Floquet Heating in Interacting Atomic Gases with an Oscillating Force

We theoretically investigate the collisional heating of a cold atom system subjected to time-periodic forces. We show within the Floquet framework that this heating rate due to two-body collisions has a general semiclassical expression $\mathcal{P}\propto \rho \sigma v_{\rm col} E_0$, depending on the kinetic energy $E_0$ associated with the shaking, particle number density $\rho$, elastic collision cross section $\sigma$, and an effective collisional velocity $v_{\rm col}$ determined by the dominant energy scale in the system. We further show that the collisional heating is suppressed by Pauli blocking in cold fermionic systems, and by the modified density of states in systems in lower dimensions. Our results provide an exactly solvable example and reveal some general features of Floquet heating in interacting systems.