# Nonequilibrium thermodynamics and optimal cooling of a dilute atomic gas

## TL;DR

This paper develops a theoretical and experimental framework to analyze and optimize the nonequilibrium thermodynamics of a few-atom gas during cooling, focusing on entropy production and thermalization processes.

## Contribution

It introduces a method to optimize cooling sequences by minimizing entropy production and verifies a refined second law in a few-particle system.

## Key findings

- Single Raman pulse creates a nonequilibrium state that does not thermalize alone.
- Combining free evolution and cooling pulses achieves thermalization.
- Optimized pulse spacing minimizes entropy production and enhances cooling efficiency.

## Abstract

Characterizing and optimizing thermodynamic processes far from equilibrium is a challenge. This is especially true for nanoscopic systems made of few particles. We here theoretically and experimentally investigate the nonequilibrium dynamics of a gas of few noninteracting Cesium atoms confined in a nonharmonic optical dipole trap and exposed to degenerate Raman sideband cooling pulses. We determine the axial phase-space distribution of the atoms after each Raman cooling pulse by tracing the evolution of the gas with position-resolved fluorescence imaging. We evaluate from it the entropy production and the statistical length between each cooling steps. A single Raman pulse leads to a nonequilibrium state that does not thermalize on its own, due to the absence of interparticle collisions. Thermalization may be achieved by combining free phase-space evolution and trains of cooling pulses. We minimize the entropy production to a target thermal state to specify the optimal spacing between a sequence of equally spaced pulses and achieve in this way optimal thermalization. We finally use the statistical length to verify a refined version of the second law of thermodynamics. Altogether, these findings provide a general, theoretical and experimental, framework to analyze and optimize far-from-equilibrium processes of few-particle systems.