Publications

Bounds on the entanglement entropy of droplet states in the XXZ spin chain
Beaud, V. and Warzel, Simone
Journal of Mathematical Physics , Volume 59, page: 012109
January 2018

Abstract: We consider a class of one-dimensional quantum spin systems on the finite lattice Λ⊂ℤ, related to the XXZ spin chain in its Ising phase. It includes in particular the so-called droplet Hamiltonian. The entanglement entropy of energetically low-lying states over a bipartition Λ = B ∪ Bc is investigated and proven to satisfy a logarithmic bound in terms of min{n, |B|, |Bc|}, where n denotes the maximal number of down spins in the considered state. Upon addition of any (positive) random potential, the bound becomes uniformly constant on average, thereby establishing an area law. The proof is based on spectral methods: a deterministic bound on the local (many-body integrated) density of states is derived from an energetically motivated Combes–Thomas estimate.

Decoherence-protected memory for a single-photon qubit
Körber, Matthias, Morin, O., Langenfeld, S., Neuzner, A., Ritter, Stephan and Rempe, Gerhard
Nature Photonics , Volume 12, page: 18-21
December 2017

Abstract: Distributed quantum computation in a quantum network is based on the idea that qubits can be preserved and efficiently exchanged between long-lived, stationary network nodes via photonic links4. Although long qubit lifetimes have been observed and non-qubit excitations have been memorized the long-lived storage and efficient retrieval of a photonic qubit by means of a light–matter interface remains an outstanding challenge. Here, we report on a qubit memory based on a single atom coupled to a high-finesse optical resonator. By mapping the qubit between an interface basis with strong light–matter coupling and a memory basis with low decoherence, we achieve a coherence time exceeding 100 ms with a time-independent storage-and-retrieval efficiency of 22%. The former constitutes an improvement by two orders of magnitude and thus implements an efficient photonic qubit memory with a coherence time that exceeds the lower bound needed for direct qubit teleportation in a global quantum internet.

Edge Switching Transformations of Quantum Graphs
Aizenman, Michael, Schanz, H., Smilansky, U. and Warzel, Simone
Acta Physica Polonica A , Volume 132(6), page: 1699-1703
December 2017

Abstract: Discussed here are the effects of basics graph transformations on the spectra of associated quantum graphs. In particular it is shown that under an edge switch the spectrum of the transformed Schrödinger operator is interlaced with that of the original one. By implication, under edge swap the spectra before and after the transformation, denoted by {Eₙ}^{∞}ₙ₌₁ and {Ẽₙ}^{∞}ₙ₌₁ correspondingly, are level-2 interlaced, so that Eₙ-₂ ≤ Ẽₙ ≤ Eₙ₊₂. The proofs are guided by considerations of the quantum graphs' discrete analogs.

Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems
Bordia, Pranjal, Lüschen, Henrik, Scherg, Sebastian, Gopalakrishnan, Sarang, Knap, Michael, Schneider, Ulrich and Bloch, Immanuel
Physical Review X , Volume 7, page: 041047
November 2017

Abstract: In a many-body localized (MBL) quantum system, the ergodic hypothesis breaks down, giving rise to a fundamentally new many-body phase. Whether and under which conditions MBL can occur in higher dimensions remains an outstanding challenge both for experiments and theory. Here, we experimentally explore the relaxation dynamics of an interacting gas of fermionic potassium atoms loaded in a two-dimensional optical lattice with different quasiperiodic potentials along the two directions. We observe a dramatic slowing down of the relaxation for intermediate disorder strengths. Furthermore, beyond a critical disorder strength, we see negligible relaxation on experimentally accessible time scales, indicating a possible transition into a two-dimensional MBL phase. Our experiments reveal a distinct interplay of interactions, disorder, and dimensionality and provide insights into regimes where controlled theoretical approaches are scarce.

Dynamical quantum phase transitions in systems with continuous symmetry breaking
Weidinger, Simon A., Heyl, Markus, Silva, Alessandro and Knap, Michael
Physics Review B , Volume 96, page: 134313
October 2017

Abstract: Interacting many-body systems that are driven far away from equilibrium can exhibit phase transitions between dynamically emerging quantum phases, which manifest as singularities in the Loschmidt echo. Whether and under which conditions such dynamical transitions occur in higher-dimensional systems with spontaneously broken continuous symmetries is largely elusive thus far. Here, we study the dynamics of the Loschmidt echo in the three-dimensional O(N) model following a quantum quench from a symmetry-breaking initial state. The O(N) model exhibits a dynamical transition in the asymptotic steady state, separating two phases with a finite and vanishing order parameter, that is associated with the broken symmetry. We analytically calculate the rate function of the Loschmidt echo and find that it exhibits periodic kink singularities when this dynamical steady-state transition is crossed. The singularities arise exactly at the zero crossings of the oscillating order parameter. As a consequence, the appearance of the kink singularities in the transient dynamics is directly linked to a dynamical transition in the order parameter. Furthermore, we argue, that our results for dynamical quantum phase transitions in the O(N) model are general and apply to generic systems with continuous symmetry breaking.

Quantum sensing of weak radio-frequency signals by pulsed Mollow absorption spectroscopy
Joas, T., Waeber, A. M., Braunbeck, G. and Reinhard, Friedemann
Nat. Commun. , Volume 8, page: 964
October 2017

Abstract: Quantum sensors—qubits sensitive to external fields—have become powerful detectors for various small acoustic and electromagnetic fields. A major key to their success have been dynamical decoupling protocols which enhance sensitivity to weak oscillating (AC) signals. Currently, those methods are limited to signal frequencies below a few MHz. Here we harness a quantum-optical effect, the Mollow triplet splitting of a strongly driven two-level system, to overcome this limitation. We microscopically understand this effect as a pulsed dynamical decoupling protocol and find that it enables sensitive detection of fields close to the driven transition. Employing a nitrogen-vacancy center, we detect GHz microwave fields with a signal strength (Rabi frequency) below the current detection limit, which is set by the center’s spectral linewidth 1∕T2*. Pushing detection sensitivity to the much lower 1/T2 limit, this scheme could enable various applications, most prominently coherent coupling to single phonons and microwave photons.

Correcting coherent errors with surface codes
Bravyi, Sergey, Englbrecht, Matthias, König, Robert and Peard, Nolan
October 2017

Abstract: We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted Z-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on the 2D surface code in the presence of coherent errors. The algorithm has runtime O(n2), where n is the number of physical qubits. It allows us to simulate systems with more than one thousand qubits and obtain the first error threshold estimates for several toy models of coherent noise. Numerical results are reported for storage of logical states subject to Z-rotation errors and for logical state preparation with general SU(2) errors. We observe that for large code distances the effective logical-level noise is well-approximated by random Pauli errors even though the physical-level noise is coherent. Our algorithm works by mapping the surface code to a system of Majorana fermions.

submitted
Quantum simulations with ultracold atoms in optical lattices
Gross, Christian and Bloch, Immanuel
Science , Volume 357(6355), page: 995-1001
September 2017

Abstract: Abstract Quantum simulation, a subdiscipline of quantum computation, can provide valuable insight into difficult quantum problems in physics or chemistry. Ultracold atoms in optical lattices represent an ideal platform for simulations of quantum many-body problems. Within this setting, quantum gas microscopes enable single atom observation and manipulation in large samples. Ultracold atom–based quantum simulators have already been used to probe quantum magnetism, to realize and detect topological quantum matter, and to study quantum systems with controlled long-range interactions. Experiments on many-body systems out of equilibrium have also provided results in regimes unavailable to the most advanced supercomputers. We review recent experimental progress in this field and comment on future directions.

Non-Ergodic Delocalization in the Rosenzweig-Porter Model
von Soosten, P. and Warzel, Simone
Mathematical Physics
September 2017

Abstract: We consider the Rosenzweig-Porter model H=V+T−−√Φ, where V is a N×N diagonal matrix, Φ is drawn from the N×N Gaussian Orthogonal Ensemble, and N−1≪T≪1. We prove that the eigenfunctions of H are typically supported in a set of approximately NT sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. Our proof is based on martingale estimates along the characteristic curves of the stochastic advection equation satisfied by the local resolvent of the Brownian motion representation of H.

submitted
Noise-induced subdiffusion in strongly localized quantum systems
Gopalakrishnan, Sarang, Islam, K. Ranjibul and Knap, Michael
Phys. Rev. Lett. , Volume 119, page: 046601
July 2017

Abstract: We consider the dynamics of strongly localized systems subject to dephasing noise with arbitrary correlation time. Although noise inevitably induces delocalization, transport in the noise-induced delocalized phase is subdiffusive in a parametrically large intermediate-time window. We argue for this intermediate-time subdiffusive regime both analytically and using numerical simulations on single-particle localized systems. Furthermore, we show that normal diffusion is restored in the long-time limit, through processes analogous to variable-range hopping. With numerical simulations based on Lanczos exact diagonalization, we demonstrate that our qualitative conclusions are also valid for interacting systems in the many-body localized phase.

Quantum sensing
Degen, C. L., Reinhard, Friedemann and Cappellaro, P
Rev. Mod. Phys. , Volume 89(3)
July 2017

Abstract: “Quantum sensing” describes the use of a quantum system, quantum properties, or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors or atomic clocks. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions, and flux qubits. The field is expected to provide new opportunities—especially with regard to high sensitivity and precision—in applied physics and other areas of science. This review provides an introduction to the basic principles, methods, and concepts of quantum sensing from the viewpoint of the interested experimentalist.

Theory of parametrically amplified electron-phonon superconductivity
Babadi, Mehrtash, Knap, Michael, Martin, Ivar, Refael, Gil and Demler, Eugene
Phys. Rev. B , Volume 96, page: 014512
July 2017

Abstract: Ultrafast optical manipulation of ordered phases in strongly correlated materials is a topic of significant theoretical, experimental, and technological interest. Inspired by a recent experiment on light-induced superconductivity in fullerenes [M. Mitrano et al., Nature (London) 530, 461 (2016)], we develop a comprehensive theory of light-induced superconductivity in driven electron-phonon systems with lattice nonlinearities. In analogy with the operation of parametric amplifiers, we show how the interplay between the external drive and lattice nonlinearities lead to significantly enhanced effective electron-phonon couplings. We provide a detailed and unbiased study of the nonequilibrium dynamics of the driven system using the real-time Green's function technique. To this end, we develop a Floquet generalization of the Migdal-Eliashberg theory and derive a numerically tractable set of quantum Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We study the role of parametric phonon generation and electronic heating in destroying the transient superconducting state. Finally, we predict the transient formation of electronic Floquet bands in time- and angle-resolved photoemission spectroscopy experiments as a consequence of the proposed mechanism.

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