# Semiclassical theory of synchronization-assisted cooling

## TL;DR

This paper presents a semiclassical analysis of atomic ensemble cooling inside an optical cavity, revealing a three-stage process involving individual cooling, synchronization-enhanced cooling, and a stationary dipole-dipole correlation regime.

## Contribution

It introduces a mean-field model to describe the asymptotic cooling regime and uncovers the formation of antiferromagnetic-like order in the internal excitations.

## Key findings

- Momentum distribution width can reach the order of photon recoil.
- Internal excitations form a spatial antiferromagnetic-like order.
- Three distinct cooling regimes are identified and characterized.

## Abstract

We analyse the dynamics leading to radiative cooling of an atomic ensemble confined inside an optical cavity when the atomic dipolar transitions are incoherently pumped and can synchronize. Our study is performed in the semiclassical regime and assumes that cavity decay is the largest rate in the system dynamics. We identify three regimes characterising the cooling. At first hot atoms are individually cooled by the cavity friction forces. After this stage, the atoms' center-of-mass motion is further cooled by the coupling to the internal degrees of freedom while the dipoles synchronize. In the latest stage dipole-dipole correlations are stationary and the center-of-mass motion is determined by the interplay between friction and dispersive forces due to the coupling with the collective dipole. We analyse this asymptotic regime by means of a mean-field model and show that the width of the momentum distribution can be of the order of the photon recoil. Furthermore, the internal excitations oscillate spatially with the cavity standing wave forming an antiferromagnetic-like order.