Kinetic theory of cavity cooling and self-organisation of a cold gas

TL;DR

This paper develops a theoretical framework for understanding cavity cooling and self-organization in cold gases, deriving equations that predict thresholds and steady-state behaviors, confirmed by numerical simulations.

Contribution

It introduces a non-linear Fokker-Planck model for large ensembles, providing explicit formulas for cooling, diffusion, and self-organization thresholds in cavity-coupled cold gases.

Findings

Cooling rate is largely independent of particle number below threshold.

Steady-state velocity distribution is a q-Gaussian influenced by cavity linewidth.

Numerical simulations confirm the analytical self-organization threshold.

Abstract

We study spatial self-organisation and dynamical phase-space compression of a dilute cold gas of laser-illuminated polarisable particles in an optical resonator. Deriving a non-linear Fokker--Planck equation for the particles' phase-space density allows us to treat arbitrarily large ensembles in the far-detuning limit and explicitly calculate friction forces, momentum diffusion and steady-state temperatures. In addition, we calculate the self-organisation threshold in a self-consistent analytic form. For a homogeneous ensemble below threshold the cooling rate for fixed laser power is largely independent of the particle number. Cooling leads to a $q$-Gaussian velocity distribution with a steady-state temperature determined by the cavity linewidth. Numerical simulations using large ensembles of particles confirm the analytical threshold condition for the appearance of an ordered state, where the particles are trapped in a periodic pattern and can be cooled to temperatures close to a single vibrational excitation.