Quantifying and Controlling Prethermal Nonergodicity in Interacting Floquet Matter

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 manybody 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.

Colloquium: Nonthermal pathways to ultrafast control in quantum materials

“…In practice, a high-frequency driving limit is absent in most real materials, since higher-lying bands and collective excitations provide a multitude of possibilities for resonant absorption at higher frequencies. Similarly, while MBL is realizable in cold atomic systems (Singh et al, 2019), it is typically destabilized in solids due to energy dissipation to the lattice or other degrees of freedom. Nonetheless, sufficiently slow energy absorption, for instance due to off-resonant driving or other ergodic obstructions to heating, can realize 'prethermal' dynamical regimes at short times (Fig.…”

Analytical solution for the steady states of the driven Hubbard model

“…This heating competes with any transient order established by the effective Hamiltonian, causing it to melt away and leading to the formation of a featureless, infinite temperature state in the long-time * joseph.tindall@physics.ox.ac.uk limit [29,30]. As a result, engineering Floquet Hamiltonians which are stable to heating on long timescales, allowing their prethermal states to be transiently observable is a current research endeavor attracting significant attention [31][32][33][34][35][36][37][38].…”

Dynamical Quantum Phase Transitions in the 1D Nonintegrable Spin‐1/2 Transverse Field XZZ Model

“…where k * is the particular mode driven from cos(2Φ k * ) = 0 which leads to vanish the argument in the logarithm in Eq. (8). It has to be mentioned that the self-consistent relations Eq.…”

“…Progress in the experimental control of ultracold atoms trapped in optical lattices has made a real possibility to study the nonequilibrium phenomena beyond the Ginzburg-Landau paradigm [1] where the behaviors of the systems basically are not susceptible to general principles of equilibrium. [2,3] This has led to the observation of many-body localization and prethermalization, [4][5][6][7][8] time crystals, [9][10][11] momentum-time skyrmions, [12] and dynamics in gauge theories. [13,14] In analog to some approaches such as the Kibble-Zurek mechanism [15] and measurement quench, [16,17] in recent years, the theory of dynamical quantum phase transition (DQPT) manifested with nonanalytic behaviors of the rate function in the time domain, that is, the logarithm function of the Loschmidt echo (LE), has attracted tremendous attention.…”