Quantifying and controlling prethermal nonergodicity in interacting Floquet matter.

Periodic driving is a powerful tool for engineering quantum states. In many-body systems, a key ingredient is the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the inevitable effects of heating. The underlying localized nonergodic nature of the wave function in this metastable regime is largely unexplored experimentally. 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, resulting in 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 complete experimental control and quantitative characterization of prethermal Floquet matter demonstrated here opens new possibilities for dynamical quantum engineering.