Publications

Bloch oscillations in the absence of a lattice.
Meinert, Florian, Knap, Michael, Kirilov, Emil, Jag-Lauber, Katharina, Zvonarev, Mikhail B., Demler, Eugene and Nägerl, Hanns-Christoph
Science , Volume 356, page: 945
June 2017

Abstract: The interplay of strong quantum correlations and far-from-equilibrium conditions can give rise to striking dynamical phenomena. We experimentally investigated the quantum motion of an impurity atom immersed in a strongly interacting one-dimensional Bose liquid and subject to an external force. We found that the momentum distribution of the impurity exhibits characteristic Bragg reflections at the edge of an emergent Brillouin zone. Although Bragg reflections are typically associated with lattice structures, in our strongly correlated quantum liquid they result from the interplay of short-range crystalline order and kinematic constraints on the many-body scattering processes in the one-dimensional system. As a consequence, the impurity exhibits periodic dynamics, reminiscent of Bloch oscillations, although the quantum liquid is translationally invariant. Our observations are supported by large-scale numerical simulations.

The Localization Transition in the Ultrametric Ensemble
von Soosten, P. and Warzel, Simone
Mathematical Physics
May 2017

Abstract: We study the hierarchical analogue of power-law random band matrices, a symmetric ensemble of random matrices with independent entries whose variances decay exponentially in the metric induced by the tree topology on N. We map out the entirety of the localization regime by proving the localization of eigenfunctions and Poisson statistics of the suitably scaled eigenvalues. Our results complement existing works on complete delocalization and random matrix universality, thereby proving the existence of a phase transition in this model.

submitted
Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system.
Weidinger, Simon A. and Knap, Michael
Sci. Rep. , Volume 7, page: 45382
April 2017

Abstract: We study the regimes of heating in the periodically driven O(N)-model, which represents a generic model for interacting quantum many-body systems. By computing the absorbed energy with a non-equilibrium Keldysh Green's function approach, we establish three dynamical regimes: at short times a single-particle dominated regime, at intermediate times a stable Floquet prethermal regime in which the system ceases to absorb, and at parametrically late times a thermalizing regime. Our simulations suggest that in the thermalizing regime the absorbed energy grows algebraically in time with an the exponent that approaches the universal value of 1/2, and is thus significantly slower than linear Joule heating. Our results demonstrate the parametric stability of prethermal states in a generic many-body system driven at frequencies that are comparable to its microscopic scales. This paves the way for realizing exotic quantum phases, such as time crystals or interacting topological phases, in the prethermal regime of interacting Floquet systems.

Quantum advantage with shallow circuits
Bravyi, Sergey, Gosset, David and König, Robert
April 2017

Abstract: We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An instance of the problem is specified by a quadratic form q that maps n-bit strings to integers modulo four. The goal is to identify a linear boolean function which describes the action of q on a certain subset of n-bit strings. We prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the 2D Hidden Linear Function problem with high probability must have depth logarithmic in n. In contrast, we show that this problem can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates acting locally on a two-dimensional grid.

URL: Quantum advantage with shallow circuits
submitted
Rare region effects and dynamics near the many-body localization transition.
Agarwal, Kartiek, Altman, Ehud, Demler, Eugene, Gopalakrishnan, Sarang, Huse, David A. and Knap, Michael
Annalen der Physik, Special issue on Many-Body Localization
January 2017

Abstract: The low-frequency response of systems near the many-body localization phase transition, on either side of the transition, is dominated by contributions from rare regions that are locally “in the other phase”, i.e., rare localized regions in a system that is typically thermal, or rare thermal regions in a system that is typically localized. Rare localized regions affect the properties of the thermal phase, especially in one dimension, by acting as bottlenecks for transport and the growth of entanglement, whereas rare thermal regions in the localized phase act as local “baths” and dominate the low-frequency response of the MBL phase. We review recent progress in understanding these rare-region effects, and discuss some of the open questions associated with them: in particular, whether and in what circumstances a single rare thermal region can destabilize the many-body localized phase.

Dynamical Cooper pairing in non-equilibrium electron-phonon systems.
Knap, Michael, Babadi, Mehrtash, Refael, Gil, Martin, Ivar and Demler, Eugene
Phys. Rev. B , Volume 94
December 2016

Abstract: We analyze Cooper pairing instabilities in strongly driven electron-phonon systems. The light-induced nonequilibrium state of phonons results in a simultaneous increase of the superconducting coupling constant and the electron scattering. We demonstrate that the competition between these effects leads to an enhanced superconducting transition temperature in a broad range of parameters. Our results may explain the observed transient enhancement of superconductivity in several classes of materials upon irradiation with high intensity pulses of terahertz light, and may pave new ways for engineering high-temperature light-induced superconducting states.

Finite-temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
Punk, Matthias
Phys. Rev. B , Volume 94(195113)
November 2016

Abstract: We study finite-temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent z=2, in contrast to z=3 found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to Ω/γ(T) at small momenta, where γ(T) is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte Carlo simulations at finite temperature, where results consistent with z=2 were found.

Ultrafast many-body interferometry of impurities coupled to a Fermi sea
Cetina, Marko, Jag, Michael, Lous, Rianne S., Fritsche, Isabella, Walraven, Jook T. M., Grimm, Rudolf, Levinsen, Jesper, Parish, Meera M., Schmidt, Richard, Knap, Michael and Demler, Eugene
Science , Volume 354(6308), page: 96-99
October 2016

Abstract: The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed matter systems, the time scale for such “ultrafast” processes is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we observed nonequilibrium dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the nonperturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasi-particles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods applied to strongly interacting quantum gases enable the study of the dynamics of quantum matter under extreme nonequilibrium conditions.

Adiabatic Quantum Search in Open Systems
Wild, Dominik S., Gopalakrishnan, Sarang, Knap, Michael, Yao, Norman Y. and Lukin, Mikhail D.
Phys. Rev. Lett. , Volume 117(150501)
October 2016

Abstract: Adiabatic quantum algorithms represent a promising approach to universal quantum computation. In isolated systems, a key limitation to such algorithms is the presence of avoided level crossings, where gaps become extremely small. In open quantum systems, the fundamental robustness of adiabatic algorithms remains unresolved. Here, we study the dynamics near an avoided level crossing associated with the adiabatic quantum search algorithm, when the system is coupled to a generic environment. At zero temperature, we find that the algorithm remains scalable provided the noise spectral density of the environment decays sufficiently fast at low frequencies. By contrast, higher order scattering processes render the algorithm inefficient at any finite temperature regardless of the spectral density, implying that no quantum speedup can be achieved. Extensions and implications for other adiabatic quantum algorithms will be discussed.

Matrix Product Approximations to Multipoint Functions in Two-Dimensional Conformal Field Theory
König, Robert and Scholz, Volkher B.
Physical Review Letters , Volume 117, page: 121601
September 2016

Abstract: Matrix product states (MPSs) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped 1D systems are approximable by MPSs, as shown by Hastings [M. B. Hastings, J. Stat. Mech. (2007) P08024]. By contrast, whether MPSs and more general tensor networks can accurately reproduce correlations in critical quantum systems or quantum field theories has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions. Here, we provide a complete positive answer to this question in the case of MPSs and 2D conformal field theory: we give quantitative estimates for the approximation error when approximating correlation functions by MPSs. Our work is constructive and yields an explicit MPS, thus providing both suitable initial values and a rigorous justification of variational methods.

Regimes of heating and dynamical response in driven many-body localized systems
Gopalakrishnan, Sarang, Knap, Michael and Demler, Eugene
Phys. Rev. B , Volume 94(094201)
September 2016

Abstract: We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective “heating rate” in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power law of time. We discuss the mechanisms underlying this crossover in the MBL phase. We comment on implications for the subdiffusive thermal phase near the MBL transition, and for response in imperfectly isolated MBL systems.

Spin structure factors of chiral quantum spin liquids on the kagome lattice
Halimeh, Jad C. and Punk, Matthias
Phys. Rev. B , Volume 94(104413)
September 2016

Abstract: We calculate dynamical spin structure factors for gapped chiral spin liquid states in the spin-1/2 Heisenberg antiferromagnet on the kagome lattice using Schwinger-boson mean-field theory. In contrast to static (equal-time) structure factors, the dynamical structure factor shows clear signatures of time-reversal symmetry breaking for chiral spin liquid states. In particular, momentum inversion k→−k symmetry as well as the sixfold rotation symmetry around the Γ point are lost. We highlight other interesting features, such as a relatively flat onset of the two-spinon continuum for the cuboc1 state. Our work is based on the projective symmetry group classification of time-reversal symmetry breaking Schwinger-boson mean-field states by Messio, Lhuillier, and Misguich.

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