# Floquet Heating in Interacting Atomic Gases with an Oscillating Force

## TL;DR

This paper provides a theoretical analysis of Floquet heating in cold atomic gases under periodic driving, deriving a general expression for the heating rate and exploring suppression mechanisms like Pauli blocking and dimensional effects.

## Contribution

It introduces a semiclassical formula for Floquet heating due to two-body collisions and analyzes suppression effects in fermionic and lower-dimensional systems.

## Key findings

- Heating rate proportional to particle density, collision cross section, and kinetic energy.
- Pauli blocking reduces heating in fermionic systems.
- Lower dimensional systems exhibit suppressed Floquet heating.

## Abstract

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.