Floquet prethermalization and Rabi oscillations in optically excited Hubbard clusters

Floquet engineering is a growing field of study to realize exotic many-body quantum states beyond the realm of equilibrium material science. The Floquet picture in terms of effective Hamiltonians is stable in the limit of high-frequency driving, where the heating rate is suppressed. In contrast, when the driving frequency is comparable to the energies of the system, the effect of heating is non-negligible, and the analysis becomes intricate. However, even in this case, the existence of quasi-steady states, so-called Floquet prethermal states (FPSs), have been demonstrated, which expands the boundary of Floquet engineering to a realistic driving range. In this work, we have investigated the optically excited Hubbard clusters by exact diagonalization. We show that FPSs emerge not only off resonance but also for resonant excitation, provided a small field amplitude. Notably, FPSs at resonance occur with Rabi oscillations. At stronger fields, thermalization to infinite temperature is observed. We elucidate the origin of the FPSs using time-dependent perturbation theory and the two-site Hubbard model.