU(N)-symmetric version of iDMRG to compute entanglement spectra on (infinitely long) cylinders in all topological sectors provide unambiguous signatures of the SU(N)1 character of the chiral liquids. An SU(4)-symmetric chiral PEPS, constructed in a manner similar to its SU(2) and SU(3) analogs, is shown to give a good variational ansatz of the N=4 ground state, with chiral edge modes originating from the PEPS holographic bulk-edge correspondence. Finally, we discuss the possible observation of such Abelian CSL in ultracold atom setups where the possibility of varying N provides a tuning parameter similar to the magnetic field in the physics of the FQH effect.

##### 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

Science 374, 1237-1241 (2021).

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

##### Primordial black holes from confinement

G. Dvali, F. Kühnel, M. Zantedeschi

Physical Review D 104, 123507 (2021).

A mechanism for the formation of primordial black holes is proposed. Here, heavy quarks of a confining gauge theory produced by de Sitter fluctuations are pushed apart by inflation and get confined after horizon reentry. The large amount of energy stored in the color flux tubes connecting the quark pair leads to black-hole formation. These are much lighter and can be of higher spin than those produced by standard collapse of horizon-size inflationary overdensities. Other difficulties exhibited by such mechanisms are also avoided. Phenomenological features of the new mechanism are discussed as well as accounting for both the entirety of the dark matter and the supermassive black holes in the galactic centers. Under proper conditions, the mechanism can be realized in a generic confinement theory, including ordinary QCD. We discuss a possible string-theoretic realization via D-branes. Interestingly, for conservative values of the string scale, the produced gravity waves are within the range of recent NANOGrav data. Simple generalizations of the mechanism allow for the existence of a significant scalar component of gravity waves with distinct observational signatures.

##### Purcell enhanced coupling of nanowire quantum emitters to silicon photonic waveguides

N. Mukhundhan, A. Ajay, J. Bissinger, J.J. Finley, G. Koblmüller

Optics Express 29 (26), 43068-43081 (2021).

We design a quantum dot (QD) embedded in a vertical-cavity photonic nanowire (NW), deterministically integrated on a silicon-on-insulator (SOI) waveguide (WG), as a novel quantum light source in a quantum photonic integrated circuit (QPIC). Using a broadband QD emitter, we perform finite-difference time domain simulations to systematically tune key geometrical parameters and to explore the coupling mechanisms of the emission to the NW and WG modes. We find distinct Fabry-Perot resonances in the Purcell enhanced emission that govern the outcoupled power into the fundamental TE mode of the SOI-WG. With an optimized geometry that places the QD emitter in a finite NW in close proximity to the WG, we obtain peak outcoupling efficiencies for polarized emission as high as eighty percent. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.

##### Comparative study of state-of-the-art matrix-product-state methods for lattice models with large local Hilbert spaces without U(1) symmetry

J. Stolppa, T. Köhler, S.R. Manmana, E. Jeckelmann, F. Heidrich-Meisner, S. Paeckel

Computer Physics Communications 269, 108106 (2021).

Lattice models consisting of high-dimensional local degrees of freedom without global particle-number conservation constitute an important problem class in the field of strongly correlated quantum many-body systems. For instance, they are realized in electron-phonon models, cavities, atom-molecule resonance models, or superconductors. In general, these systems elude a complete analytical treatment and need to be studied using numerical methods where matrix-product states (MPSs) provide a flexible and generic ansatz class. Typically, MPS algorithms scale at least quadratic in the dimension of the local Hilbert spaces. Hence, tailored methods, which truncate this dimension, are required to allow for efficient simulations. Here, we describe and compare three state-of-the-art MPS methods each of which exploits a different approach to tackle the computational complexity. We analyze the properties of these methods for the example of the Holstein model, performing high-precision calculations as well as a finite-size-scaling analysis of relevant ground-state observables. The calculations are performed at different points in the phase diagram yielding a comprehensive picture of the different approaches.

##### Exploration of doped quantum magnets with ultracold atoms

A. Bohrdt, L. Homeier, C. Reinmoser, E. Demlerde, F. Grusdt

Annals of Physics 435, 168651 (2021).

In the last decade, quantum simulators, and in particular cold atoms in optical lattices, have emerged as a valuable tool to study strongly correlated quantum matter. These experiments are now reaching regimes that are numerically difficult or impossible to access. In particular they have started to fulfill a promise which has contributed significantly to defining and shaping the field of cold atom quantum simulations, namely the exploration of doped and frustrated quantum magnets and the search for the origins of high-temperature superconductivity in the fermionic Hubbard model. Despite many future challenges lying ahead, such as the need to further lower the experimentally accessible temperatures, remarkable studies have already been conducted. Among them, spin-charge separation in one-dimensional systems has been demonstrated, extended-range antiferromagnetism in two-dimensional systems has been observed, connections to modern day large-scale numerical simulations were made, and unprecedented comparisons with microscopic trial wavefunctions have been carried out at finite doping. In many regards, the field has acquired new realms, putting old ideas to a new test and producing new insights and inspiration for the next generation of physicists. In the first part of this paper, we review the results achieved in cold atom realizations of the Fermi-Hubbard model in recent years. We put special emphasis on the new probes available in quantum gas microscopes, such as higher-order correlation functions, full counting statistics, the ability to study far-from -equilibrium dynamics, machine learning and pattern recognition of instantaneous snapshots of the many-body wavefunction, and access to non-local correlators. Our review is written from a theoretical perspective, but aims to provide basic understanding of the experimental procedures. We cover one- dimensional systems, where the phenomenon of spin-charge separation is ubiquitous, and two-dimensional systems where we distinguish between situations with and without doping. Throughout, we focus on the strong coupling regime where the Hubbard inter-actions U dominate and connections to t - J models can be justified. In the second part of this paper, with the stage set and the current state of the field in mind, we propose a new direction for cold atoms to explore: namely mixed-dimensional bilayer systems, where the charge motion is restricted to individual layers which remain coupled through spin-exchange. These systems can be directly realized experimentally and we argue that they have a rich phase diagram, potentially including a strongly correlated BEC-to-BCS cross-over and regimes with different superconducting order parameters, as well as complex parton phases and possibly even analogs of tetraquark states. In particular, we propose a novel, strong pairing mechanism in these systems, which puts the formation of hole pairs at experimentally accessible, elevated temperatures within reach. Ultimately we propose to explore how the physics of the mixed-dimensional bilayer system can be connected to the rich phenomenology of the single-layer Hubbard model. (C) 2021 Elsevier Inc. All rights reserved.

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

J. Feldmeier, M. Knap

Physical Review Letters 127, 235301 (2021).

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.

##### Magnon transport in Y3Fe5O12/Pt nanostructures with reduced effective magnetization

J. Gückelhorn, T. Wimmer, M. Müller, S. Geprägs, H. Huebl, R. Gross, M. Althammer

Physical Review B 104, L180410 (2021).

For applications making use of magnonic spin currents damping effects, which decrease the spin conductivity, have to be minimized. We here investigate the magnon transport in a yttrium iron garnet thin film with strongly reduced effective magnetization. We show that in a three-terminal device the effective magnon conductivity can be increased by a factor of up to six by a current applied to a modulator electrode, which generates damping compensation above a threshold current. Moreover, we find a linear dependence of this threshold current on the applied magnetic field. We can explain this behavior by the reduced effective magnetization and the associated nearly circular magnetization precession.

##### Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

A. Tilloy, H.M. Wiseman

Quantum 5, 594 (2021).

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrodinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrodinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists 'unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between 'true' (Markovian) collapse models and non-Markovian models.

##### Quantum Circuits Assisted by Local Operations and Classical Communication: Transformations and Phases of Matter

L. Piroli, G. Styliaris, J.I. Cirac

Physical Review Letters 127, 220503 (2021).

We introduce deterministic state-transformation protocols between many-body quantum states that can be implemented by low-depth quantum circuits followed by local operations and classical communication. We show that this gives rise to a classification of phases in which topologically ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by local operations and classical communication in this scenario, allowing one to perform certain large-depth quantum circuits in terms of low-depth ones.

##### Bulk topological signatures of a quasicrystal

G. Rai, H. Schlömer, C. Matsumura, S. Haas, A. Jagannathan

Physical Review B 104, 184202 (2021).

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total on-site charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the topological label of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain-the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

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

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

Nature 599, 383-392 (2021).

The design and control of material interfaces is a foundational approach to realize technologically useful effects and engineer material properties. This is especially true for two-dimensional (2D) materials, where van der Waals stacking allows disparate materials to be freely stacked together to form highly customizable interfaces. This has underpinned a recent wave of discoveries based on excitons in stacked double layers of transition metal dichalcogenides (TMDs), the archetypal family of 2D semiconductors. In such double-layer structures, the elegant interplay of charge, spin and moiré superlattice structure with many-body effects gives rise to diverse excitonic phenomena and correlated physics. Here we review some of the recent discoveries that highlight the versatility of TMD double layers to explore quantum optics and many-body effects. We identify outstanding challenges in the field and present a roadmap for unlocking the full potential of excitonic physics in TMD double layers and beyond, such as incorporating newly discovered ferroelectric and magnetic materials to engineer symmetries and add a new level of control to these remarkable engineered materials.

##### Encoding-dependent generalization bounds for parametrized quantum circuits

M.C. Caro, E. Gil-Fuster, J.J. Meyer, J. Eisert, R. Sweke

Quantum 5, 582 (2021).

A large body of recent work has begun to explore the potential of parametrized quantum circuits (PQCs) as machine learning models, within the framework of hybrid quantum-classical optimization. In particular, theoretical guarantees on the out-of-sample performance of such models, in terms of generalization bounds, have emerged. However, none of these generalization bounds depend explicitly on how the classical input data is encoded into the PQC. We derive generalization bounds for PQC-based models that depend explicitly on the strategy used for data-encoding. These imply bounds on the performance of trained PQC-based models on unseen data. Moreover, our results facilitate the selection of optimal data-encoding strategies via structural risk minimization, a mathematically rigorous framework for model selection. We obtain our generalization bounds by bounding the complexity of PQC-based models as measured by the Rademacher complexity and the metric entropy, two complexity measures from statistical learning theory. To achieve this, we rely on a representation of PQC-based models via trigonometric functions. Our generalization bounds emphasize the importance of well-considered data-encoding strategies for PQC-based models.

##### Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects

V. Alba, B. Bertini, M. Fagotti, L. Piroli, P. Ruggiero

Journal of Statistical Mechanics-Theory and Experiment 11, 114004 (2021).

We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of the theory. Finally, we present some open questions and suggest perspectives on possible future directions.

##### Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer

S. Mardazad, Y.H. Xu, M. Grundner, U. Schollwock, H.B. Ma, S. Paeckel

Journal of Chemical Physics 155, 194101 (2021).

In this work, we study singlet fission in tetracene para-dimers, covalently linked by a phenyl group. In contrast to most previous studies, we account for the full quantum dynamics of the combined excitonic and vibrational system. For our simulations, we choose a numerically unbiased representation of the molecule's wave function, enabling us to compare with experiments, exhibiting good agreement. Having access to the full wave function allows us to study in detail the post-quench dynamics of the excitons. Here, one of our main findings is the identification of a time scale t(0) & AP; 35 fs dominated by coherent dynamics. It is within this time scale that the larger fraction of the singlet fission yield is generated. We also report on a reduced number of phononic modes that play a crucial role in the energy transfer between excitonic and vibrational systems. Notably, the oscillation frequency of these modes coincides with the observed electronic coherence time t(0). We extend our investigations by also studying the dependency of the dynamics on the excitonic energy levels that, for instance, can be experimentally tuned by means of the solvent polarity. Here, our findings indicate that the singlet fission yield can be doubled, while the electronic coherence time t(0) is mainly unaffected.& nbsp; 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/).

##### 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

##### Variational method in relativistic quantum field theory without cutoff

A. Tilloy

Physical Review D 104, L091904 (2021).

The variational method is a powerful approach to solve many-body quantum problems nonperturbatively. However, in the context of relativistic quantum field theory, it needs to meet three seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the three, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the three requirements jointly in 1 + 1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.

##### Relativistic continuous matrix product states for quantum fields without cutoff

A. Tilloy

Physical Review D 104, 096007 (2021).

I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine (1 +Y 1)dimensional QFT without UV cutoff and directly in the thermodynamic limit. The main idea is to work directly in the basis that diagonalizes the free part of the model considered, which allows one to fit its short distance behavior exactly. This makes computations slightly less trivial than with standard CMPS. However, they remain feasible, and I present all the steps needed for the optimization. The asymptotic cost as a function of the bond dimension remains the same as for standard CMPS. I illustrate the method on the self-interacting scalar field, also known as the phi(4)(2) model. Aside from providing unequaled precision in the continuum, the numerical results obtained are truly variational, and thus provide rigorous energy upper bounds.

##### Locally Accurate Tensor Networks for Thermal States and Time Evolution

Á.M. Alhambra, J.I. Cirac

PRX Quantum 2, 040331 (2021).

Tensor-network methods are routinely used in approximating various equilibrium and nonequilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct projected entangled-pair operators that approximate, for all local observables, (i) their thermal expectation values and (ii) their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.

##### Beyond the standard quantum limit for parametric amplification of broadband signals

M. Renger, S. Pogorzalek, Q. Chen, Y. Nojiri, K. Inomata, Y. Nakamura, M. Partanen, A. Marx, R. Gross, F. Deppe, K.G. Fedorov

Npj Quantum Information 7, 160 (2021).

The low-noise amplification of weak microwave signals is crucial for countless protocols in quantum information processing. Quantum mechanics sets an ultimate lower limit of half a photon to the added input noise for phase-preserving amplification of narrowband signals, also known as the standard quantum limit (SQL). This limit, which is equivalent to a maximum quantum efficiency of 0.5, can be overcome by employing nondegenerate parametric amplification of broadband signals. We show that, in principle, a maximum quantum efficiency of unity can be reached. Experimentally, we find a quantum efficiency of 0.69 +/- 0.02, well beyond the SQL, by employing a flux-driven Josephson parametric amplifier and broadband thermal signals. We expect that our results allow for fundamental improvements in the detection of ultraweak microwave signals.

##### Spectral asymmetry of phonon sideband luminescence in monolayer and bilayer WSe2

- V. Funk, K. Wagner, E. Wietek, J.D. Ziegler, J. Förste, J. Lindlau, M. Förg, K. Watanabe, T. Taniguchi, A. Chernikov, A. Högele

Physical Review Research 3, L042019 (2021).

We report an experimental study of temperature-dependent spectral line shapes of phonon sideband emission stemming from dark excitons in monolayer and bilayer WSe2. Using photoluminescence spectroscopy in the range from 4 to 100 K, we observe a pronounced asymmetry in the phonon-assisted luminescence from momentum-indirect exciton reservoirs. We demonstrate that the corresponding spectral profiles are distinct from those of bright excitons with direct radiative decay pathways. The line-shape asymmetry reflects thermal distribution of exciton states with finite center-of-mass momenta, characteristic for phonon sideband emission. The extracted temperature of the exciton reservoirs is found to generally follow that of the crystal lattice, with deviations reflecting overheated populations. The latter are most pronounced in the bilayer case and at lowest temperatures. Our results add to the understanding of phonon-assisted recombination of momentum-dark excitons and, more generally, establish means to access the thermal distribution of finite-momentum excitons in atomically thin semiconductors with indirect band gaps.

##### Rotational Resonances and Regge-like Trajectories in Lightly Doped Antiferromagnets

A. Bohrdt, E. Demler, F. Grusdt

Physical Review Letters 127, 197004 (2021).

Understanding the nature of charge carriers in doped Mott insulators holds the key to unravelling puzzling properties of strongly correlated electron systems, including cuprate superconductors. Several theoretical models suggested that dopants can be understood as bound states of partons, the analogues of quarks in high-energy physics. However, direct signatures of spinon-chargon bound states are lacking, both in experiment and theory. Here we propose a rotational variant of angle-resolved photo-emission spectroscopy (ARPES) and calculate rotational spectra numerically using the density-matrix renormalization group. We identify long-lived rotational resonances for an individual dopant, which we interpret as a direct indicator of the microscopic structure of spinon-chargon bound states. Similar to Regge trajectories reflecting the quark structure of mesons, we establish a linear dependence of the rotational energy on the superexchange coupling. The rotational peaks we find are strongly suppressed in standard ARPES spectra, but we suggest a multiphoton extension of ARPES which allows us to access rotational spectra. Our findings suggest that multiphoton spectroscopy experiments should provide new insights into emergent universal features of strongly correlated electron systems.

##### Benchmarking a Novel Efficient Numerical Method for Localized 1D Fermi-Hubbard Systems on a Quantum Simulator

B.H. Madhusudhana, S. Scherg, T. Kohlert, I. Bloch, M. Aidelsburger

Prx Quantum 2, 040325 (2021).

Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are, in principle, able to simulate quantum dynamics well outside the domain of classical computers, they are noisy and limited in the variability of the initial state of the dynamics and the observables that can be measured. Despite these limitations, here we show that such a quantum simulator can be used to in effect solve for the dynamics of a many-body system. We develop an efficient numerical technique that facilitates classical simulations in regimes not accessible to exact calculations or other established numerical techniques. The method is based on approximations that are well suited to describe localized one-dimensional Fermi-Hubbard systems. Since this new method does not have an error estimate and the approximations do not hold in general, we use a neutral-atom Fermi-Hubbard quantum simulator with

L

exp

≃

290

lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to

700

tunneling times. We then use these approximations in order to derive a simple prediction of the behavior of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system we consider is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.

##### Research Landscape – 6G Networks Research in Europe: 6G-life: Digital Transformation and Sovereignty of Future Communication Networks

F. Fitzek, H. Boche

IEEE Network 35 (6), 4-6 (2021).

This column aims to increase the visibility and exposure of network-related research projects/activities around the world. The theme of this inaugural column is “6G Networks Research in Europe — Overview of Current Status and Future Directions.” While 5G technology is being deployed worldwide, research efforts in academia and industry are already shaping the vision for 6G. 6G is expected to meet the expectations that 5G cannot, deliver the next level of experience in all areas of society through hyperconnectivity, and provide services that may seem like science fiction today. In the 6G era, the human, physical, and digital worlds will merge in unison to enable rich multi-sensory experiences involving humans, machines, and the physical world. Some 6G services already stand out, including immersive extended reality, holographic communications, and virtual replicas. Achieving 6G will require major innovations in several areas, including wireless connectivity and integration of non-terrestrial networks, incorporating artificial intelligence into the very fabric of communication networks, and networked sensing. While there is still much innovation to come in 5G with new versions of the standard, 6G research is well underway around the world, including in Europe, to make 6G commercially available by 2030. The major projects underway in Europe include the following: 6G-life, Hexa-X, AI@EDGE, DAEMON, and MARSAL

##### Lossy quantum defect theory of ultracold molecular collisions

A. Christianen, G.C. Groenenboom, T. Karman

Physical Review A 104, 043327 (2021).

We consider losses in collisions of ultracold molecules described by a simple statistical short-range model that explicitly accounts for the limited lifetime of classically chaotic collision complexes. This confirms that thermally sampling many isolated resonances leads to a loss cross section equal to the elastic cross section derived by Mayle et al. [Phys. Rev. A 85, 062712 (2012)] and this makes precise the conditions under which this is the case. Surprisingly, we find that the loss is nonuniversal. We also consider the case that loss broadens the short-range resonances to the point that they become overlapping. The overlapping resonances can be treated statistically even if the resonances are sparse compared to kBT, which may be the case for many molecules. The overlap results in Ericson fluctuations which yield a nonuniversal short-range boundary condition that is independent of energy over a range much wider than is sampled thermally. Deviations of experimental loss rates from the present theory beyond statistical fluctuations and the dependence on a background phase shift are interpreted as nonchaotic dynamics of short-range collision complexes.

##### Fermionic systems for quantum information people

S. Szalay, Z. Zimborás, M. Máté, G. Barcza, C. Schilling, Ö. Legeza

Journal of Physics a-Mathematical and Theoretical 54, 393001 (2021).

The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan-Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.

##### Application of the small-tip-angle approximation in the toggling frame for the design of analytic robust pulses in quantum control

L. Van Damme, D. Sugny, S.J. Glaser

Physical Review A 104, 042226 (2021).

We apply the small-tip-angle approximation in the toggling frame in order to analytically design robust pulses against resonance offsets for state to state transfer in two-level quantum systems. We show that a broadband or a local robustness up to an arbitrary order can be achieved. We provide different control parametrizations to satisfy experimental constraints and limitations on the amplitude or energy of the pulse. A comparison with numerical optimal solutions is made.

##### Open-Cavity in Closed-Cycle Cryostat as a Quantum Optics Platform

S. Vadia, J. Scherzer, H. Thierschmann, C. Schäfermeier, C. Dal Savio, T. Taniguchi, K. Watanabe, D. Hunger, K. Karraï, A. Högele

Prx Quantum 2, 040318 (2021).

The introduction of an optical resonator can enable efficient and precise interaction between a photon and a solid-state emitter. It facilitates the study of strong light-matter interaction, polaritonic physics and presents a powerful interface for quantum communication and computing. A pivotal aspect in the progress of light-matter interaction with solid-state systems is the challenge of combining the requirements of cryogenic temperature and high mechanical stability against vibrations while maintaining sufficient degrees of freedom for in situ tunability. Here, we present a fiber-based open Fabry-Perot cavity in a closed-cycle cryostat exhibiting ultrahigh mechanical stability while providing wide-range tunability in all three spatial directions. We characterize the setup and demonstrate the operation with the root-mean-square cavity-length fluctuation of less than 90 pm at temperature of 6.5 K and integration bandwidth of 100 kHz. Finally, we benchmark the cavity performance by demonstrating the strong-coupling formation of exciton polaritons in monolayer WSe2 with a cooperativity of 1.6. This set of results manifests the open cavity in a closed-cycle cryostat as a versatile and powerful platform for low-temperature cavity QED experiments.

##### Efficient conversion of closed-channel-dominated Feshbach molecules of (NaK)-Na-23-K-40 to their absolute ground state

R. Bause, A. Kamijo, X.-Y. Chen, M. Duda, A. Schindewolf, I. Bloch, and X.-Y. Luo

Physical Review A 104, 043321 (2021).

We demonstrate the transfer of 23Na40K molecules from a closed-channel-dominated Feshbach-molecule state to the absolute ground state. The Feshbach molecules are initially created from a gas of sodium and potassium atoms via adiabatic ramping over a Feshbach resonance at 78.3 G. The molecules are then transferred to the absolute ground state using stimulated Raman adiabatic passage with an intermediate state in the spin-orbit-coupled complex ∣∣c3Σ+,v=35,J=1⟩∼|B1Π,v=12,J=1⟩. Our measurements show that the pump transition dipole moment linearly increases with the closed-channel fraction. Thus, the pump-beam intensity can be two orders of magnitude lower than is necessary with open-channel-dominated Feshbach molecules. We also demonstrate that the phase noise of the Raman lasers can be reduced by filter cavities, significantly improving the transfer efficiency.

##### Deterministic Identification Over Channels With Power Constraints

M.J. Salariseddigh, U. Pereg, H. Boche, C. Deppe

IEEE Transactions on Information Theory 68 (1), 1-24 (2021).

The deterministic identification (DI) capacity is developed in multiple settings of channels with power constraints. A full characterization is established for the DI capacity of the discrete memoryless channel (DMC) with and without input constraints. Originally, Ahlswede and Dueck established the identification capacity with local randomness at the encoder, resulting in a double exponential number of messages in the block length n . In the deterministic setup, the number of messages scales exponentially, as in Shannon’s transmission paradigm, but the achievable identification rates are higher. An explicit proof was not provided for the deterministic setting. In this paper, a detailed proof is presented for the DMC. Furthermore, Gaussian channels with fast and slow fading are considered, when channel side information is available at the decoder. A new phenomenon is observed as we establish that the number of messages scales as 2nlog(n)R by deriving lower and upper bounds on the DI capacity on this scale. Consequently, the DI capacity of the Gaussian channel is infinite in the exponential scale and zero in the double exponential scale, regardless of the channel noise.

##### Weak-Measurement-Induced Asymmetric Dephasing: Manifestation of Intrinsic Measurement Chirality

K. Snizhko, P. Kumar, N. Rao, Y. Gefen

Physical Review Letters 127, 170401 (2021).

Geometrical dephasing is distinct from dynamical dephasing in that it depends on the trajectory traversed, hence it reverses its sign upon flipping the direction in which the path is traced. Here we study sequences of generalized (weak) measurements that steer a system in a closed trajectory. The readout process is marked by fluctuations, giving rise to dephasing. Rather than classifying the latter as "dynamical" and "geometrical," we identify a contribution which is invariant under reversing the sequence ordering and, in analogy with geometrical dephasing, one which flips its sign upon the reversal of the winding direction, possibly resulting in partial suppression of dephasing (i.e., "coherency enhancement"). This dephasing asymmetry (under winding reversal) is a manifestation of intrinsic chirality, which weak measurements can (and generically do) possess. Furthermore, the dephasing diverges at certain protocol parameters, marking topological transitions in the measurement-induced phase factor.

##### Control over Light Emission in Low-Refractive-Index Artificial Materials Inspired by Reciprocal Design

L. Maiwald, T. Sommer, M.S. Sidorenko, R.R. Yafyasov, M.E. Mustafa, M. Schulz, M.V. Rybin, M. Eich, A.Y. Petrov

Advanced Optical Materials 2, 2100785 (2021).

Reciprocal space engineering allows tailoring the scattering response of media with a low refractive-index contrast. Here it is shown that a quasiperiodic leveled-wave structure with well-defined reciprocal space and random real space distribution can be engineered to open a complete photonic bandgap (CPBG) for any refractive-index contrast. For these structures, an analytical estimation is derived, which predicts that there is an optimal number of Bragg peaks for any refractive-index contrast. A finite 2D or 3D CPBG is expected at this optimal number even for an arbitrarily small refractive-index contrast. Results of numerical simulations of dipole emission in 2D and 3D structures support the estimations. In 3D simulations, an emission suppression of almost 10 dB is demonstrated with a refractive index down to 1.38. The 3D structures are realized by additive manufacturing on millimeter scale for a material with a refractive index of n ≈ 1.59. Measurements confirm a strong suppression of microwave transmission in the expected frequency range.

##### Dynamics of Negativity of a Wannier-Stark Many-Body Localized System Coupled to a Bath

E. Wybo, M. Knap, F. Pollmann

Physica Status Solidi B-Basic Solid State Physics 2100161 (2021).

An interacting system subjected to a strong linear potential can host a many-body localized (MBL) phase when being slightly perturbed. This so-called Wannier-Stark or "tilted-field" MBL phase inherits many properties from the well-investigated disordered MBL phase, and provides an alternative route to experimentally engineer interacting localized systems without quenched disorder. Herein, the dynamics of entanglement in a Wannier-Stark MBL system coupled to a dephasing environment is investigated. As an accessible entanglement proxy, the third Renyi negativity R 3 is used, which reduces to the third Renyi entropy in case the system is isolated from the environment. This measure captures the characteristic logarithmic growth of interacting localized phases in the intermediate-time regime, where the effects of the coupling to the environment are not yet dominating the dynamics. Thus, it forms a tool to distinguish Wannier-Stark MBL from noninteracting Wannier-Stark localization up to intermediate time-scales, and to quantify quantum correlations in mixed-state dynamics.

##### Electrically tunable Feshbach resonances in twisted bilayer semiconductors

I. Schwart, Y. Shimazaki, C. Kuhlenkamp, K. Watanabe, T. Taniguchi, M. Kroner, A. Imamoglu

Science 374, 336-340 (2021).

Moiré superlattices in transition metal dichalcogenide bilayers provide a platform for exploring strong correlations with optical spectroscopy. Despite the observation of rich Mott-Wigner physics stemming from an interplay between the periodic potential and Coulomb interactions, the absence of tunnel coupling–induced hybridization of electronic states has ensured a classical layer degree of freedom. We investigated a MoSe2 homobilayer structure where interlayer coherent tunneling allows for electric field–controlled manipulation and measurement of the ground-state hole-layer pseudospin. We observed an electrically tunable two-dimensional Feshbach resonance in exciton-hole scattering, which allowed us to control the strength of interactions between excitons and holes located in different layers. Our results may enable the realization of degenerate Bose-Fermi mixtures with tunable interactions.

##### Maximizing efficiency of dipolar recoupling in solid-state NMR using optimal control sequences

Z. Tosner, M.J. Brandl, J. Blahut, S.J. Glaser, B. Reif

Science Advances 7 (42), (2021).

Dipolar recoupling is a central concept in the nuclear magnetic resonance spectroscopy of powdered solids and is used to establish correlations between different nuclei by magnetization transfer. The efficiency of conventional cross-polarization methods is low because of the inherent radio frequency (rf) field inhomogeneity present in the magic angle spinning (MAS) experiments and the large chemical shift anisotropies at high magnetic fields. Very high transfer efficiencies can be obtained using optimal control-derived experiments. These sequences had to be optimized individually for a particular MAS frequency. We show that by adjusting the length and the rf field amplitude of the shaped pulse synchronously with sample rotation, optimal control sequences can be successfully applied over a range of MAS frequencies without the need of reoptimization. This feature greatly enhances their applicability on spectrometers operating at differing external fields where the MAS frequency needs to be adjusted to avoid detrimental resonance effects.

##### 6G: The Personal Tactile Internet—And Open Questions for Information Theory

G.P. Fettweis, H. Boche

IEEE BITS the Information Theory Magazine 1 (1), 71-82 (2021).

The initial vision of cellular communications was to deliver ubiquitous voice communications to anyone anywhere. In a simplified view, 1G delivered voice services for business customers, and only 2G for consumers. Next, this also initiated the appetite for cellular data, for which 3G was designed. However, Blackberry delivered business smartphones, and 4G made smartphones a consumer device. The promise of 5G is to start the Tactile Internet, to control real and virtual objects in real-time via cellular. However, the hype around 5G is, again, focusing on business customers, in particular in the context of campus networks. Consequently, 6G must provide an infrastructure to enable remote-controlled mobile robotic solutions for everyone—the Personal Tactile Internet. Which role can information and communication theory play in this context, and what are the big challenges ahead?

##### Hybridized magnon modes in the quenched skyrmion crystal

R. Takagi, M. Garst, J. Sahliger, C.H. Back, Y. Tokura, S. Seki

Physical Review B 104, 144410 (2021).

Magnetic skyrmions have attracted attention as particlelike swirling spin textures with nontrivial topology, and their self-assembled periodic order i.e., the skyrmion crystal (SkX) is anticipated to host unique magnonic properties. In this paper, we investigate magnetic resonance in the quenched SkX state, which is obtained by the rapid cooling of the high-temperature equilibrium SkX phase in the chiral magnetic insulator Cu2OSeO3. At low temperatures, sextupole and octupole excitation modes of skyrmions are identified, which are usually inactive for oscillating magnetic fields B-nu with GHz-range frequency. but turn out to be detectable through the hybridization with the B-nu-active counterclockwise and breathing modes, respectively. The observed magnetic excitation spectra are well reproduced by theoretical calculations, which demonstrates that the effective magnetic anisotropy enhanced at low temperatures is the key for the observed hybridization between the B.-active and B-nu-inactive modes.

##### Confinement and Mott Transitions of Dynamical Charges in One-Dimensional Lattice Gauge Theories

M. Kebrič, L. Barbiero, C. Reinmoser, U. Schollwöck, F. Grusdt

Physical Review Letters 127, 167203 (2021).

Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate nonlocal interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. Here we show that confinement in 1D Z(2) lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a nonlocal basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery rescaling. We include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long-range order. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.

##### Low-temperature suppression of the spin Nernst angle in Pt

T. Wimmer, J. Gückelhorn, S. Wimmer, S. Mankovsky, H. Ebert, M. Opel, S. Geprägs, R. Gross, H. Huebl, M. Althammer

Physical Review B 104, L140404 (2021).

The coupling between electrical, thermal, and spin transport results in a plethora of novel transport phenomena. However, disentangling different effects is experimentally very challenging. We demonstrate that bilayers consisting of the antiferromagnetic insulator hematite (alpha-Fe2O3) and Pt allow one to precisely measure the transverse spin Nernst magnetothermopower (TSNM) and observe the low-temperature suppression of the platinum (Pt) spin Nernst angle. We show that the observed signal stems from the interplay between the interfacial spin accumulation in Pt originating from the spin Nernst effect and the orientation of the Neel vector of alpha-Fe2O3, rather than its net magnetization. Since the latter is negligible in an antiferromagnet, our device is superior to ferromagnetic structures, allowing one to unambiguously distinguish the TSNM from thermally excited magnon transport, which usually dominates in ferri/ferromagnets due to their nonzero magnetization. Evaluating the temperature dependence of the effect, we observe a vanishing TSNM below similar to 100 K. We compare these results with theoretical calculations of the temperature-dependent spin Nernst conductivity and find excellent agreement. This provides evidence for a vanishing spin Nernst angle of Pt at low temperatures and the dominance of extrinsic contributions to the spin Nernst effect.

##### Three qubits in less than three baths: Beyond two-body system-bath interactions in quantum refrigerators

A. Ghoshal, S. Das, A.K. Pal, A. Sen(De), U. Sen

Physical Review A 104, 042208 (2021).

We show that quantum absorption refrigerators, which have traditionally been studied as of three qubits, each of which is connected to a thermal reservoir, can also be constructed by using three qubits and two thermal baths, where two of the qubits, including the qubit to be locally cooled, are connected to a common bath. With a careful choice of the system, bath, and qubit-bath interaction parameters within the Born-Markov and rotating-wave approximations, one of the qubits attached to the common bath achieves a cooling in the steady state. We observe that the proposed refrigerator may also operate in a parameter regime where no or negligible steady-state cooling is achieved, but there is considerable transient cooling. The steady-state temperature can be lowered significantly by an increase in the strength of the few-body interaction terms existing due to the use of the common bath in the refrigerator setup. The proposed refrigerator built with three qubits and two baths is shown to provide steady-state cooling for both Markovian qubit-bath interactions between the qubits and canonical bosonic thermal reservoirs, and a simpler reset model for the qubit-bath interactions.

##### 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

Physical Review Letters 127, 150504 (2021).

Current quantum simulation experiments are starting to explore nonequilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and timescales. Therefore, the question emerges as to 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 that undergoes a nonequilibrium phase transition from an ergodic to a many-body localized phase. We employ supervised and unsupervised training methods to distinguish nonequilibrium from equilibrium data, using the network performance 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.

##### Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene

F.R. Geisenhof, F. Winterer, A.M. Seiler, J. Lenz, T. Xu, F. Zhang, R.T. Weitz

Nature 598, 53–58 (2021).

The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators(1-3) and the delicate design of moire heterostructures(4-8). However, the seemingly simple bilayer graphene without magnetic doping or moire engineering has long been predicted to host competing ordered states with QAH effects(9-11). Here we explore states in bilayer graphene with a conductance of 2 e(2) h(-1) (where e is the electronic charge and h is Planck's constant) that not only survive down to anomalously small magnetic fields and up to temperatures of five kelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin-valley Hall behaviour(9).

##### Orthogonal Quantum Many-Body Scars

H. Zhao, A. Smith, F. Mintert, J. Knolle

Physical Review Letters 127, 150601 (2021).

Quantum many-body scars have been put forward as counterexamples to the eigenstate thermalization hypothesis. These atypical states are observed in a range of correlated models as long-lived oscillations of local observables in quench experiments starting from selected initial states. The long-time memory is a manifestation of quantum nonergodicity generally linked to a subextensive generation of entanglement entropy, the latter of which is widely used as a diagnostic for identifying quantum many-body scars numerically as low entanglement outliers. Here we show that by adding kinetic constraints to a fractionalized orthogonal metal, we can construct a minimal model with orthogonal quantum many-body scars leading to persistent oscillations with infinite lifetime coexisting with rapid volume-law entanglement generation. Our example provides new insights into the link between quantum ergodicity and many-body entanglement while opening new avenues for exotic nonequilibrium dynamics in strongly correlated multicomponent quantum systems.

##### Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid

J. Koepsell, D. Bourgund, P. Sompet, S. Hirthe, A. Bohrdt, Y. Wang, F. Grusdt, E. Demler, G. Salomon, C. Gross, I. Bloch

Science 374, 82-86 (2021).

The competition between antiferromagnetism and hole motion in two-dimensional Mott insulators lies at the heart of a doping-dependent transition from an anomalous metal to a conventional Fermi liquid. We observe such a crossover in Fermi-Hubbard systems on a cold-atom quantum simulator and reveal the transformation of multipoint correlations between spins and holes upon increasing doping at temperatures around the superexchange energy. Conventional observables, such as spin susceptibility, are furthermore computed from the microscopic snapshots of the system. Starting from a magnetic polaron regime, we find the system evolves into a Fermi liquid featuring incommensurate magnetic fluctuations and fundamentally altered correlations. The crossover is completed for hole dopings around 30%. Our work benchmarks theoretical approaches and discusses possible connections to lowertemperature phenomena.

##### Simple mitigation of global depolarizing errors in quantum simulations

J. Vovrosh, K.E. Khosla, S. Greenaway, C. Self, M.S. Kim, J. Knolle

Physical Review E 104, 035309 (2021).

To get the best possible results from current quantum devices error mitigation is essential. In this work we present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data. We highlight the effectiveness of our mitigation via two examples of recent interest in quantum many-body physics: entanglement measurements and real-time dynamics of confinement in quantum spin chains. Our technique enables us to get quantitative results from the IBM quantum computers showing signatures of confinement, i.e., we are able to extract the meson masses of the confined excitations which were previously out of reach. Additionally, we show the applicability of this mitigation protocol in a wider setting with numerical simulations of more general tasks using a realistic error model. Our protocol is device-independent, simply implementable, and leads to large improvements in results if the global errors are well described by depolarization.

##### Exploiting the photonic nonlinearity of free-space subwavelength arrays of atoms

C.C. Rusconi, T. Shi, J.I. Cirac

Physical Review A 104, 033718 (2021).

Ordered ensembles of atoms, such as atomic arrays, exhibit distinctive features from their disordered counterpart. In particular, while collective modes in disordered ensembles show a linear optical response, collective subradiant excitations of subwavelength arrays are endowed with an intrinsic nonlinearity. Such nonlinearity has both a coherent and a dissipative component: two excitations propagating in the array scatter off each other leading to formation of correlations and to emission into free-space modes. We show how to take advantage of such nonlinearity to coherently prepare a single excitation in a subradiant (dark) collective state of a one-dimensional array as well as to perform an entangling operation on dark states of parallel arrays. We discuss the main source of errors represented by disorder introduced by atomic center-of-mass fluctuations, and we propose a practical way to mitigate its effects.

##### Robust formation of nanoscale magnetic skyrmions in easy-plane anisotropy thin film multilayers with low damping

L. Flacke, V. Ahrens, S. Mendisch, L. Körber, T. Böttcher, E. Meidinger, M. Yaqoob, M. Müller, L. Liensberger, A. Kákay, M. Becherer, P. Pirro, M. Althammer, S. Geprägs, H. Huebl, R. Gross, M. Weiler

Physical Review B 104, L100417 (2021).

We experimentally demonstrate the formation of room-temperature skyrmions with radii of about 25 nm in easy-plane anisotropy multilayers with an interfacial Dzyaloshinskii-Moriya interaction (DMI). We detect the formation of individual magnetic skyrmions by magnetic force microscopy and find that the skyrmions are stable in out-of-plane fields up to about 200 mT. We determine the interlayer exchange coupling as well as the strength of the interfacial DMI. Additionally, we investigate the dynamic microwave spin excitations by broadband magnetic resonance spectroscopy. From the uniform Kittel mode we determine the magnetic anisotropy and low damping alpha(G) < 0.04. We also find clear magnetic resonance signatures in the nonuniform (skyrmion) state. Our findings demonstrate that skyrmions in easy-plane multilayers are promising for spin-dynamical applications.

##### Integrating Quantum Simulation for Quantum-Enhanced Classical Network Emulation

S. DiAdamo, J. Nötzel, S. Sekavcnik, R. Bassoli, R. Ferrara, C. Deppe, F.H.P. Fitzek, H. Boche

IEEE Communications Letters 35 (12), 3922 - 3926 (2021).

We describe a method of investigating the near-term potential of quantum communication technology for communication networks from the perspective of current networks. For this, we integrate an instance of the quantum network simulator QuNetSim at the link layer into the communication network emulator ComNetsEmu. This novel augmented version of ComNetsEmu is thereby enabled to run arbitrary quantum protocols between any directly connected pair of network hosts. To give an example of the proposed method, we implement the link layer method of generating and storing entanglement while idle, to accelerate data transmission at later times using superdense coding.

##### Classical Prethermal Phases of Matter

A. Pizzi, A. Nunnenkamp, J. Knolle

Physical Review Letters 127, 140602 (2021).

Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain. Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, we provide the first numerical proof of prethermal phases of matter in a system with short-range interactions. Concretely, we find higher-order as well as fractional discrete time crystals breaking the time-translational symmetry of the drive with unexpectedly large integer as well as fractional periods. Our work paves the way toward the exploration of novel prethermal phenomena by means of classical Hamiltonian dynamics with virtually no limitations on the system's geometry or size, and thus with direct implications for experiments.

##### Classical approaches to prethermal discrete time crystals in one, two, and three dimensions

A. Pizzi, A. Nunnenkamp, J. Knolle

Physical Review B 104, 094308 (2021).

We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [A. Pizzi, A. Nunnenkamp, and J. Knolle, Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these nonequilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive.

##### Proof of spherical flocking based on quantitative rearrangement inequalities

R.L. Frank, E.H. Lieb

Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze 22 (3), 1241-1263 (2021).

Our recent work on the Burchard-Choksi-Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set. Here we show that this set is, in fact, a round ball. The essential mathematical structure needed in our proof is a strict rearrangement inequality with a quantitative error estimate, which we deduce from recent deep results of M. Christ.

##### Tunable cooperativity in coupled spin-cavity systems

L. Liensberger, F.X. Haslbeck, A. Bauer, H. Berger, R. Gross, H. Huebl, C. Pfleiderer, M. Weiler

Physical Review B 104, L100415 (2021).

We experimentally study the tunability of the cooperativity in coupled spin-cavity systems by changing the magnetic state of the spin system via an external control parameter. As a model system, we use the skyrmion host material Cu2OSeO3 coupled to a microwave cavity resonator. We measure a dispersive coupling between the resonator and magnon modes in different magnetic phases of the material and model our results by using the input-output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon-photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.

##### Compositional Studies of Metals with Complex Order by means of the Optical Floating-Zone Technique

A. Bauer, G. Benka, A. Neubauer, A. Regnat, A. Engelhardt, C. Resch, S. Wurmehl, C.G.F. Blum, T. Adams, A. Chacon, R. Jungwirth, R. Georgii, A. Senyshyn, B. Pedersen, M. Meven, C. Pfleiderer

Physica Status Solidi B-Basic Solid State Physics 2100159 (2021).

The availability of large high-quality single crystals is an important prerequisite for many studies in solid-state research. The optical floating-zone technique is an elegant method to grow such crystals, offering potential to prepare samples that may be hardly accessible with other techniques. As elaborated in this report, examples include single crystals with intentional compositional gradients, deliberate off-stoichiometry, or complex metallurgy. For the cubic chiral magnets Mn1–xFexSi and Fe1–xCoxSi, single crystals are prepared in which the composition is varied during growth from x = 0 to 0.15 and from x = 0.1 to 0.3, respectively. Such samples allow us to efficiently study the evolution of the magnetic properties as a function of composition, as demonstrated by means of neutron scattering. For the archetypical chiral magnet MnSi and the itinerant antiferromagnet CrB2, single crystals with varying initial manganese (0.99–1.04) and boron (1.95–2.1) content are grown. Measurements of the low-temperature properties address the correlation between magnetic transition temperature and sample quality. Furthermore, single crystals of the diborides ErB2, MnB2, and VB2 are prepared. In addition to high vapor pressures, these materials suffer from peritectic formation, potential decomposition, and high melting temperature, respectively.

##### Skeleton of matrix-product-state-solvable models connecting topological phases of matter

N.G. Jones, J. Bibo, B. Jobst, F. Pollmann, A. Smith, R. Verresen

Physical Review Research 3, 033265 (2021).

Models whose ground states can be written as an exact matrix-product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a connected network of MPS-solvable models, which we call the MPS skeleton. As a case study where we can completely unearth this skeleton, we focus on the one-dimensional BDI class-noninteracting spinless fermions with time-reversal symmetry. This class, labeled by a topological winding number, contains the Kitaev chain and is Jordan-Wigner-dual to various symmetry-breaking and symmetry-protected topological (SPT) spin chains. We show that one can read off from the Hamiltonian whether its ground state is an MPS: defining a polynomial whose coefficients are the Hamiltonian parameters, MPS-solvability corresponds to this polynomial being a perfect square. We provide an explicit construction of the ground state MPS, its bond dimension growing exponentially with the range of the Hamiltonian. This complete characterization of the MPS skeleton in parameter space has three significant consequences: (i) any two topologically distinct phases in this class admit a path of MPS-solvable models between them, including the phase transition which obeys an area law for its entanglement entropy; (ii) we illustrate that the subset of MPS-solvable models is dense in this class by constructing a sequence of MPS-solvable models which converge to the Kitaev chain (equivalently, the quantum Ising chain in a transverse field); (iii) a subset of these MPS states can be particularly efficiently processed on a noisy intermediate-scale quantum computer.

##### Signatures of Quantum Phase Transitions after Quenches in Quantum Chaotic One-Dimensional Systems

A. Haldar, K. Mallayya, M. Heyl, F. Pollmann, M. Rigol, A. Das

Physical Review X 11, 031062 (2021).

Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters. Accurately locating those transitions is challenging experimentally and theoretically. Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions. Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains. Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points. We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions.

##### Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics

S. Scopa, P. Calabrese, L. Piroli

Physical Review B 104, 115423 (2021).

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings in the time domain by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provide an exact description, at large space-time scales, for arbitrary temperature T, particle density, and interactions. At T = 0 and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low T > 0 effects of SCS survive and characterize explicitly the value of T for which the two distinguishable excitations melt.

##### Entanglement renormalization for quantum fields with boundaries and defects

A. Franco-Rubio

Physical Review B 104, 125131 (2021).

The continuous multiscale entanglement renormalization ansatz (cMERA) [J. Haegeman et al., Phys. Rev. Lett. 110, 100402 (2013)] gives a variational wave functional for ground states of quantum field-theoretic Hamiltonians. A cMERA is defined as the result of applying to a reference unentangled state a unitary evolution generated by a quasilocal operator, the entangler. This makes the extension of the formalism to the case where boundaries and defects are present nontrivial. Here we show how this generalization works, using the (1+1)-dimensional free boson cMERA as a proof-of-principle example, and restricting ourselves to conformal boundaries and defects. In our prescription, the presence of a boundary or defect induces a modification of the entangler localized only to its vicinity, in analogy with the so-called principle of minimal updates for the lattice tensor network MERA.

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

R.L. Frank, P.T. Nam

Calculus of Variations and Partial Differential Equations 60, 223 (2021).

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.

##### Computable Time Concentration of Bandlimited Signals and Systems

H. Boche, U.J. Mönich

Ieee Transactions on Signal Processing 69, 5523 - 5538 (2021).

Turing computability deals with the question of what is theoretically computable on a digital computer, and hence is relevant whenever digital hardware is used. In this paper we study different possibilities to define computable bandlimited signals and systems. We consider a definition that uses finite Shannon sampling series as approximating functions and another that employs computable continuous functions together with an effectively computable time concentration. We discuss the advantages and drawbacks of both definitions and analyze the connections and differences. In particular, we show that both definitions are equivalent for many practically relevant signal classes, e.g. for bandlimited signals with finite energy, but also that there are important differences, such as for the impulse responses of BIBO stable LTI systems.

##### Computable Rényi mutual information: Area laws and correlations

S.O. Scalet, Á.M. Alhambra, G. Styliaris, J.I. Cirac

Quantum 5, 541 (2021).

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all correlation functions. However, calculating it exactly or approximately is often challenging in practice. Here, we consider alternative definitions based on Rényi divergences. Their main advantage over their von Neumann counterpart is that they can be expressed as a variational problem whose cost function can be efficiently evaluated for families of states like matrix product operators while preserving all desirable properties of a measure of correlations. In particular, we show that they obey a thermal area law in great generality, and that they upper bound all correlation functions. We also investigate their behavior on certain tensor network states and on classical thermal distributions.

##### 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.

##### Machine-learned phase diagrams of generalized Kitaev honeycomb magnets

N. Rao, K. Liu, M. Machaczek, L. Pollet

Physical Revies Research 3, 033223 (2021).

We use a recently developed interpretable and unsupervised machine-learning method, the tensorial kernel support vector machine, to investigate the low-temperature classical phase diagram of a generalized HeisenbergKitaev-Gamma (J-K-F) model on a honeycomb lattice. Aside from reproducing phases reported by previous quantum and classical studies, our machine finds a hitherto missed nested zigzag-stripy order and establishes the robustness of a recently identified modulated S-3 x Z(3) phase, which emerges through the competition between the Kitaev and Gamma spin liquids, against Heisenberg interactions. The results imply that, in the restricted parameter space spanned by the three primary exchange interactions-J, K, and Gamma, the representative Kitaev material alpha-RuCl3 lies close to the boundaries of several phases, including a simple ferromagnet, the unconventional S-3 x Z(3), and nested zigzag-stripy magnets. A zigzag order is stabilized by a finite Gamma' and/or J(3) term, whereas the four magnetic orders may compete in particular if Gamma' is antiferromagnetic.

##### Dispersion forces between weakly disordered van der Waals crystals

J. von Milczewski, J.R. Tolsma

Physical Review B 104, 125111 (2021).

We describe a many-body theory for interlayer dispersion forces between weakly disordered atomically thin crystals and numerically investigate the role of disorder for different layer-separation distances and for different densities of induced electrons and holes. In contrast to the common wisdom that disorder tends to enhance the importance of Coulomb interactions in Fermi liquids, we find that short-range disorder tends to weaken interlayer dispersion forces. This is in line with previous findings that suggest that transitioning from metallic to insulating propagation weakens interlayer dispersion forces. We demonstrate that disorder alters the scaling laws of dispersion forces and we comment on the role of the maximally crossed vertex-correction diagrams responsible for logarithmic divergences in the resistivity of two-dimensional metals.

##### Growth and Helicity of Noncentrosymmetric Cu2OSeO3 Crystals

A. Aqeel, J. Sahliger, G. Li, J. Baas, G.R. Blake, T.T.M. Palstra, C.H. Back

Physica Status Solidi B-Basic Solid State Physics 2100152 (2021).

Cu2OSeO3 single crystals are grown with an optimized chemical vapor transport technique using SeCl4 as a transport agent (TA). The optimized growth method allows to selectively produce large high-quality single crystals. The method is shown to consistently produce Cu2OSeO3 crystals of maximum size 8 x 7 x 4 mm with a transport duration of around three weeks. It is found that this method, with SeCl4 as TA, is more efficient and simple compared with the commonly used growth techniques reported in literature with HCl gas as TA. The Cu2OSeO3 crystals have very high quality and their absolute structures are fully determined by simple single-crystal X-ray diffraction. Enantiomeric crystals with either left- or right-handed chiralities are observed. The magnetization and ferromagnetic resonance data show the same magnetic phase diagram as reported earlier.

##### Higher-order spin-hole correlations around a localized charge impurity

Y. Wang, A. Bohrdt, S. Ding, J. Koepsell, E. Demler, F. Grusdt

Physical Review Research 3, 033204 (2021).

Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy J. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.

##### 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.

##### 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.

##### Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States

B. Nachtergaele, R. Sims, A. Young

Ann. Henri Poincaré 23, 393–511 (2022).

- We study the stability with respect to a broad class of perturbations of gapped ground-state phases of quantum spin systems defined by frustration-free Hamiltonians. The core result of this work is a proof using the Bravyi–Hastings–Michalakis (BHM) strategy that under a condition of local topological quantum order (LTQO), the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential. Compared to previous work, we expand the class of frustration-free quantum spin models that can be handled to include models with more general boundary conditions, and models with discrete symmetry breaking. Detailed estimates allow us to formulate sufficient conditions for the validity of positive lower bounds for the gap that are uniform in the system size and that are explicit to some degree. We provide a survey of the BHM strategy following the approach of Michalakis and Zwolak, with alterations introduced to accommodate more general than just periodic boundary conditions and more general lattices. We express the fundamental condition known as LTQO by means of an indistinguishability radius, which we introduce. Using the uniform finite-volume results, we then proceed to study the thermodynamic limit. We first study the case of a unique limiting ground state and then also consider models with spontaneous breaking of a discrete symmetry. In the latter case, LTQO cannot hold for all local observables. However, for perturbations that preserve the symmetry, we show stability of the gap and the structure of the broken symmetry phases. We prove that the GNS Hamiltonian associated with each pure state has a non-zero spectral gap above the ground state.

##### 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

Semiconductor Science and Technology 36, 09LT04 (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.

##### Complexity Blowup in Simulating Analog Linear Time-Invariant Systems on Digital Computers

H. Boche, V. Pohl

IEEE Transactions on Signal Processing 69, (2021).

This paper proves that every non-trivial, linear time-invariant (LTI) system of the first order shows a complexity blowup if it is simulated on a digital computer. This means that there exists a low-complexity input signal, which can be generated on a Turing machine in polynomial time, but such that the output signal of the LTI system has high complexity in the sense that the computation time for determining an approximation up to n significant digits grows faster than any polynomial in n. Moreover, this input signal can easily and explicitly be generated from the given system parameters by a Turing machine. It is also shown that standard techniques for simulating higher-order LTI systems with real poles show the same complexity blowup. Finally, it is shown that a similar complexity blowup occurs for the calculation of Fourier series approximations and Fourier transforms

##### Decoherence mitigation by real-time noise acquisition

G. Braunbeck, M. Kaindl, A.M. Waeber, F. Reinhard

Journal of Applied Physics 5, 054302 (2021).

We present a scheme to neutralize the dephasing effect induced by classical noise on a qubit. The scheme builds upon the key idea that this kind of noise can be recorded by a classical device during the qubit evolution, and that its effect can be undone by a suitable control sequence that is conditioned on the measurement result. We specifically demonstrate this scheme on a nitrogen-vacancy center that strongly couples to current noise in a nearby conductor. By conditioning the readout observable on a measurement of the current, we recover the full qubit coherence and the qubit's intrinsic coherence time T-2. We demonstrate that this scheme provides a simple way to implement single-qubit gates with an infidelity of 10(-2) even if they are driven by noisy sources, and we estimate that an infidelity of 10(-5) could be reached with additional improvements. We anticipate this method to find widespread adoption in experiments using fast control pulses driven from strong currents, in particular, in nanoscale magnetic resonance imaging, where control of peak currents of 100 mA with a bandwidth of 100 MHz is required. Published under an exclusive license by AIP Publishing.

##### RF Antenna Design for 3D Quantum Memories

F. Deppe, E. Xie, K.G. Fedorov, G. Andersson, J. Muller, A. Marx, R. Gross

International Symposium of the Applied-Computational-Electromagnetics-Society (ACES) (2021).

A quantum memory has to meet the conflicting requirements of strong coupling for fast readout and weak coupling for long storage. Multimode rectangular superconducting 3D cavities are known to satisfy both properties. Here, we systematically study the external coupling to the two lowest-frequency modes of an aluminum cavity. First, we introduce a general analytical scheme to describe the capacitive coupling of the antenna pin and validate this model experimentally. On this basis, we engineer an antenna which is overcoupled to the first mode, but undercoupled to the second mode.

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

I. Bardet, A. Capel, C. Rouzé

Annales Henri Poincare 23, 101–140 (2022).

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.

##### Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

T. Mori, H. Zhao, F. Mintert, J. Knolle, R. Moessner

Physical Review Letters 127, 050602 (2021).

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (omega/g)(-C) (ln()(omega/)(g)) with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.

##### 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.

##### Locality of temperature and correlations in the presence of non-zero-temperature phase transitions

S. Hernández-Santana, A. Molnár, C. Gogolin, J.I. Cirac, A. Acín

New Journal of Physics 23, 073052 (2021).

While temperature is well understood as an intensive quantity in standard thermodynamics, it is less clear whether the same holds in quantum systems displaying correlations with no classical analogue. The problem lies in the fact that, under the presence of non-classical correlations, subsystems of a system in thermal equilibrium are, in general, not described by a thermal state at the same temperature as the global system and thus one cannot simply assign a local temperature to them. However, there have been identified situations in which correlations in thermal states decay sufficiently fast so that the state of their subsystems can be very well approximated by the reduced states of equilibrium systems that are only slightly bigger than the subsystems themselves, hence allowing for a valid local definition of temperature. In this work, we address the question of whether temperature is locally well defined for a bosonic system with local interactions that undergoes a phase transition at non-zero temperature. We consider a three-dimensional bosonic model in the grand canonical state and verify that a certain form of locality of temperature holds regardless of the temperature, and despite the presence of infinite-range correlations at and below the critical temperature of the phase transition.

##### Entanglement distribution in the quantum symmetric simple exclusion process

D. Bernard, L. Piroli

Physical Review E 104, 014146 (2021).

We study the probability distribution of entanglement in the quantum symmetric simple exclusion process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of M particles, and we focus on the late-time distribution of Rényi-q entropies for a subsystem of size ℓ. By means of a Coulomb gas approach from random matrix theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For q>1, we show that, depending on the value of the ratio ℓ/M, the entropy distribution displays either two or three distinct regimes, ranging from low to high entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.

##### Rayleigh edge waves in two-dimensional crystals with Lorentz forces: From skyrmion crystals to gyroscopic media

C. Benzoni, B. Jeevanesan, S. Moroz

Physical Review B 104, 024435 (2021).

We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality of the low-frequency edge waves, and study their properties. To illustrate the Rayleigh edge waves in real time, we have carried out finite-difference simulations of the model. Apart from skyrmion crystals, our results are also applicable to edge waves of gyroelastic media and screened Wigner crystals in magnetic fields. Our work opens a pathway towards controlled manipulation of elastic signals along boundaries of crystals with broken time-reversal symmetry.

##### 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.

##### Flat and correlated plasmon bands in graphenek/alpha-RuCl3 heterostructures

H.-K. Jin, J. Knolle

Physical Review B 104, 045140 (2021).

We develop a microscopic theory for plasmon excitations of graphene/alpha-RuCl3 heterostructures. Within a Kondo-Kitaev model with various interactions, a heavy Fermi liquid hosting flat bands emerges in which the itinerant electrons of graphene effectively hybridize with the fractionalized fermions of the Kitaev quantum spin liquid. We find novel correlated plasmon bands induced by the interplay of flat bands and interactions and argue that our theory is consistent with the available experimental data on graphene/alpha-RuCl3 heterostructures. We predict novel plasmon branches beyond the long-wavelength limit and discuss the implications for probing correlation phenomena in other flat band systems.

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

S. Scherg, T. Kohlert, P. Sala, F. Pollmann, H.M. Bharath, I. Bloch, M. Aidelsburger

Nature Communications 12, 4490 (2021).

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.

##### Inferring hidden symmetries of exotic magnets from detecting explicit order parameters

N. Rao, K. Liu, L. Pollet

Physical Review E 104, 015311 (2021).

An unconventional magnet may be mapped onto a simple ferromagnet by the existence of a high-symmetry point. Knowledge of conventional ferromagnetic systems may then be carried over to provide insight into more complex orders. Here we demonstrate how an unsupervised and interpretable machine-learning approach can be used to search for potential high-symmetry points in unconventional magnets without any prior knowledge of the system. The method is applied to the classical Heisenberg-Kitaev model on a honeycomb lattice, where our machine learns the transformations that manifest its hidden O(3) symmetry, without using data of these high-symmetry points. Moreover, we clarify that, in contrast to the stripy and zigzag orders, a set of D2 and D2h ordering matrices provides a more complete description of the magnetization in the Heisenberg-Kitaev model. In addition, our machine also learns the local constraints at the phase boundaries, which manifest a subdimensional symmetry. This paper highlights the importance of explicit order parameters to many-body spin systems and the property of interpretability for the physical application of machine-learning techniques.

##### Variational quantum algorithm with information sharing

C.N. Self, K.E. Khosla, A.W.R. Smith, F. Sauvage, P.D. Haynes, J. Knolle, F. Mintert, M.S. Kim

Npj Quantum Information 7, 116 (2021).

We introduce an optimisation method for variational quantum algorithms and experimentally demonstrate a 100-fold improvement in efficiency compared to naive implementations. The effectiveness of our approach is shown by obtaining multi-dimensional energy surfaces for small molecules and a spin model. Our method solves related variational problems in parallel by exploiting the global nature of Bayesian optimisation and sharing information between different optimisers. Parallelisation makes our method ideally suited to the next generation of variational problems with many physical degrees of freedom. This addresses a key challenge in scaling-up quantum algorithms towards demonstrating quantum advantage for problems of real-world interest.

##### Density of states of the lattice Schwinger model

I. Papaefstathiou, D. Robaina, J.I. Cirac, M.C. Bañuls

Physical Review D 104, 014514 (2021).

Using a recently introduced tensor network method, we study the density of states of the lattice Schwinger model, a standard testbench for lattice gauge theory numerical techniques, but also the object of recent experimental quantum simulations. We identify regimes of parameters where the spectrum appears to be symmetric and displays the expected continuum properties even for finite lattice spacing and number of sites. However, we find that for moderate system sizes and lattice spacing of ga similar to 0(1), the spectral density can exhibit very different properties with a highly asymmetric form. We also explore how the method can be exploited to extract thermodynamic quantities.

##### Identification over the Gaussian Channel in the Presence of Feedback

W. Labidi, H. Boche, C. Deppe, M. Wiese

IEEE International Symposium on Information Theory (ISIT) 278-283 (2021).

We analyze message identification via Gaussian channels with noiseless feedback, which is part of the Post Shannon theory. The consideration of communication systems beyond Shannon's approach is useful in order to increase the efficiency of information transmission for certain applications. If the noise variance is positive, we propose a coding scheme that generates infinite common randomness between the sender and the receiver. We show that any identification rate via the Gaussian channel with noiseless feedback can be achieved. The remarkable result is that this applies to both rate definitions 1/n log M (as defined by Shannon for transmission) and 1/n log log M (as defined by Ahlswede and Dueck for identification). We can even show that our result holds regardless of the selected scaling for the rate.

##### 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.

##### Continuum approach to real time dynamics of (1+1)D gauge field theory: Out of horizon correlations of the Schwinger model

I. Kukuljan

Physical Review D 104, L021702 (2021).

We develop a truncated Hamiltonian method to study nonequilibrium real time dynamics in the Schwinger model—the quantum electrodynamics in D=1+1. This is a purely continuum method that captures reliably the invariance under local and global gauge transformations and does not require a discretization of space-time. We use it to study a phenomenon that is expected not to be tractable using lattice methods: we show that the (1+1)D quantum electrodynamics admits the dynamical horizon violation effect which was recently discovered in the case of the sine-Gordon model. Following a quench of the model, oscillatory long-range correlations develop, manifestly violating the horizon bound. We find that the oscillation frequencies of the out-of-horizon correlations correspond to twice the masses of the mesons of the model suggesting that the effect is mediated through correlated meson pairs. We also report on the cluster violation in the massive version of the model, previously known in the massless Schwinger model. The results presented here reveal a novel nonequilibrium phenomenon in (1+1)D quantum electrodynamics and make a first step towards establishing that the horizon violation effect is present in gauge field theory.

##### Infinite-Dimensional Programmable Quantum Processors

M. Gschwendtner, A. Winter

PRX Quantum 2, 030308 (2021).

A universal programmable quantum processor uses "program" quantum states to apply an arbitrary quantum channel to an input state. We generalize the concept of a finite-dimensional programmable quantum processor to infinite dimension assuming an energy constraint on the input and output of the target quantum channels. By proving reductions to and from finite-dimensional processors, we obtain upper and lower bounds on the program dimension required to approximately implement energy-limited quantum channels. In particular, we consider the implementation of Gaussian channels. Due to their practical relevance, we investigate the resource requirements for gauge-covariant Gaussian channels. Additionally, we give upper and lower bounds on the program dimension of a processor implementing all Gaussian unitary channels. These lower bounds rely on a direct information-theoretic argument, based on the generalization from finite to infinite dimension of a certain "replication lemma" for unitaries.

##### 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.

##### Weak Quasi-Factorization for the Belavkin-Staszewski Relative Entropy

A. Bluhm, A. Capel, A. Perez-Hernandez

IEEE International Symposium on Information Theory (ISIT) 118-123 (2021).

Quasi-factorization-type inequalities for the relative entropy have recently proven to be fundamental in modern proofs of modified logarithmic Sobolev inequalities for quantum spin systems. In this paper, we show some results of weak quasi-factorization for the Belavkin-Staszewski relative entropy, i.e. upper bounds for the BS-entropy between two bipartite states in terms of the sum of two conditional BS-entropies, up to some multiplicative and additive factors.

##### Ultrafast hot-carrier relaxation in silicon monitored by phase-resolved transient absorption spectroscopy

M. Wörle, A.W. Holleitner, R. Kienberger, H. Iglev

Physical Review B 104, L041201 (2021).

The relaxation dynamics of hot carriers in silicon (100) is studied via a holistic approach based on phase-resolved transient absorption spectroscopy with few-cycle optical pulses. After excitation by a sub-5-fs light pulse, strong electron-electron coupling leads to an ultrafast single electron momentum relaxation time of 10 fs. The thermalization of the hot carriers is visible in the temporal evolution of the effective mass and the collision time as extracted from the Drude model. The optical effective mass decreases from 0.3m(e) to about 0.125m(e) with a time constants of 58 fs, while the collision time increases from 3 fs for the shortest timescales with a saturation at approximately 18 fs with a time constant of 150 fs. The observation shows that both Drude parameters exhibit different dependences on the carrier temperature. The presented information on the electron mass dynamics as well as the momentum-, and electron-phonon scattering times with unprecedented time resolution is important for all hot-carrier optoelectronic devices.

##### Common Randomness Generation over Slow Fading Channels

R. Ezzine, M. Wiese, C. Deppe, H. Boche

IEEE International Symposium on Information Theory (ISIT) 1925-1930 (2021).

This paper analyzes the problem of common randomness (CR) generation from correlated discrete sources aided by unidirectional communication over Single-Input SingleOutput (SISO) slow fading channels with additive white Gaussian noise (AWGN) and arbitrary state distribution. Slow fading channels are practically relevant in many situations in wireless communications. We completely solve the SISO slow fading case by establishing its corresponding outage CR capacity using our characterization of its channel outage capacity. The generated CR could be exploited to improve the performance gain in the identification scheme. The latter is known to be more efficient than the classical transmission scheme in many new applications, which demand ultra-reliable low latency communication.

##### Supersymmetric Boundaries of One-Dimensional Phases of Fermions beyond Symmetry-Protected Topological States

A. Turzillo, M. You

Physical Review Letters 127, 026402 (2021).

It has recently been demonstrated that protected supersymmetry emerges on the boundaries of one-dimensional intrinsically fermionic symmetry protected trivial (SPT) phases. Here we investigate the boundary supersymmetry of one-dimensional fermionic phases beyond SPT phases. Using the connection between Majorana edge modes and real supercharges, we compute, in terms of the bulk phase invariants, the number of protected boundary supercharges.

##### One-dimensional long-range Falikov-Kimball model: Thermal phase transition and disorder-free localization

T. Hodson, J. Willsher, J. Knolle

Physical Review B 104, 045116 (2021).

Disorder or interactions can turn metals into insulators. One of the simplest settings in which to study this physics is given by the Falikov-Kimball (FK) model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogeneous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite-temperature charge-density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalized FK model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov chain Monte Carlo method to map the phase diagram and compute the energy-resolved localization properties of the fermions. We compare the behavior of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

##### Optimal two-photon excitation of bound states in non-Markovian waveguide QED

R. Trivedi, D. Malz, S. Sun, S. Fan, J. Vučković

Physical Review A 104, 013705 (2021).

Bound states arise in waveguide QED systems with a strong frequency-dependence of the coupling between emitters and photonic modes. While exciting such bound-states with single-photon wave-packets is not possible, photon-photon interactions mediated by the emitters can be used to excite them with two-photon states. In this Letter, we use scattering theory to provide upper limits on this excitation probability for a general non-Markovian waveguide QED system and show that this limit can be reached by a two-photon wave packet with vanishing uncertainty in the total photon energy. Furthermore, we also analyze multi-emitter waveguide QED systems with multiple bound states and provide a systematic construction of two-photon wave packets that can excite a given superposition of these bound states. As specific examples, we study bound-state trapping in waveguide QED systems with single and multiple emitters and a time-delayed feedback.

##### Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases

A. Bullivant,C. Delcamp

Journal of High Energy Physics 25 (2021).

We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyonic string-like excitations that terminate at gapped boundaries. Using a tube algebra approach, we classify such excitations and derive the corresponding representation theory. Via a dimensional reduction argument, we relate this tube algebra to that describing (2+1)d boundary point-like excitations at interfaces between two gapped boundaries. Such point-like excitations are well known to be encoded into a bicategory of module categories over the input fusion category. Exploiting this correspondence, we define a bicategory that encodes the string-like excitations ending at gapped boundaries, showing that it is a sub-bicategory of the centre of the input bicategory of group-graded 2-vector spaces. In the process, we explain how gapped boundaries in (3+1)d can be labelled by so-called pseudo-algebra objects over this input bicategory.

##### Ensemble Reduced Density Matrix Functional Theory for Excited States and Hierarchical Generalization of Pauli's Exclusion Principle

C. Schilling, S. Pittalis

Physical Review Letters 127, 023001 (2021).

We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an approach to be unfeasible are overcome. First, we resort to a generalization of the Ritz variational principle to ensemble states with fixed weights. This in combination with the constrained search formalism allows us to establish a universal functional of the one-particle reduced density matrix. Second, we employ tools from convex analysis to circumvent the too involved N-representability constraints. Remarkably, this identifies Valone's pioneering work on RDMFT as a special case of convex relaxation and reveals that crucial information about the excitation structure is contained in the functional's domain. Third, to determine the crucial latter object, a methodology is developed which eventually leads to a generalized exclusion principle. The corresponding linear constraints are calculated for systems of arbitrary size.

##### Room temperature cavity electromechanics in the sideband-resolved regime

A.T. Le, A. Brieussel, E.M. Weig

Journal of Applied Physics 130, 014301 (2021).

We demonstrate a sideband-resolved cavity electromechanical system operating at room temperature. It consists of a nanomechanical resonator, a strongly pre-stressed silicon nitride string, dielectrically coupled to a three-dimensional microwave cavity made of copper. The electromechanical coupling is characterized by two measurements, the cavity-induced eigenfrequency shift of the mechanical resonator and the optomechanically induced transparency. While the former is dominated by dielectric effects, the latter reveals a clear signature of the dynamical backaction of the cavity field on the resonator. This unlocks the field of cavity electromechanics for room temperature applications.

##### 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.

##### The Computational and Latency Advantage of Quantum Communication Networks

R. Ferrara, R. Bassoli, C. Deppe, F. Fitzek, H. Boche

IEEE Communications Magazine 59 (6), 132 - 137 (2021).

This article summarizes the current status of classical communication networks and identifies some critical open research challenges that can only be solved by leveraging quantum technologies. Until now, the main goal of quantum communication networks has been security. However, quantum networks can do more than just exchange secure keys or serve the needs of quantum computers. In fact, the scientific community is still investigating the possible use cases/benefits that quantum communication networks can bring. Thus, this article aims to point out and clearly describe how quantum communication networks can enhance in-network distributed computing and reduce the overall end-to-end latency, beyond the intrinsic limits of classical technologies. Furthermore, we also explain how entanglement can reduce the communication complexity (overhead) that future classical virtualized networks will experience.

##### Quantum Information Processing and Precision Measurement Using a Levitated Nanodiamond

H.J. Zhang, X.Y. Chen, Z.Q. Yin

Advanced Quantum Technologies 4 (8), (2021).

The nanodiamond, which hosts nitrogen-vacancy (NV) centers, has been levitated in vacuum either through optical tweezers or through an ion trap. It combines the advantages of the large mass and long coherent discrete internal energy levels, which makes it an ideal platform for quantum information processing and precision measurement. In this review, the quantum information processing and the precision measurement based on the levitated nanodiamond are briefly summarized. The basic physics of the levitated nanodiamond and the NV centers is first introduced. Then the methods of manipulating motional states of the nanodiamond with the NV centers are discussed. The magnetic coupling mechanisms between the NV centers and the translational mode or the torsional mode are discussed, and the method of cooling the mechanical modes with the NV centers is discussed. Several applications are discussed, such as the mass spectrometry, the gravitational acceleration measurement, etc. The levitated nanodiamond can also be used for realizing universal quantum logic gates and quantum simulation. Finally, the conclusion and perspective are given.

##### 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.

##### The quantum sine-Gordon model with quantum circuits

A. Roy, D. Schuricht, J. Hauschild, F. Pollmann, H. Saleur

Nuclear Physics B 968, 115445 (2021).

Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator built out of Josephson junctions for one of the paradigmatic models of an integrable quantum field theory: the quantum sine-Gordon (qSG) model in 1+1 space-time dimensions. We analyze the lattice model using the density matrix renormalization group technique and benchmark our numerical results with existing Bethe ansatz computations. Furthermore, we perform analytical form-factor calculations for the two-point correlation function of vertex operators, which closely agree with our numerical computations. Finally, we compute the entanglement spectrum of the qSG model. We compare our results with those obtained using the integrable lattice-regularization based on the quantum XYZ chain and show that the quantum circuit model is less susceptible to corrections to scaling compared to the XYZ chain. We provide numerical evidence that the parameters required to realize the qSG model are accessible with modern-day superconducting circuit technology, thus providing additional credence towards the viability of the latter platform for simulating strongly interacting quantum field theories. (C) 2021 The Author(s). Published by Elsevier B.V.

##### Quantum simulation with fully coherent dipole-dipole interactions mediated by three-dimensional subwavelength atomic arrays

- K. Brechtelsbauer, D. Malz

Physical Review A 104, 013701 (2021).

Quantum simulators employing cold atoms are among the most promising approaches to tackle quantum many-body problems. Nanophotonic structures are widely employed to engineer the band structure of light and are thus investigated as a means to tune the interactions between atoms placed in their vicinity. A key shortcoming of this approach is that excitations can decay into free photons, limiting the coherence of such quantum simulators. Here, we overcome this challenge by proposing to use a simple cubic three-dimensional array of atoms to produce an omnidirectional band gap for light and show that it enables coherent, dissipation-free interactions between embedded impurities. We show explicitly that the band gaps persist for moderate lattice sizes and finite filling fraction, which makes this effect readily observable in experiment. Our paper paves the way toward analog spin quantum simulators with long-range interactions using ultracold atomic lattices, and is an instance of the emerging field of atomic quantum metamaterials.

##### Programmability of covariant quantum channels

M. Gschwendtner, A. Bluhm, A. Winter

Quantum 5, 488 (2021).

A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels which is applied to an input register. It is well-known that such a device is impossible with a finite-dimensional program register for any set that contains infinitely many unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning that a universal programmable quantum processor does not exist. The situation changes if the system has symmetries. Indeed, here we consider group-covariant channels. If the group acts irreducibly on the channel input, these channels can be implemented exactly by a programmable quantum processor with finite program dimension (via teleportation simulation, which uses the Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging the representation theory of the symmetry group action, we show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds on the program register dimension of a processor implementing all group-covariant channels approximately.

##### 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.

##### Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

C. Miles, A. Bohrdt, R. Wu, C. Chiu, M. Xu, G. Ji, M. Greiner, K.Q. Weinberger, E. Demler, E.-A. Kim

Nature Communications 12, 3905 (2021).

Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data. Physical principles underlying machine learning analysis of quantum gas microscopy data are not well understood. Here the authors develop a neural network based approach to classify image data in terms of multi-site correlation functions and reveal the role of fourth-order correlations in the Fermi-Hubbard model.

##### The role of chalcogen vacancies for atomic defect emission in MoS2

E. Mitterreiter, B. Schuler, A. Micevic, D. Hernangómez-Pérez, K. Barthelmi, K.A. Cochrane, J. Kiemle, F. Sigger, J. Klein, E. Wong, E.S. Barnard, K. Watanabe, T. Taniguchi, M. Lorke, F. Jahnke, J.J. Finley, A.M. Schwartzberg, D.Y. Qiu, S. Refaely-Abramson, A.W. Holleitner, A. Weber-Bargioni, C. Kastl

Nature Communications 12, 3822 (2021).

For two-dimensional (2D) layered semiconductors, control over atomic defects and understanding of their electronic and optical functionality represent major challenges towards developing a mature semiconductor technology using such materials. Here, we correlate generation, optical spectroscopy, atomic resolution imaging, and ab initio theory of chalcogen vacancies in monolayer MoS2. Chalcogen vacancies are selectively generated by in-vacuo annealing, but also focused ion beam exposure. The defect generation rate, atomic imaging and the optical signatures support this claim. We discriminate the narrow linewidth photoluminescence signatures of vacancies, resulting predominantly from localized defect orbitals, from broad luminescence features in the same spectral range, resulting from adsorbates. Vacancies can be patterned with a precision below 10nm by ion beams, show single photon emission, and open the possibility for advanced defect engineering of 2D semiconductors at the ultimate scale. The relation between the microscopic structure and the optical properties of atomic defects in 2D semiconductors is still debated. Here, the authors correlate different fabrication processes, optical spectroscopy and electron microscopy to identify the optical signatures of chalcogen vacancies in monolayer MoS2.

##### 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.

##### 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.

##### Turing Meets Shannon: Algorithmic Constructability of Capacity-Achieving Codes

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

IEEE International Conference on Communications (ICC) 21175619 (2021).

Proving a capacity result usually involves two parts: achievability and converse which establish matching lower and upper bounds on the capacity. For achievability, only the existence of good (capacity-achieving) codes is usually shown. Although the existence of such optimal codes is known, constructing such capacity-achieving codes has been open for a long time. Recently, significant progress has been made and optimal code constructions have been found including for example polar codes. A crucial observation is that all these constructions are done for a fixed and given channel and this paper addresses the question whether or not it is possible to find universal algorithms that can construct optimal codes for a whole class of channels. For this purpose, the concept of Turing machines is used which provides the fundamental performance limits of digital computers. It is shown that there exists no universal Turing machine that takes the channel from the class of interest as an input and outputs optimal codes. Finally, implications on channel-aware transmission schemes are discussed.

##### Quantum broadcast channels with cooperating decoders: An information-theoretic perspective on quantum repeaters

U. Pereg, C. Deppe, H. Boche

Journal of Mathematical Physics 62, 062204 (2021).

Communication over a quantum broadcast channel with cooperation between the receivers is considered. The first form of cooperation addressed is classical conferencing, where receiver 1 can send classical messages to receiver 2. Another cooperation setting involves quantum conferencing, where receiver 1 can teleport a quantum state to receiver 2. When receiver 1 is not required to recover information and its sole purpose is to help the transmission to receiver 2, the model reduces to the quantum primitive relay channel. The quantum conferencing setting is intimately related to quantum repeaters as the sender, receiver 1, and receiver 2 can be viewed as the transmitter, the repeater, and the destination receiver, respectively. We develop lower and upper bounds on the capacity region in each setting. In particular, the cutset upper bound and the decode-forward lower bound are derived for the primitive relay channel. Furthermore, we present an entanglement-formation lower bound, where a virtual channel is simulated through the conference link. At last, we show that as opposed to the multiple access channel with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual. Published under an exclusive license by AIP Publishing.

##### Algorithmic Detection of Adversarial Attacks on Message Transmission and ACK/NACK Feedback

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

IEEE International Conference on Communications (ICC) (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 decide in which state the communication system is. 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 attacks on the actual message transmission.

##### 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.

##### 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.

##### Time-Domain Concentration and Approximation of Computable Bandlimited Signals

H. Boche, U.J. Moenich

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 5469-5473 (2021).

We study the time-domain concentration of bandlimited signals form a computational point of view. To this end we employ the concept of Turing computability that exactly describes what can be theoretically computed on a digital machine. A previous definition of computability for bandlimited signals is based on the idea of effective approximation with finite Shannon sampling series. In this paper we provide a different definition that uses the time-domain concentration of the signals. For computable bandlimited signals with finite L p -norm, we prove that both definitions are equivalent. We further show that local computability together with the computability of the L p -norm imply the computability of the signal itself. This provides a simple test for computability.

##### Real Number Signal Processing can Detect Denial-of-Service Attacks

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 4765-4769 (2021).

Wireless communication systems are inherently vulnerable to adversarial attacks since malevolent jammers might jam and disrupt the legitimate transmission intentionally. Of particular interest are so- called denial-of-service (DoS) attacks in which the jammer is able to completely disrupt the communication. Accordingly, it is of crucial interest for the legitimate users to detect such DoS attacks. Turing machines provide the fundamental limits of today’s digital computers and therewith of the traditional signal processing. It has been shown that these are incapable of detecting DoS attacks. This stimulates the question of how powerful the signal processing must be to enable the detection of DoS attacks. This paper investigates the general computation framework of Blum-Shub-Smale machines which allows the processing and storage of arbitrary reals. It is shown that such real number signal processing then enables the detection of DoS attacks.

##### On Information Asymmetry in Online Reinforcement Learning

E. Tampubolon, H. Ceribasi, H. Boche

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 4955-4959 (2021).

In this work, we study the system of two interacting non-cooperative Q-learning agents, where one agent has the privilege of observing the other's actions. We show that this information asymmetry can lead to a stable outcome of population learning, which does not occur in an environment of general independent learners. Furthermore, we discuss the resulted post-learning policies, show that they are almost optimal in the underlying game sense, and provide numerical hints of almost welfare-optimal of the resulted policies.

##### Communication Over Block Fading Channels – An Algorithmic Perspective On Optimal Transmission Schemes

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

IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 4750-4754 (2021).

Wireless channels are considered that change over time but remain constant for a certain (coherence) period. This behavior is perfectly captured by block fading channels and affects the performance of the corresponding wireless communication systems. Desired closed-form characterizations of optimal transmission schemes remain unknown in many cases. This paper approaches this issue from a fundamental, algorithmic point of view by studying whether or not it is in principle possible to construct or find such optimal transmission schemes algorithmically (without putting any constraints on the computational complexity of such algorithms). To this end, the concept of averaged channels is considered as a model for block fading and it is shown that, although the averaged channel itself is computable, the corresponding capacity need not be computable, i.e., there exists no (universal) algorithm that takes the channel as an input and computes the corresponding capacity expression. Subsequently, examples of block fading channels are presented for which it is even impossible to find an algorithm that computes for every blocklength the corresponding optimal transmission scheme.

##### 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.

##### Confinement and entanglement dynamics on a digital quantum computer

J. Vovrosh, J. Knolle

Scientific Reports 11, 11577 (2021).

Confinement describes the phenomenon when the attraction between two particles grows with their distance, most prominently found in quantum chromodynamics (QCD) between quarks. In condensed matter physics, confinement can appear in quantum spin chains, for example, in the one dimensional transverse field Ising model (TFIM) with an additional longitudinal field, famously observed in the quantum material cobalt niobate or in optical lattices. Here, we establish that state-of-the-art quantum computers have reached capabilities to simulate confinement physics in spin chains. We report quantitative confinement signatures of the TFIM on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. We also find the confinement induced slow down of entanglement spreading by implementing randomized measurement protocols for the second order Rényi entanglement entropy. Our results are a crucial step for probing non-perturbative interacting quantum phenomena on digital quantum computers beyond the capabilities of classical hardware.

##### 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.

##### Series Editorial: Internet of Things and Sensor Networks

R. Ferrara, R. Bassoli, C. Deppe, F.H.P. Fitzek, H. Boche

Ieee Communications Magazine 59 (6), 132-137 (2021).

Today, the Internet of Things (IoT) continues to evolve as a predominant technical trend. In the face of the global pandemic, many conventional IoT paradigms are, however, expected to shift in response to pressing societal challenges. For instance, we are preparing to observe substantial investments in the telemedicine and healthcare sectors as well as efficient work-from-home solutions. This accentuates the need for edge intelligence in supporting the increasingly massive IoT deployments augmented with machine learning capabilities, among many others.

##### 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.

##### Parallel quantum simulation of large systems on small NISQ computers

F. Barratt, J. Dborin, M. Bal, V. Stojevic, F. Pollmann, A.G. Green

Npj Quantum Information 7, 79 (2021).

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translates infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution of arbitrary one-dimensional systems. The illustrative simulated output of these codes for achievable circuit sizes is given.

##### 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.

##### 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.

##### Entanglement growth in diffusive systems with large spin

T. Rakovszky, F. Pollmann, C. von Keyserlingk

Communications Physics 4, 91 (2021).

##### 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.

##### Binary classification with classical instances and quantum labels

M.C. Caro

Quantum Machine Intelligence 3, 18 (2021).

In classical statistical learning theory, one of the most well-studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A quantum analog of this task, with training data given as a quantum state has also been intensely studied and is now known to have the same sample complexity as its classical counterpart. We propose a novel quantum version of the classical binary classification task by considering maps with classical input and quantum output and corresponding classical-quantum training data. We discuss learning strategies for the agnostic and for the realizable case and study their performance to obtain sample complexity upper bounds. Moreover, we provide sample complexity lower bounds which show that our upper bounds are essentially tight for pure output states. In particular, we see that the sample complexity is the same as in the classical binary classification task w.r.t. its dependence on accuracy, confidence and the VC-dimension.

##### All-Electrical Magnon Transport Experiments in Magnetically Ordered Insulators

M. Althammer

Phys. Status Solidi-Rapid Res. Lett. 15 (8), 2100130 (2021).

Angular momentum transport is one of the cornerstones of spintronics. Spin angular momentum is not only transported by mobile charge carriers but also by the quantized excitations of the magnetic lattice in magnetically ordered systems. In this regard, magnetically ordered insulators (MOIs) provide a platform for magnon spin transport experiments without additional contributions from spin currents carried by mobile electrons. In combination with charge-to-spin current conversion processes in conductors with finite spin-orbit coupling, it is possible to realize all-electrical magnon transport schemes in thin-film heterostructures. Herein, an insight into such experiments and recent breakthroughs achieved is provided. Special attention is given to charge-current-based manipulation via an adjacent normal metal of magnon transport in MOIs in terms of spin-transfer torque. Moreover, the influence of two magnon modes with opposite spin in antiferromagnetic insulators on all-electrical magnon transport experiments is discussed.

##### 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, 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.

##### Controlling exciton many-body states by the electric-field effect in monolayer MoS2

J. Klein, A. Hötger, M. Florian, A. Steinhoff, A. Delhomme, T. Taniguchi, K. Watanabe, F. Jahnke, A.W. Holleitner, M. Potemski, C. Faugeras, J.J. Finley, A.V. Stier

Physical Review Research 3, L022009 (2021).

We report magneto-optical spectroscopy of gated monolayer MoS2 in high magnetic fields up to 28T and obtain new insights on the many-body interaction of neutral and charged excitons with the resident charges of distinct spin and valley texture. For neutral excitons at low electron doping, we observe a nonlinear valley Zeeman shift due to dipolar spin-interactions that depends sensitively on the local carrier concentration. As the Fermi energy increases to dominate over the other relevant energy scales in the system, the magneto-optical response depends on the occupation of the fully spin-polarized Landau levels (LL) in both K/K′ valleys. This manifests itself in a many-body state. Our experiments demonstrate that the exciton in monolayer semiconductors is only a single particle boson close to charge neutrality. We find that away from charge neutrality it smoothly transitions into polaronic states with a distinct spin-valley flavor that is defined by the LL quantized spin and valley texture.

##### 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.

##### 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.

##### Higher-order and fractional discrete time crystals in clean long-range interacting systems

A. Pizzi, J. Knolle, A. Nunnenkamp

Nature Communications 12, 2341 (2021).

Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n>1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n>2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.

##### 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.

##### Gapless state of interacting Majorana fermions in a strain-induced Landau level

A. Agarwala, S. Bhattacharjee, J. Knolle, R. Moessner

Physical Review B 103, 134427 (2021).

Mechanical strain can generate a pseudomagnetic field, and hence Landau levels (LL), for low-energy excitations of quantum matter in two dimensions. We study the collective state of the fractionalized Majorana fermions arising from residual generic spin interactions in the central LL, where the projected Hamiltonian reflects the spin symmetries in intricate ways: emergent U(1) and particle-hole symmetries forbid any bilinear couplings, leading to an intrinsically strongly interacting system; also, they allow the definition of a filling fraction, which is fixed at 1/2. We argue that the resulting many-body state is gapless within our numerical accuracy, implying ultra-short-ranged spin correlations, while chirality correlators decay algebraically. This amounts to a Kitaev 'non-Fermi' spin liquid and shows that interacting Majorana Fermions can exhibit intricate behavior akin to fractional quantum Hall physics in an insulating magnet.

##### Adiabatic formation of bound states in the one-dimensional Bose gas

R. Koch, A. Bastianello, J.S. Caux

Physical Review B 103, 165121 (2021).

We consider the one-dimensional interacting Bose gas in the presence of time-dependent and spatially inhomogeneous contact interactions. Within its attractive phase, the gas allows for bound states of an arbitrary number of particles, which are eventually populated if the system is dynamically driven from the repulsive to the attractive regime. Building on the framework of generalized hydrodynamics, we analytically determine the formation of bound states in the limit of adiabatic changes in the interactions. Our results are valid for arbitrary initial thermal states and, more generally, generalized Gibbs ensembles.

##### 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.

##### Necessary criteria for Markovian divisibility of linear maps

M.C. Caro, B. Graswald

Journal of Mathematical Physics 62, 042203 (2021).

We describe how to extend the notion of infinitesimal Markovian divisibility from quantum channels to general linear maps and compact and convex sets of generators. We give a general approach toward proving necessary criteria for (infinitesimal) Markovian divisibility. With it, we prove two necessary criteria for infinitesimal divisibility of quantum channels in any finite dimension d: an upper bound on the determinant in terms of a Theta (d)-power of the smallest singular value and in terms of a product of Theta (d) smallest singular values. These allow us to analytically construct, in any given dimension, a set of channels that contains provably non-infinitesimal Markovian divisible ones. Moreover, we show that, in general, no such non-trivial criteria can be derived for the classical counterpart of this scenario.

##### On the Effectiveness of Fekete's Lemma in Information Theory

H. Boche, Y. Böck, C. Deppe

IEEE Information Theory Workshop (ITW) 20867558 (2021).

Fekete's lemma is a well known assertion that states the existence of limit values of superadditive sequences. In information theory, superadditivity of rate functions occurs in a variety of channel models, making Fekete's lemma essential to the corresponding capacity problems. We analyze Fekete's lemma with respect to effective convergence and computability and show that Fekete's lemma exhibits no constructive derivation. In particular, we devise a superadditive, computable sequence of rational numbers so that the associated limit value in the sense of Fekete's lemma is not a computable number. We further characterize the requirements for effective convergence and investigate the speed of convergence, as proposed by Rudolf Ahlswede in his 2006 Shannon lecture.

##### 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.

##### 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.

##### 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.

##### On the semi-decidability of remote state estimation and stabilization via noisy communication channels

H. Boche, Y. N. Böck, C. Deppe

60th IEEE Conference on Decision and Control 2021CDC (2021).

We consider the task of remote state estimation and stabilization of disturbed linear plants via noisy communication channels. In 2007 Matveev and Savkin established a surprising link between this problem and Shannon's theory of zero-error communication. By applying very recent results of computability of the channel reliability function and computability of the zero-error capacity of noisy channels by Boche and Deppe, we analyze if, on the set of linear time-invariant systems paired with a noisy communication channel, it is uniformly decidable by means of a Turing machine whether remote state estimation and stabilization is possible. The answer to this question largely depends on whether the plant is disturbed by random noise or not. Our analysis incorporates scenarios both with and without channel feedback, as well as a weakened form of state estimation and stabilization. In the broadest sense, our results yield a fundamental limit to the capabilities of computer-aided design and autonomous systems, assuming they are based on real-world digital computers.

##### On the Semi-Decidability of Remote State Estimation and Stabilization via Noisy Communication Channels

H. Boche, Y. N. Böck, C. Deppe

We consider the task of remote state estimation and stabilization of disturbed linear plants via noisy communication channels. In 2007 Matveev and Savkin established a surprising link between this problem and Shannon's theory of zero-error communication. By applying very recent results of computability of the channel reliability function and computability of the zero-error capacity of noisy channels by Boche and Deppe, we analyze if, on the set of linear time-invariant systems paired with a noisy communication channel, it is uniformly decidable by means of a Turing machine whether remote state estimation and stabilization is possible. The answer to this question largely depends on whether the plant is disturbed by random noise or not. Our analysis incorporates scenarios both with and without channel feedback, as well as a weakened form of state estimation and stabilization. In the broadest sense, our results yield a fundamental limit to the capabilities of computer-aided design and autonomous systems, assuming they are based on real-world digital computers.

##### 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.

##### Universal Length Dependence of Tensile Stress in Nanomechanical String Resonators

M. Bückle, Y.S. Klaß, F.B. Nägele, R. Braive, E.M. Weig

Physical Review Applied 15, 034063 (2021).

We investigate the tensile stress in freely suspended nanomechanical string resonators, and observe a material-independent dependence on the resonator length. We compare strongly stressed string resonators fabricated from four different material systems based on amorphous silicon nitride, crystalline silicon carbide as well as crystalline indium gallium phosphide. The tensile stress is found to increase by approximately 50% for shorter resonators. We establish a simple elastic model to describe the observed length dependence of the tensile stress. The model accurately describes our experimental data. This opens a perspective for stress engineering the mechanical quality factor of nanomechanical string resonators.

##### 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.

##### Butterfly effect and spatial structure of information spreading in a chaotic cellular automaton

S.-W. Liu, J. Willsher, T. Bilitewski, J.-J. Li, A. Smith, K. Christensen, R. Moessner, J. Knolle

Physical Review B 103, 094109 (2021).

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total on-site charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the topological label of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain—the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

##### 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.

##### Real- and Imaginary-Time Evolution with Compressed Quantum Circuits

S.-H. Lin, R. Dilip, A.G. Green, A. Smith, F. Pollmann

Prx Quantum 2, 010342 (2021).

The current generation of noisy intermediate-scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse-field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real-time evolution.

##### Visualizing quasiparticles from quantum entanglement for general one-dimensional phases

E. Wybo, F. Pollmann, S.L. Sondhi, Y. You

Physical Review B 103, 115120 (2021).

In this paper, we present a quantum information framework for the entanglement behavior of the low-energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence between the correlation matrix and the QP entanglement Hamiltonian for free fermions and find an extended in-gap state in the QP entanglement Hamiltonian as a consequence of the position uncertainty of the QP. A more general understanding of such an in-gap state can be extended to a Kramers theorem for the QP entanglement Hamiltonian, which also applies to strongly interacting systems. Further, we present a set of ubiquitous entanglement spectrum features, dubbed entanglement fragmentation, conditional mutual information, and measurement-induced nonlocal entanglement for QPs in 1D symmetry protected topological phases. Our result thus provides another framework to identify different phases of matter in terms of their QP entanglement.

##### 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.

##### Gaussian state entanglement witnessing through lossy compression

W. Kłobus, P. Cieśliński, L. Knips, P. Kurzyński, W. Laskowski

Physical Review A 103, 032412 (2021).

We study the possibility of witnessing Gaussian entanglement between two continuous-variable systems with the help of two spatially separated qubits. Its key ingredient is a local lossy state transfer from the original systems onto local qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems.

##### 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.

##### Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

T. Köhler, J. Stolpp, S. Paeckel

Scipost Physics 10, 058 (2021).

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrix-product-state representation and the single-site reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L = 501 while accounting for N-ph = 63 phonons per site with high precision in the CDW phase.

##### 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.

##### Raman sideband cooling in optical tweezer arrays for Rydberg dressing

N. Lorenz, L. Festa, L.-M. Steinert, C. Gross

Scipost Physics 10, 052 (2021).

Single neutral atoms trapped in optical tweezers and laser-coupled to Rydberg states provide a fast and flexible platform to generate configurable atomic arrays for quantum simulation. The platform is especially suited to study quantum spin systems in various geometries. However, for experiments requiring continuous trapping, inhomogeneous light shifts induced by the trapping potential and temperature broadening impose severe limitations. Here we show how Raman sideband cooling allows one to overcome those limitations, thus, preparing the stage for Rydberg dressing in tweezer arrays.

##### 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.

##### Improved active fiber-based retroreflector with intensity stabilization and a polarization monitor for the near UV

V. Wirthl, L. Maisenbacher, J. Weitenberg, A. Hertlein, A. Grinin, A. Matveev, R. Pohl, T.W. Hänsch, T. Udem

Optics Express 29, 7024-7048 (2021).

We present an improved active fiber-based retroreflector (AFR) providing high-quality wavefront-retracing anti-parallel laser beams in the near UV. We use our improved AFR for first-order Doppler-shift suppression in precision spectroscopy of atomic hydrogen, but our setup can be adapted to other applications where wavefront-retracing beams with defined laser polarization are important. We demonstrate how weak aberrations produced by the fiber collimator may remain unobserved in the intensity of the collimated beam but limit the performance of the AFR. Our general results on characterizing these aberrations with a caustic measurement can be applied to any system where a collimated high-quality laser beam is required. Extending the collimator design process by wave optics propagation tools, we achieved a four-lens collimator for the wavelength range 380-486 nm with the beam quality factor of M-2 similar or equal to 1.02, limited only by the not exactly Gaussian beam profile from the single-mode fiber. Furthermore, we implemented precise fiber-collimator alignment and improved the collimation control by combining a precision motor with a piezo actuator. Moreover, we stabilized the intensity of the wavefront-retracing beams and added in-situ monitoring of polarization from polarimetry of the retroreflected light. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

##### 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 ν = 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.

##### Bistability and time crystals in long-ranged directed percolation

A. Pizzi, A. Nunnenkamp, J. Knolle

Nature Communications 12, 1061 (2021).

Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions. In the presence of a periodic modulation of the update rules, we find that the system responds with a period larger than that of the modulation for an exponentially (in system size) long time. This breaking of discrete time translation symmetry of the underlying dynamics is enabled by a self-correcting mechanism of the long-ranged interactions which compensates noise-induced imperfections. Our work thus provides a firm example of a classical discrete time crystal phase of matter and paves the way for the study of novel non-equilibrium phases in the unexplored field of driven probabilistic cellular automata. A model of a classical discrete time crystal satisfying the criteria of persistent subharmonic response robust against thermal noise and defects has been lacking. Here, the authors show that these criteria are satisfied in one-dimensional probabilistic cellular automata with long-range interactions and bistability.

##### Study of spin symmetry in the doped t-J model using infinite projected entangled pair states

J.-W. Li, B. Bruognolo, A. Weichselbaum, J. von Delft

Physical Review B 103, 075127 (2021).

We study the two-dimensional t-J model on a square lattice using infinite projected entangled pair states (iPEPS). At small doping, multiple orders, such as antiferromagnetic order, stripe order and superconducting order, are intertwined or compete with each other. We demonstrate the role of spin symmetry at small doping by either imposing SU(2) spin symmetry or its U(1) subgroup in the iPEPS ansatz, thereby excluding or allowing spontaneous spin-symmetry breaking, respectively, in the thermodynamic limit. From a detailed comparison of our simulations, we provide evidence that stripe order is pinned by long-range antiferromagnetic order. We also find SU(2) iPEPS, enforcing a spin-singlet state, yields a uniform charge distribution and favors d-wave singlet pairing.

##### 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.

##### Algorithmic Computability of the Signal Bandwidth

H. Boche, U.J. Monich

Ieee Transactions on Information Theory 67 (4), 2450 - 2471 (2021).

The bandwidth of a bandlimited signal is an important number that is relevant in many applications and concepts. For example, according to the Shannon sampling theorem, the bandwidth determines the minimum sampling rate that is required for a perfect reconstruction. In this paper we consider bandlimited signals with finite energy and bandlimited signals that are absolutely integrable and analyze whether the bandwidth of these signals can be determined algorithmically. We employ the concept of Turing computability, a theoretical model that describes the fundamental limits of what can be solved algorithmically on a digital hardware, and ask if, for a given computable bandlimited signal, it is possible to compute its bandwidth on a Turing machine. We show that this is not possible in general, because there exist computable bandlimited signals for which the bandwidth is a non-computable real number. Even the weaker question if the bandwidth of a given signal is smaller than a predefined value cannot be always answered algorithmically. Further, we prove that in the case where the bandwidth in not computable, it is even impossible to algorithmically determine a sequence of upper bounds that converges to the actual bandwidth of the signal. As a positive result, we show that the set of signals whose bandwidth is larger than some given value is semi-decidable.

##### 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 22, 1499–1534 (2021).

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

L. Weiss, A. Gritsch, B. Merkel, A. 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.

##### Quantum many-body simulations of the two-dimensional Fermi-Hubbard model in ultracold optical lattices

B.-B. Chen, C. Chen, Z. Chen, J. Cui, Y. Zhai, A. Weichselbaum, J. von Delft, Z.Y. Meng, W. Li

Physical Review B 103, L041107 (2021).

Understanding quantum many-body states of correlated electrons is one main theme in modern condensedmatter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Plrys. Rev. X 8. 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. We observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.

##### 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, 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.

##### Quantum Channel State Masking

U. Pereg, C. Deppe, H. Boche

IEEE Transactions on Information Theory 67 (4), 2245 - 2268 (2021).

Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full characterization is established for the entanglement-assisted masking equivocation region with a maximally correlated channel state, and a regularized formula is given for the quantum capacity-leakage function without assistance. For Hadamard channels without assistance, we derive single-letter inner and outer bounds, which coincide in the standard case of a channel that does not depend on a state.

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

A. Heinz, J. Trautmann, N. Šantić, A. J. Park, I. Bloch, 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.

##### 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.

##### New signatures of the spin gap in quantum point contacts

K.L. Hudson, A. Srinivasan, O. Goulko, J. Adam, Q. Wang, L.A. Yeoh, O. Klochan, I. Farrer, D.A. Ritchie, A. Ludwig, A.D. Wieck, J. von Delft, A.R. Hamilton

Nature Communications 12, 5 (2021).

One dimensional semiconductor systems with strong spin-orbit interaction are both of fundamental interest and have potential applications to topological quantum computing. Applying a magnetic field can open a spin gap, a pre-requisite for Majorana zero modes. The spin gap is predicted to manifest as a field dependent dip on the first 1D conductance plateau. However, disorder and interaction effects make identifying spin gap signatures challenging. Here we study experimentally and numerically the 1D channel in a series of low disorder p-type GaAs quantum point contacts, where spin-orbit and hole-hole interactions are strong. We demonstrate an alternative signature for probing spin gaps, which is insensitive to disorder, based on the linear and non-linear response to the orientation of the applied magnetic field, and extract a spin-orbit gap Delta E approximate to 500 mu eV. This approach could enable one-dimensional hole systems to be developed as a scalable and reproducible platform for topological quantum applications. In one-dimensional systems, the combination of a strong spin-orbit interaction and an applied magnetic field can give rise to a spin-gap, however experimental identification is difficult. Here, the authors present new signatures for the spin-gap, and verify these experimentally in hole QPCs.

##### 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.

##### Formation of spatial patterns by spin-selective excitations of interacting fermions

T. Köhler, S. Paeckel, C. Meyer, S.R. Manmana

Physical Review B 102, 235166 (2020).

We describe the formation of charge- and spin-density patterns induced by spin-selective photoexcitations of interacting fermionic systems in the presence of a microstructure. As an example, we consider a one-dimensional Hubbard-like system with a periodic magnetic microstructure, which has a uniform charge distribution in its ground state, and in which a long-lived charge-density pattern is induced by the spin-selective photoexcitation. Using tensor-network methods, we study the full quantum dynamics in the presence of electron-electron interactions and identify doublons as the main decay channel for the induced charge pattern. Our setup is compared to the optically induced spin transfer (OISTR) mechanism, in which ultrafast optically induced spin transfer in Heusler and magnetic compounds is associated to the difference of the local density of states of the different elements in the alloys. We find that applying a spin-selective excitation there induces spatially periodic patterns in local observables. Implications for pump-probe experiments on correlated materials and experiments with ultracold gases on optical lattices are discussed.

##### 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.

##### 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.

##### Signatures of a degenerate many-body state of interlayer excitons in a van der Waals heterostack

L. Sigl, F. Sigger, F. Kronowetter, J. Kiemle, J. Klein, K. Watanabe, T. Taniguchi, J.J. Finley, U. Wurstbauer, A.W. Holleitner

Physical Review Research 2, 042044(R) (2020).

Atomistic van der Waals heterostacks are ideal systems for high-temperature exciton condensation because of large exciton binding energies and long lifetimes. Charge transport and electron energy-loss spectroscopy showed first evidence of excitonic many-body states in such two-dimensional materials. Pure optical studies, the most obvious way to access the phase diagram of photogenerated excitons, have been elusive. We observe several criticalities in photogenerated exciton ensembles hosted in MoSe2-WSe2 heterostacks with respect to photoluminescence intensity, linewidth, and temporal coherence pointing towards the transition to a coherent many-body quantum state, consistent with the predicted critical degeneracy temperature. For this state, the estimated occupation is approximately 100% and the phenomena survive above 10 K.Y

##### 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.

##### 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.

##### 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.

##### Z(2) lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

L. Homeier, C. Schweizer, M. Aidelsburger, A. Fedorov, F. 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.

##### From Luttinger liquids to Luttinger droplets via higher-order bosonization identities

S. Huber, M.2 Kollar

Physical Review Research 2, 043336 (2020).

We derive generalized Kronig identities expressing quadratic fermionic terms including momentum transfer to bosonic operators and use them to obtain the exact solution for one-dimensional fermionic models with linear dispersion in the presence of position-dependent local interactions and scattering potential. In these Luttinger droplets, which correspond to Luttinger liquids with spatial variations or constraints, the position dependencies of the couplings break the translational invariance of correlation functions and modify the Luttinger-liquid interrelations between excitation velocities.

##### 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.

##### 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.

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

M. Iqbal, N. Schuch

Physical Review X 11, 041014 (2021).

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.

##### 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.

##### Turing Meets Shannon: Computable Sampling Type Reconstruction With Error Control

H. Boche, U.J. Moenich

Ieee Transactions on Signal Processing 68, 6350-6365 (2020).

The conversion of analog signals into digital signals and vice versa, performed by sampling and interpolation, respectively, is an essential operation in signal processing. When digital computers are used to compute the analog signals, it is important to effectively control the approximation error. In this paper we analyze the computability, i.e., the effective approximation of bandlimited signals in the Bernstein spaces B-pi(p),1 <= p < infinity, and of the corresponding discrete-time signals that are obtained by sampling. We show that for 1 < p < infinity, computability of the discrete-time signal implies computability of the continuous-time signal. For p = 1 this correspondence no longer holds. Further, we give a necessary and sufficient condition for computability and show that the Shannon sampling series provides a canonical approximation algorithm for p > 1. We discuss BIBO stable LTI systems and the time-domain concentration behavior of bandlimited signals as applications.

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

B. Merkel, A. Ulanowski, A. 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.

##### On the Solvability of the Peak Value Problem for Bandlimited Signals With Applications

H. Boche, U.J. Mönich

Ieee Transactions on Signal Processing 69, 103-118 (2020).

In this paper we study from an algorithmic perspective the problem of finding the peak value of a bandlimited signal. This problem plays an important role in the design and optimization of communication systems. We show that the peak value problem, i.e., computing the peak value of a bandlimited signal from its samples, can be solved algorithmically if oversampling is used. Without oversampling this is not possible. There exist bandlimited signals, for which the sequence of samples is computable, but the signal itself is not. This problem is directly related to the question whether there is a link between computability in the digital domain and the analog domain, and hence to a fundamental signal processing problem. We show that there is an asymmetry between continuous-time and discrete-time computability. Further, we study the decay behavior of computable bandlimited signals, which describes the concentration of the signals in the time domain, and, for locally computable bandlimited signals, we analyze if it is always possible to decide algorithmically whether the peak value is smaller than a given threshold.

##### 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.

##### 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.

##### 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.

##### Photon-level broadband spectroscopy and interferometry with two frequency combs

N. Picque, T.W. Hänsch

Proceedings of the National Academy of Sciences of the United States of America 117 (43), 26688-26691 (2020).

We probe complex optical spectra at high resolution over a broad span in almost complete darkness. Using a single photon-counting detector at light power levels that are a billion times weaker than commonly employed, we observe interferences in the counting statistics with two separate mode-locked femtosecond lasers of slightly different repetition frequencies, each emitting a comb of evenly spaced spectral lines over a wide spectral span. Unique advantages of the emerging technique of dual-comb spectroscopy, such as multiplex data acquisition with many comb lines, potential very high resolution, and calibration of the frequency scale with an atomic clock, can thus be maintained for scenarios where only few detectable photons can be expected. Prospects include spectroscopy of weak scattered light over long distances, fluorescence spectroscopy of single trapped atoms or molecules, or studies in the extreme-ultraviolet or even soft-X-ray region with comb sources of low photon yield. Our approach defies intuitive interpretations in a picture of photons that exist before detection.

##### 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.

##### Renormalized Lindblad driving: A numerically exact nonequilibrium quantum impurity solver

M. Lotem, A. Weichselbaum, J. von Delft, M. Goldstein

Physical Review Research 2, 043052 (2021).

The accurate characterization of nonequilibrium strongly correlated quantum systems has been a longstanding challenge in many-body physics. Notable among them are quantum impurity models, which appear in various nanoelectronic and quantum computing applications. Despite their seeming simplicity, they feature correlated phenomena, including small emergent energy scales and non-Fermi-liquid physics, requiring renormalization group treatment. This has typically been at odds with the description of their nonequilibrium steady state under finite bias, which exposes their nature as open quantum systems. We present a numerically exact method for obtaining the nonequilibrium state of a general quantum impurity coupled to metallic leads at arbitrary voltage or temperature bias, which we call "RL-NESS" (renormalized Lindblad-driven nonequilibrium steady state). It is based on coherently coupling the impurity to discretized leads which are treated exactly. These leads are furthermore weakly coupled to reservoirs described by Lindblad dynamics which impose voltage or temperature bias. Going beyond previous attempts, we exploit a hybrid discretization scheme for the leads together with Wilson's numerical renormalization group, in order to probe exponentially small energy scales. The steady state is then found by evolving a matrix-product density operator via real-time Lindblad dynamics, employing a dissipative generalization of the time-dependent density matrix renormalization group. In the long-time limit, this procedure successfully converges to the steady state at finite bond dimension due to the introduced dissipation, which bounds the growth of entanglement. We thoroughly test the method against the exact solution of the noninteracting resonant level model. We then demonstrate its power using an interacting two-level model, for which it correctly reproduces the known limits, and gives the full I-V curve between them.

##### 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.

##### Slave-boson description of pseudogap metals in t-J models

J. Brunkert, M. Punk

Physical Review Research 2, 043019 (2020).

We present a simple modification of the standard U(1) slave boson construction for the single band t-J model which accounts for two-particle bound states of spinons and holons. This construction naturally gives rise to fractionalized Fermi-liquid ground states, featuring small, hole-like pocket Fermi surfaces with an anisotropic quasiparticle weight in the absence of broken symmetries. In a specific parameter regime our approach maps the square lattice t-J model to a generalized quantum dimer model, which was introduced as a toy model for the metallic pseudogap phase in hole-doped cuprates in [Proc. Natl. Acad. Sci. USA 112, 9552 (2015)]. Our slave boson construction captures essential features of the nodal-antinodal dichotomy and straightforwardly describes sharp, Fermi arc-like features in the electron spectral function. Moreover, it allows us to study quantum phase transitions between fractionalized Fermi-liquid phases and superconductors or ordinary Fermi liquids.

##### Warum der neue Mobilfunkstandard wirklich revolutionär ist. Was durch 5G für Deutschland auf dem Spiel steht

F.H.P. Fitzek, H. Boche

Frankfurter Allgemeiene Zeitung Digitec 243, 20 (2022).

##### 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.

##### 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.

##### Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using the Anderson-Holstein model

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

Physical Review Research 2, 033379 (2020).

We analyze ultrafast tunneling experiments in which electron transport through a localized orbital is induced by a single-cycle terahertz (THz) pulse. We include both electron-electron and electron-phonon interactions on the localized orbital using the Anderson-Holstein model and consider two possible filling factors, the singly occupied Kondo regime and the doubly occupied regime relevant to recent experiments with a pentacene molecule. Our analysis is based on variational non-Gaussian states and provides the accurate description of the degrees of freedom at very different energies, from the high microscopic energy scales to the Kondo temperature TK. To establish the validity of this method we apply this formalism to study the Anderson model in the Kondo regime in the absence of coupling to phonons. We demonstrate that it correctly reproduces key properties of the model, including the screening of the impurity spin, formation of the resonance at the Fermi energy, and a linear conductance of 2e(2)/h. We discuss the suppression of the Kondo resonance by the electron-phonon interaction on the impurity site. When analyzing THz-STM experiments we compute the time dependence of the key physical quantities, including current, the number of electrons on the localized orbital, and the number of excited phonons. We find long-lived oscillations of the phonon that persist long after the end of the pulse. We compare the results for the interacting system to the noninteracting resonant level model.

##### Quantitative functional renormalization group description of the two-dimensional Hubbard model

C. Hille, F.B. Kugler, C.J. Eckhardt, Y.-Y. He, A. Kauch, C. Honerkamp, A. Toschi, S. Andergassen

Physical Review Research 2, 033372 (2020).

Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In particular, we show that the recently introduced multiloop extension of the fRG flow equations for the self-energy and two-particle vertex allows for a precise match with the parquet approximation also for two-dimensional lattice problems. The refinement with respect to previous fRG-based computation schemes relies on an accurate treatment of the frequency and momentum dependences of the two-particle vertex, which combines a proper inclusion of the high-frequency asymptotics with the so-called truncated unity fRG for the momentum dependence. The adoption of the latter scheme requires, as an essential step, a consistent modification of the flow equation of the self-energy. We quantitatively compare our fRG results for the self-energy and momentum-dependent susceptibilities and the corresponding solution of the parquet approximation to determinant quantum Monte Carlo data, demonstrating that the fRG is remarkably accurate up to moderate interaction strengths. The presented methodological improvements illustrate how fRG flows can be brought to a quantitative level for two-dimensional problems, providing a solid basis for the application to more general systems.

##### 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.

##### Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2) x SU(3) Spin-Orbital Kondo Model

E. Walter, K. M. Stadler, S.-S. B. Lee, Y. Wang, G. Kotliar, A. Weichselbaum, J. von Delft

Physical Review X 10, 031052 (2020).

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, T-sp < T-orb, the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-ofthe-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig's conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an SU(2) x SU(3) spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity's spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as chi(imp)(sp) similar to omega(-gamma), with gamma > 1.

##### 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.

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

D. González-Cuadra, A. Dauphin, M. Aidelsburger, M. Lewenstein, A. 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