Cooling of atomic ensembles in optical cavities: Semiclassical limit

TL;DR

This paper develops a semiclassical model for cooling atomic ensembles inside optical cavities, deriving equations of motion and analyzing stationary distributions, with results matching previous models under certain conditions.

Contribution

It introduces a Fokker-Planck framework for atomic dynamics in optical cavities, extending understanding of cooling mechanisms in the semiclassical limit.

Findings

Derived a Fokker-Planck equation for atomic motion

Predicted atomic distribution in vacuum state regime

Confirmed agreement with previous models in specific parameters

Abstract

The semiclassical dynamics of atoms are theoretically studied, when the atoms are confined inside a standing-wave high-finesse resonator. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently scattered into the cavity mode. We derive a Fokker-Planck equation for the atomic center-of-mass variables which allows us to determine the equations of motion in the semiclassical limit for any value of the intensity of the laser field. We extract its prediction for the dynamics when the resonator is essentially in the vacuum state and the atoms are cooled by scattering photons into the cavity mode, which then decays. Its predictions for the stationary atomic distribution are compared with the ones of the Fokker-Planck equation in [P. Domokos, P. Horak, and H. Ritsch, J. Phys. B 34, 187 (2001)], which has been derived under different assumptions. We find full agreement in the considered parameter regime.