Statistical Floquet prethermalization of the Bose-Hubbard model

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large frequencies. In particular, for quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we develop a semiclassical description of Floquet prethermal states and link the suppressed heating rate to the low probability of finding many particles on a single site. We derive an analytic expression for the exponential suppression of heating valid at strong interactions and large temperatures, which matches the exact numerical solution of the model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.