Prethermal Floquet Steady States and Instabilities in the Periodically Driven, Weakly Interacting Bose-Hubbard Model

We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [$(\pi,\pi)$-momentum] condensates are stable on intermediate time scales. We find that condensate stability is \emph{enhanced} by increasing the drive strength, because this decreases the bandwidth of quasiparticle excitations and thus impedes resonant absorption and heating. Our results are directly relevant to a number of current experiments with ultracold bosons.