Publications

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.

Note: Editors' Suggestion

Low-Energy Fock-Space Localization for Attractive Hard-Core Particles in Disorder
Beaud, V. and Warzel, Simone
Annales Henri Poincaré , Volume 18(10), page: 3143–3166
June 2017

Abstract: We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is suggested by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. The proof relies on an energetically motivated Combes–Thomas estimate and an effective one-particle analysis. As an application, we show the exponential decay of the two-point function in the infinite system uniformly in the particle number.

Multiple-Quantum Transitions and Charge-Induced Decoherence of Donor Nuclear Spins in Silicon
Franke, David P., Pflüger, Moritz P. D., Itoh, Kohei M. and Brandt, Martin S.
PRL , Volume 118
June 2017

Abstract: We study single- and multiquantum transitions of the nuclear spins of an ensemble of ionized arsenic donors in silicon and find quadrupolar effects on the coherence times, which we link to fluctuating electrical field gradients present after the application of light and bias voltage pulses. To determine the coherence times of superpositions of all orders in the 4-dimensional Hilbert space, we use a phase-cycling technique and find that, when electrical effects were allowed to decay, these times scale as expected for a fieldlike decoherence mechanism such as the interaction with surrounding 29Si nuclear spins.

Scrambling and thermalization in a diffusive quantum many-body system
Bohrdt, A., Mendl, C. B., Endres, Manuel and Knap, Michael

Abstract: Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose–Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. Our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.

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