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arXiv:1809.05554 · Physical Review X

Quantifying and Controlling Prethermal Nonergodicity in Interacting Floquet Matter

K. Singh, C. J. Fujiwara, Z. A. Geiger, E. Q. Simmons, Mikhail Lipatov, A. Cao, P. Dotti, S. Rajagopal, R. Senaratne, T. Shimasaki, M. Heyl, A. Eckardt, David Weld

Published Oct 29, 2019• 42 citations
arXivHTMLPDF

Abstract

The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating.This dependence motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime.We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation.Using a double-quench protocol, we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions.We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space.Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization.The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.

DOI
10.1103/physrevx.9.041021

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The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating.This dependence motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime.We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation.Using a double-quench protocol, we measure an inverse participation ratio quantifying the degree of prethermal localization as a function of tunable drive parameters and interactions.We obtain a complete prethermal map of the drive-dependent properties of Floquet matter spanning four square decades of parameter space.Following the full time evolution, we observe sequential formation of two prethermal plateaux, interaction-driven ergodicity, and strongly frequency-dependent dynamics of long-time thermalization.The quantitative characterization of the prethermal Floquet matter realized in these experiments, along with the demonstration of control of its properties by variation of drive parameters and interactions, opens a new frontier for probing far-from-equilibrium quantum statistical mechanics and new possibilities for dynamical quantum engineering.
Periodic driving is a powerful tool for engineering tunable many-body quantum states. Such Floquet engineering relies on the existence of a localized prethermal regime, a state which remains incompletely understood. We report experiments on a many-body Floquet system consisting of ultracold atoms in an optical lattice subjected to sign-changing amplitude modulation. A double-quench protocol enables measurement of an inverse participation ratio quantifying the degree of prethermal localization as a function of continuously tunable drive parameters and interactions. Following the time evolution of the driven system, we observe the sequential formation of two localized prethermal plateaux, interaction-driven delocalization, and strongly frequency-dependent dynamics of departure from the prethermal state. The experimental control and quantitative characterization of Floquet prethermalization opens new possibilities for dynamical quantum engineering.
Floquet engineering is a versatile tool that uses periodic driving of a quantum system to build novel many-body quantum states with drive-dependent properties. In this thesis I will detail experiments performed in the Weld group which explore a many-body Floquet system consisting of tunably-interacting ultracold atoms in an optical lattice amplitude-modulated at up to a thousand percent. I will discuss experiments in which we use Floquet engineering to coherently control long-range quantum transport in hybridized Floquet-Bloch bands. I will also discuss our use of a double quench protocol to experimentally control and quantitatively characterize Floquet prethermalization associated with a periodic generalized Gibbs ensemble.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases.While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinitetemperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system-leading to long-lived "prethermal" regimes.In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model.By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude.The tunability of the lattice potentials allows us to explore one-and twodimensional systems in a range of different interacting regimes.Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension.Our results show experimental evidence of the phenomenon of Floquet prethermalization and provide insight into the characterization of heating for driven bosonic systems.
Periodic driving has emerged as a powerful tool in the quest to engineer new and exotic quantum phases. While driven many-body systems are generically expected to absorb energy indefinitely and reach an infinite-temperature state, the rate of heating can be exponentially suppressed when the drive frequency is large compared to the local energy scales of the system -- leading to long-lived 'prethermal' regimes. In this work, we experimentally study a bosonic cloud of ultracold atoms in a driven optical lattice and identify such a prethermal regime in the Bose-Hubbard model. By measuring the energy absorption of the cloud as the driving frequency is increased, we observe an exponential-in-frequency reduction of the heating rate persisting over more than 2 orders of magnitude. The tunability of the lattice potentials allows us to explore one- and two-dimensional systems in a range of different interacting regimes. Alongside the exponential decrease, the dependence of the heating rate on the frequency displays features characteristic of the phase diagram of the Bose-Hubbard model, whose understanding is additionally supported by numerical simulations in one dimension. Our results show experimental evidence of the phenomenon of Floquet prethermalization, and provide insight into the characterization of heating for driven bosonic systems.
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability with respect to random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are nonuniversal: we observe Fermi's golden rule scaling, power-law scaling inconsistent with the golden rule, and non-power-law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase the temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.