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 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.
Highlights
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
Time-periodic driving is a powerful technique for synthesizing tailored quantum matter with drive-dependent properties and phase structures beyond the constraints imposed by thermodynamic equilibrium [1,2,3,4,5,6,7,8,9,10,11,12,13], and beyond a description in terms of thermal Gibbs ensembles
Since the inverse of the IPR provides a measure for the number of eigenstates of the time-evolution operator the system can access, it might appear surprising that even at large driving strengths the predicted and measured f0 remains so high throughout the dynamics; as we discuss in Appendix E, this can be understood as a consequence of the eventual dominance of higher-band kinetic energy splittings over any fixed coupling matrix element
Summary
Time-periodic driving is a powerful technique for synthesizing tailored quantum matter with drive-dependent properties and phase structures beyond the constraints imposed by thermodynamic equilibrium [1,2,3,4,5,6,7,8,9,10,11,12,13], and beyond a description in terms of thermal Gibbs ensembles. In many cases of interest, driven systems might still localize in metastable prethermal states [14,15,16,17,18] as a consequence of approximate integrals of motion given by a high-frequency approximation to the effective Floquet Hamitonian or, for weak interactions, by a macroscopic number of operators describing the occupations of singleparticle Floquet states Such prethermal states are conjectured to be described by a periodic Gibbs ensemble [15,19,20,21,22,23,24]. Quantify the formation of a prethermal nonergodic plateau and the long-time departure from it, either by a transition to a second prethermal plateau or, for stronger interactions, by the onset of ergodicity
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