1
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Martone GI, Cherroret N. Time Translation Symmetry Breaking in an Isolated Spin-Orbit-Coupled Fluid of Light. PHYSICAL REVIEW LETTERS 2023; 131:013803. [PMID: 37478429 DOI: 10.1103/physrevlett.131.013803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Revised: 05/14/2023] [Accepted: 06/08/2023] [Indexed: 07/23/2023]
Abstract
We study the interplay between intrinsic spin-orbit coupling and nonlinear photon-photon interactions in a nonparaxial, elliptically polarized fluid of light propagating in a bulk Kerr medium. We find that in situations where the nonlinear interactions induce birefringence, i.e., a polarization-dependent nonlinear refractive index, their interplay with spin-orbit coupling results in an interference between the two polarization components of the fluid traveling at different wave vectors, which entails the breaking of translation symmetry along the propagation direction. This phenomenon leads to a Floquet band structure in the Bogoliubov spectrum of the fluid, and to characteristic oscillations of its intensity correlations. We characterize these oscillations in detail and point out their exponential growth at large propagation distances, revealing the presence of parametric resonances.
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Affiliation(s)
- Giovanni I Martone
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
- CNR NANOTEC, Institute of Nanotechnology, Via Monteroni, 73100 Lecce, Italy
- INFN, Sezione di Lecce, 73100 Lecce, Italy
| | - Nicolas Cherroret
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
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2
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Jin HK, Knolle J, Knap M. Fractionalized Prethermalization in a Driven Quantum Spin Liquid. PHYSICAL REVIEW LETTERS 2023; 130:226701. [PMID: 37327444 DOI: 10.1103/physrevlett.130.226701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2022] [Revised: 03/02/2023] [Accepted: 05/15/2023] [Indexed: 06/18/2023]
Abstract
Quantum spin liquids subject to a periodic drive can display fascinating nonequilibrium heating behavior because of their emergent fractionalized quasiparticles. Here, we investigate a driven Kitaev honeycomb model and examine the dynamics of emergent Majorana matter and Z_{2} flux excitations. We uncover a distinct two-step heating profile-dubbed fractionalized prethermalization-and a quasistationary state with vastly different temperatures for the matter and the flux sectors. We argue that this peculiar prethermalization behavior is a consequence of fractionalization. Furthermore, we discuss an experimentally feasible protocol for preparing a zero-flux initial state of the Kiteav honeycomb model with a low energy density, which can be used to observe fractionalized prethermalization in quantum information processing platforms.
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Affiliation(s)
- Hui-Ke Jin
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
| | - Johannes Knolle
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße. 4, 80799 München, Germany
- Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
| | - Michael Knap
- Technical University of Munich, TUM School of Natural Sciences, Physics Department, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstraße. 4, 80799 München, Germany
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3
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Haldar A, Das A. Statistical mechanics of Floquet quantum matter: exact and emergent conservation laws. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:234001. [PMID: 34020440 DOI: 10.1088/1361-648x/ac03d2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2021] [Accepted: 05/21/2021] [Indexed: 06/12/2023]
Abstract
Equilibrium statistical mechanics rests on the assumption of chaotic dynamics of a system modulo the conservation laws of local observables: extremization of entropy immediately gives Gibbs' ensemble (GE) for energy conserving systems and a generalized version of it (GGE) when the number of local conserved quantities is more than one. Through the last decade, statistical mechanics has been extended to describe the late-time behaviour of periodically driven (Floquet) quantum matter starting from a generic state. The structure built on the fundamental assumptions of ergodicity and identification of the relevant conservation laws in this inherently non-equilibrium setting. More recently, it has been shown that the statistical mechanics of Floquet systems has a much richer structure due to the existence ofemergentconservation laws: these are approximate but stable conservation laws arisingdue to the drive, and are not present in the undriven system. Extensive numerical and analytical results support perpetual stability of these emergent (though approximate) conservation laws, probably even in the thermodynamic limit. This banks on the recent finding of a sharp threshold for Floquet thermalization in clean, interacting non-integrable Floquet systems. This indicates to the possibility of stable Floquet phases of matter in disorder-free systems. This review intends to give a self-contained theoretical overview of these developments for a broad physics audience. We conclude by briefly surveying the current experimental scenario.
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Affiliation(s)
- Asmi Haldar
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Arnab Das
- Indian Association for the Cultivation of Science (School of Physical Sciences), 2A & 2B Raja S. C. Mullick Road, Kolkata 700032, India
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4
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Beatrez W, Janes O, Akkiraju A, Pillai A, Oddo A, Reshetikhin P, Druga E, McAllister M, Elo M, Gilbert B, Suter D, Ajoy A. Floquet Prethermalization with Lifetime Exceeding 90 s in a Bulk Hyperpolarized Solid. PHYSICAL REVIEW LETTERS 2021; 127:170603. [PMID: 34739295 DOI: 10.1103/physrevlett.127.170603] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
We report the observation of long-lived Floquet prethermal states in a bulk solid composed of dipolar-coupled ^{13}C nuclei in diamond at room temperature. For precessing nuclear spins prepared in an initial transverse state, we demonstrate pulsed spin-lock Floquet control that prevents their decay over multiple-minute-long periods. We observe Floquet prethermal lifetimes T_{2}^{'}≈90.9 s, extended >60 000-fold over the nuclear free induction decay times. The spins themselves are continuously interrogated for ∼10 min, corresponding to the application of ≈5.8×10^{6} control pulses. The ^{13}C nuclei are optically hyperpolarized by lattice nitrogen vacancy centers; the combination of hyperpolarization and continuous spin readout yields significant signal-to-noise ratio in the measurements. This allows probing the Floquet thermalization dynamics with unprecedented clarity. We identify four characteristic regimes of the thermalization process, discerning short-time transient processes leading to the prethermal plateau and long-time system heating toward infinite temperature. This Letter points to new opportunities possible via Floquet control in networks of dilute, randomly distributed, low-sensitivity nuclei. In particular, the combination of minutes-long prethermal lifetimes and continuous spin interrogation opens avenues for quantum sensors constructed from hyperpolarized Floquet prethermal nuclei.
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Affiliation(s)
- William Beatrez
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Otto Janes
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Amala Akkiraju
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Arjun Pillai
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Alexander Oddo
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Paul Reshetikhin
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Emanuel Druga
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Maxwell McAllister
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Mark Elo
- Tabor Electronics, Inc., Hatasia 9, Nesher 3660301, Israel
| | - Benjamin Gilbert
- Energy Geoscience Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Dieter Suter
- Fakultät Physik, Technische Universität Dortmund, D-44221 Dortmund, Germany
| | - Ashok Ajoy
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
- Lawrence Berkeley National Laboratory, Chemical Science Division, University of California, Berkeley, Berkeley, California 94720, USA
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5
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Okamoto J, Peronaci F. Floquet prethermalization and Rabi oscillations in optically excited Hubbard clusters. Sci Rep 2021; 11:17994. [PMID: 34504126 PMCID: PMC8429774 DOI: 10.1038/s41598-021-97104-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 08/18/2021] [Indexed: 11/10/2022] Open
Abstract
We study the properties of Floquet prethermal states in two-dimensional Mott-insulating Hubbard clusters under continuous optical excitation. With exact-diagonalization simulations, we show that Floquet prethermal states emerge not only off resonance, but also for resonant excitation, provided a small field amplitude. In the resonant case, the long-lived quasi-stationary Floquet states are characterized by Rabi oscillations of observables such as double occupation and kinetic energy. At stronger fields, thermalization to infinite temperature is observed. We provide explanations to these results by means of time-dependent perturbation theory. The main findings are substantiated by a finite-size analysis.
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Affiliation(s)
- Junichi Okamoto
- Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg, Germany. .,EUCOR Centre for Quantum Science and Quantum Computing, University of Freiburg, Hermann-Herder-Str. 3, 79104, Freiburg, Germany.
| | - Francesco Peronaci
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187, Dresden, Germany
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6
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Sen A, Sen D, Sengupta K. Analytic approaches to periodically driven closed quantum systems: methods and applications. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:443003. [PMID: 34359051 DOI: 10.1088/1361-648x/ac1b61] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus (FM) expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a FM resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.
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Affiliation(s)
- Arnab Sen
- School of Physical Sciences, Indian Association for the Cultivation of Science, 2A and 2B Raja S C Mullick Road, Jadavpur 700032, India
| | - Diptiman Sen
- Center for High Energy Physics and Department of Physics, Indian Institute of Science, Bengaluru 560012, India
| | - K Sengupta
- School of Physical Sciences, Indian Association for the Cultivation of Science, 2A and 2B Raja S C Mullick Road, Jadavpur 700032, India
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7
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Rajak A, Dana I. Stability, isolated chaos, and superdiffusion in nonequilibrium many-body interacting systems. Phys Rev E 2020; 102:062120. [PMID: 33465993 DOI: 10.1103/physreve.102.062120] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2020] [Accepted: 10/29/2020] [Indexed: 11/07/2022]
Abstract
We study stability and chaotic-transport features of paradigmatic nonequilibrium many-body systems, i.e., periodically kicked and interacting particles, for arbitrary number of particles, nonintegrability strength unbounded from above, and different interaction cases. We rigorously show that under the latter general conditions and in strong nonintegrability regimes there exist fully stable orbits, accelerator-mode (AM) fixed points, performing ballistic motion in momentum. These orbits exist despite of the completely and strongly chaotic phase space with generally fast Arnol'd diffusion. It is numerically shown that an "isolated chaotic zone" (ICZ), separated from the rest of the phase space, remains localized around an AM fixed point for long times even when this point is partially stable in only a few phase-space directions. This localization should reflect an Arnol'd diffusion in an ICZ much slower than that in the rest of phase space. The time evolution of the mean kinetic energy of an initial ensemble containing an ICZ exhibits superdiffusion instead of normal chaotic diffusion.
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Affiliation(s)
- Atanu Rajak
- Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel.,Presidency University, Kolkata, West Bengal 700073, India
| | - Itzhack Dana
- Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel
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8
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Ye B, Machado F, White CD, Mong RSK, Yao NY. Emergent Hydrodynamics in Nonequilibrium Quantum Systems. PHYSICAL REVIEW LETTERS 2020; 125:030601. [PMID: 32745424 DOI: 10.1103/physrevlett.125.030601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2019] [Revised: 11/13/2019] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed "density matrix truncation" (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system's dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (undriven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L=100), we are able to directly extract the energy diffusion coefficient.
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Affiliation(s)
- Bingtian Ye
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Francisco Machado
- Department of Physics, University of California, Berkeley, California 94720, USA
| | | | - Roger S K Mong
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
- Pittsburgh Quantum Institute, Pittsburgh, Pennsylvania 15260, USA
| | - Norman Y Yao
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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9
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Kuhlenkamp C, Knap M. Periodically Driven Sachdev-Ye-Kitaev Models. PHYSICAL REVIEW LETTERS 2020; 124:106401. [PMID: 32216424 DOI: 10.1103/physrevlett.124.106401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Revised: 11/27/2019] [Accepted: 01/21/2020] [Indexed: 06/10/2023]
Abstract
Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.
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Affiliation(s)
- Clemens Kuhlenkamp
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Michael Knap
- Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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10
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Mathey S, Diehl S. Absence of Criticality in the Phase Transitions of Open Floquet Systems. PHYSICAL REVIEW LETTERS 2019; 122:110602. [PMID: 30951330 DOI: 10.1103/physrevlett.122.110602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Revised: 12/21/2018] [Indexed: 06/09/2023]
Abstract
We address the nature of phase transitions in periodically driven systems coupled to a bath. The latter enables a synchronized nonequilibrium Floquet steady state at finite entropy, which we analyze for rapid drives within a nonequilibrium renormalization group (RG) approach. While the infinitely rapidly driven limit exhibits a second-order phase transition, here we reveal that fluctuations turn the transition first order when the driving frequency is finite. This can be traced back to a universal mechanism, which crucially hinges on the competition of degenerate, near critical modes associated with higher Floquet Brillouin zones. The critical exponents of the infinitely rapidly driven system-including a new, independent one-can yet be probed experimentally upon smoothly tuning towards that limit.
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Affiliation(s)
- Steven Mathey
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
| | - Sebastian Diehl
- Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
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11
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Howell O, Weinberg P, Sels D, Polkovnikov A, Bukov M. Asymptotic Prethermalization in Periodically Driven Classical Spin Chains. PHYSICAL REVIEW LETTERS 2019; 122:010602. [PMID: 31012730 DOI: 10.1103/physrevlett.122.010602] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Revised: 10/17/2018] [Indexed: 06/09/2023]
Abstract
We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet's theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.
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Affiliation(s)
- Owen Howell
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
| | - Phillip Weinberg
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
| | - Dries Sels
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
- Department of Physics, Harvard University, 17 Oxford st., Cambridge, Massachusetts 02138, USA
- Theory of quantum and complex systems, Universiteit Antwerpen, B-2610 Antwerpen, Belgium
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
| | - Marin Bukov
- Department of Physics, University of California, Berkeley, California 94720, USA
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12
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Boulier T, Maslek J, Bukov M, Bracamontes C, Magnan E, Lellouch S, Demler E, Goldman N, Porto JV. Parametric heating in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime. PHYSICAL REVIEW. X 2019; 9:10.1103/physrevx.9.011047. [PMID: 32117577 PMCID: PMC7047775 DOI: 10.1103/physrevx.9.011047] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We experimentally investigate the effects of parametric instabilities on the short-time heating process of periodically-driven bosons in 2D optical lattices with a continuous transverse (tube) degree of freedom. We analyze three types of periodic drives: (i) linear along the x-lattice direction only, (ii) linear along the lattice diagonal, and (iii) circular in the lattice plane. In all cases, we demonstrate that the BEC decay is dominated by the emergence of unstable Bogoliubov modes, rather than scattering in higher Floquet bands, in agreement with recent theoretical predictions. The observed BEC depletion rates are much higher when shaking both along x and y directions, as opposed to only x or only y. We also report an explosion of the decay rates at large drive amplitudes, and suggest a phenomenological description beyond Bogoliubov theory. In this strongly-coupled regime, circular drives heat faster than diagonal drives, which illustrates the non-trivial dependence of the heating on the choice of drive.
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Affiliation(s)
- T. Boulier
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742 USA
- Laboratoire Charles Fabry, Institut dOptique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - J. Maslek
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742 USA
| | - M. Bukov
- Department of Physics, University of California Berkeley, CA 94720, USA
| | - C. Bracamontes
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742 USA
| | - E. Magnan
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742 USA
- Laboratoire Charles Fabry, Institut dOptique Graduate School, CNRS, Université Paris-Saclay, 91127 Palaiseau cedex, France
| | - S. Lellouch
- Laboratoire de Physique des Lasers, Atomes et Molcules, Université Lille 1 Sciences et Technologies, CNRS; F-59655 Villeneuve d’Ascq Cedex, France
| | - E. Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - N. Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - J. V. Porto
- Joint Quantum Institute, National Institute of Standards and Technology and the University of Maryland, College Park, Maryland 20742 USA
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13
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Cooper NR, Dalibard J, Spielman IB. Topological bands for ultracold atoms. REVIEWS OF MODERN PHYSICS 2019; 91:10.1103/revmodphys.91.015005. [PMID: 32189812 PMCID: PMC7079706 DOI: 10.1103/revmodphys.91.015005] [Citation(s) in RCA: 113] [Impact Index Per Article: 22.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.
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Affiliation(s)
- N R Cooper
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - J Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 place Marcelin Berthelot, 75005, Paris, France
| | - I B Spielman
- Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland, Gaithersburg, Maryland 20899, USA
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14
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Messer M, Sandholzer K, Görg F, Minguzzi J, Desbuquois R, Esslinger T. Floquet Dynamics in Driven Fermi-Hubbard Systems. PHYSICAL REVIEW LETTERS 2018; 121:233603. [PMID: 30576215 DOI: 10.1103/physrevlett.121.233603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Indexed: 06/09/2023]
Abstract
We study the dynamics and timescales of a periodically driven Fermi-Hubbard model in a three-dimensional hexagonal lattice. The evolution of the Floquet many-body state is analyzed by comparing it to an equivalent implementation in undriven systems. The dynamics of double occupancies for the near- and off-resonant driving regime indicate that the effective Hamiltonian picture is valid for several orders of magnitude in modulation time. Furthermore, we show that driving a hexagonal lattice compared to a simple cubic lattice allows us to modulate the system up to 1 s, corresponding to hundreds of tunneling times, with only minor atom loss. Here, driving at a frequency close to the interaction energy does not introduce resonant features to the atom loss.
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Affiliation(s)
- Michael Messer
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Kilian Sandholzer
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Frederik Görg
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Joaquín Minguzzi
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Rémi Desbuquois
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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15
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Kandelaki E, Rudner MS. Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems. PHYSICAL REVIEW LETTERS 2018; 121:036801. [PMID: 30085807 DOI: 10.1103/physrevlett.121.036801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2017] [Indexed: 06/08/2023]
Abstract
We study transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. We investigate the dynamics of this gap opening process, taking into account the essential role of electron-electron interactions. Crucially, scattering due to interactions (1) induces dephasing, which erases memory of the system's prequench state and yields the intrinsic timescale for gap emergence, and (2) provides a mechanism for the system to absorb energy of the drive, leading to heating which must be mitigated to ensure the success of Floquet band engineering. We characterize the gap opening process via the system's generalized spectral function and correlators probed by photoemission experiments, and we identify a parameter regime at moderate driving frequencies where a hierarchy of timescales allows a well-defined Floquet gap to be produced and studied before the deleterious effects of heating set in.
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Affiliation(s)
- Ervand Kandelaki
- Niels Bohr International Academy and Center for Quantum Devices, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
| | - Mark S Rudner
- Niels Bohr International Academy and Center for Quantum Devices, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen, Denmark
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16
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Iadecola T, Hsieh TH. Floquet Supersymmetry. PHYSICAL REVIEW LETTERS 2018; 120:210603. [PMID: 29883152 DOI: 10.1103/physrevlett.120.210603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2017] [Revised: 03/01/2018] [Indexed: 06/08/2023]
Abstract
We show that time-reflection symmetry in periodically driven (Floquet) quantum systems enables an inherently nonequilibrium phenomenon structurally similar to quantum-mechanical supersymmetry. In particular, we find Floquet analogs of the Witten index that place lower bounds on the degeneracies of states with quasienergies 0 and π. Moreover, we show that in some cases time-reflection symmetry can also interchange fermions and bosons, leading to fermion-boson pairs with opposite quasienergy. We provide a simple class of disordered, interacting, and ergodic Floquet models with an exponentially large number of states at quasienergies 0 and π, which are robust as long as the time-reflection symmetry is preserved. Floquet supersymmetry manifests itself in the evolution of certain local observables as a period-doubling effect with dramatic finite-size scaling, providing a clear signature for experiments.
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Affiliation(s)
- Thomas Iadecola
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Timothy H Hsieh
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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17
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Peronaci F, Schiró M, Parcollet O. Resonant Thermalization of Periodically Driven Strongly Correlated Electrons. PHYSICAL REVIEW LETTERS 2018; 120:197601. [PMID: 29799256 DOI: 10.1103/physrevlett.120.197601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2017] [Indexed: 06/08/2023]
Abstract
We study the dynamics of the Fermi-Hubbard model driven by a time-periodic modulation of the interaction within nonequilibrium dynamical mean-field theory. For moderate interaction, we find clear evidence of thermalization to a genuine infinite-temperature state with no residual oscillations. Quite differently, in the strongly correlated regime, we find a quasistationary extremely long-lived state with oscillations synchronized with the drive (Floquet prethermalization). Remarkably, the nature of this state dramatically changes upon tuning the drive frequency. In particular, we show the existence of a critical frequency at which the system rapidly thermalizes despite the large interaction. We characterize this resonant thermalization and provide an analytical understanding in terms of a breakdown of the periodic Schrieffer-Wolff transformation.
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Affiliation(s)
- Francesco Peronaci
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
| | - Marco Schiró
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
| | - Olivier Parcollet
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
- Center for Computational Quantum Physics, Flatiron Institute, 162 Fifth Avenue, New York, New York 10010, USA
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18
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Notarnicola S, Iemini F, Rossini D, Fazio R, Silva A, Russomanno A. From localization to anomalous diffusion in the dynamics of coupled kicked rotors. Phys Rev E 2018; 97:022202. [PMID: 29548167 DOI: 10.1103/physreve.97.022202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2017] [Indexed: 06/08/2023]
Abstract
We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on an N-coupled kicked rotors model: We find that the interplay of quantumness and interactions dramatically modifies the system dynamics, inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically through a mapping onto an N-dimensional Anderson model. The thermodynamic limit N→∞, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: Using a mean-field approximation, we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than 1. This wealth of phenomena is a genuine effect of quantum interference: The classical system for N≥2 always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity or ergodicity properties of a many-body-driven system.
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Affiliation(s)
| | - Fernando Iemini
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
| | - Davide Rossini
- Dipartimento di Fisica, Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy
| | - Rosario Fazio
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
| | | | - Angelo Russomanno
- Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy
- NEST, Scuola Normale Superiore & Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
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19
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Reitter M, Näger J, Wintersperger K, Sträter C, Bloch I, Eckardt A, Schneider U. Interaction Dependent Heating and Atom Loss in a Periodically Driven Optical Lattice. PHYSICAL REVIEW LETTERS 2017; 119:200402. [PMID: 29219341 DOI: 10.1103/physrevlett.119.200402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2017] [Indexed: 06/07/2023]
Abstract
Periodic driving of optical lattices has enabled the creation of novel band structures not realizable in static lattice systems, such as topological bands for neutral particles. However, especially driven systems of interacting bosonic particles often suffer from strong heating. We have systematically studied heating in an interacting Bose-Einstein condensate in a driven one-dimensional optical lattice. We find interaction dependent heating rates that depend on both the scattering length and the driving strength and identify the underlying resonant intra- and interband scattering processes. By comparing the experimental data and theory, we find that, for driving frequencies well above the trap depth, the heating rate is dramatically reduced by the fact that resonantly scattered atoms leave the trap before dissipating their energy into the system. This mechanism of Floquet evaporative cooling offers a powerful strategy to minimize heating in Floquet engineered quantum gases.
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Affiliation(s)
- Martin Reitter
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Jakob Näger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Karen Wintersperger
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - Christoph Sträter
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01387 Dresden, Germany
| | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstraße 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - André Eckardt
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01387 Dresden, Germany
| | - Ulrich Schneider
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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20
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Quelle A, Smith CM. Resonances in a periodically driven bosonic system. Phys Rev E 2017; 96:052105. [PMID: 29347792 DOI: 10.1103/physreve.96.052105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Indexed: 06/07/2023]
Abstract
Periodically driven systems are a common topic in modern physics. In optical lattices specifically, driving is at the origin of many interesting phenomena. However, energy is not conserved in driven systems, and under periodic driving, heating of a system is a real concern. In an effort to better understand this phenomenon, the heating of single-band systems has been studied, with a focus on disorder- and interaction-induced effects, such as many-body localization. Nevertheless, driven systems occur in a much wider context than this, leaving room for further research. Here, we fill this gap by studying a noninteracting model, characterized by discrete, periodically spaced energy levels that are unbounded from above. We couple these energy levels resonantly through a periodic drive, and discuss the heating dynamics of this system as a function of the driving protocol. In this way, we show that a combination of stimulated emission and absorption causes the presence of resonant stable states. This will serve to elucidate the conditions under which resonant driving causes heating in quantum systems.
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Affiliation(s)
- Anton Quelle
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
| | - Cristiane Morais Smith
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
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21
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Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators. Nat Commun 2017; 8:1192. [PMID: 29084937 PMCID: PMC5662750 DOI: 10.1038/s41467-017-00876-y] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2017] [Accepted: 08/01/2017] [Indexed: 11/23/2022] Open
Abstract
The search for quantum spin liquids in frustrated quantum magnets recently has enjoyed a surge of interest, with various candidate materials under intense scrutiny. However, an experimental confirmation of a gapped topological spin liquid remains an open question. Here, we show that circularly polarized light can provide a knob to drive frustrated Mott insulators into a chiral spin liquid, realizing an elusive quantum spin liquid with topological order. We find that the dynamics of a driven Kagome Mott insulator is well-captured by an effective Floquet spin model, with heating strongly suppressed, inducing a scalar spin chirality Si · (Sj × Sk) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced chiral spin liquid near the equilibrium state. The results presented suggest employing dynamical symmetry breaking to engineer quantum spin liquids and access elusive phase transitions that are not readily accessible in equilibrium. Exotic quantum phases like spin liquids have long been investigated theoretically but it is difficult to find materials that realize these states in equilibrium. Here the authors propose that optical driving could be used to induce chiral spin liquid behaviour in frustrated Mott insulators.
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22
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Lorenzo S, Marino J, Plastina F, Palma GM, Apollaro TJG. Quantum Critical Scaling under Periodic Driving. Sci Rep 2017; 7:5672. [PMID: 28720852 PMCID: PMC5515946 DOI: 10.1038/s41598-017-06025-1] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2017] [Accepted: 06/07/2017] [Indexed: 12/02/2022] Open
Abstract
Universality is key to the theory of phase transitions, stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model’s microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time τbd, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.
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Affiliation(s)
- Salvatore Lorenzo
- Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, via Archirafi 36, I-90123, Palermo, Italy.,Quantum Technology Lab, Dipartimento di Fisica, Universita' degli Studi di Milano, 20133, Milano, Italy.,INFN, Sezione di Milano, I-20133, Milano, Italy
| | - Jamir Marino
- Institute of Theoretical Physics, University of Cologne, D-50937, Cologne, Germany
| | - Francesco Plastina
- Dip. Fisica, Università della Calabria, 87036, Arcavacata di Rende (CS), Italy.,INFN - Gruppo collegato di Cosenza, Cosenza, Italy
| | - G Massimo Palma
- Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, via Archirafi 36, I-90123, Palermo, Italy.,NEST, Istituto Nanoscienze-CNR, Pisa, Italy
| | - Tony J G Apollaro
- Dipartimento di Fisica e Chimica, Università degli Studi di Palermo, via Archirafi 36, I-90123, Palermo, Italy. .,Quantum Technology Lab, Dipartimento di Fisica, Universita' degli Studi di Milano, 20133, Milano, Italy. .,NEST, Istituto Nanoscienze-CNR, Pisa, Italy. .,Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast, Belfast, BT7 1NN, United Kingdom.
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23
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Weidinger SA, Knap M. Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system. Sci Rep 2017; 7:45382. [PMID: 28368025 PMCID: PMC5377259 DOI: 10.1038/srep45382] [Citation(s) in RCA: 91] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Accepted: 02/27/2017] [Indexed: 11/08/2022] Open
Abstract
We study the regimes of heating in the periodically driven O(N)-model, which is a well established 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 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 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.
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Affiliation(s)
- Simon A. Weidinger
- Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
| | - Michael Knap
- Department of Physics, Walter Schottky Institute, and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
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24
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Meinert F, Mark MJ, Lauber K, Daley AJ, Nägerl HC. Floquet Engineering of Correlated Tunneling in the Bose-Hubbard Model with Ultracold Atoms. PHYSICAL REVIEW LETTERS 2016; 116:205301. [PMID: 27258874 DOI: 10.1103/physrevlett.116.205301] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2016] [Indexed: 06/05/2023]
Abstract
We report on the experimental implementation of tunable occupation-dependent tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic modulation of the on-site interaction energy. The tunneling rate is inferred from a time-resolved measurement of the lattice site occupation after a quantum quench. We demonstrate coherent control of the tunneling dynamics in the correlated many-body system, including full suppression of tunneling as predicted within the framework of Floquet theory. We find that the tunneling rate explicitly depends on the atom number difference in neighboring lattice sites. Our results may open up ways to realize artificial gauge fields that feature density dependence with ultracold atoms.
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Affiliation(s)
- F Meinert
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - M J Mark
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - K Lauber
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
| | - A J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - H-C Nägerl
- Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
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25
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Bukov M, Kolodrubetz M, Polkovnikov A. Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields. PHYSICAL REVIEW LETTERS 2016; 116:125301. [PMID: 27058085 DOI: 10.1103/physrevlett.116.125301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Indexed: 06/05/2023]
Abstract
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.
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Affiliation(s)
- Marin Bukov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Michael Kolodrubetz
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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26
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Mori T, Kuwahara T, Saito K. Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems. PHYSICAL REVIEW LETTERS 2016; 116:120401. [PMID: 27058060 DOI: 10.1103/physrevlett.116.120401] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Indexed: 06/05/2023]
Abstract
We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasiconserved quantity in a long time scale. These two general properties lead to an intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in nearly integrable systems.
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Affiliation(s)
- Takashi Mori
- Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Tomotaka Kuwahara
- WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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