Number-conserving rate equation for sympathetic cooling of a boson gas

TL;DR

This paper derives a number-conserving rate equation for sympathetic cooling of a bosonic gas, incorporating evaporation effects and assuming rapid thermalization of high-energy levels, advancing the theoretical understanding of cooling dynamics.

Contribution

It introduces a particle number-conserving rate equation for bosonic systems in sympathetic cooling, including evaporation and a specific thermalization assumption.

Findings

Derived a new rate equation conserving particle number

Explicitly included evaporation effects in the model

Assumed rapid thermalization of high-energy levels

Abstract

We derive a particle number-conserving rate equation for the ground state and for the elementary excitations of a bosonic system which is in contact with a gas of a different species (sympathetic cooling). We use the Giradeau-Arnowitt method and the model derived by Lewenstein et. al. with an additional assumption: the high-excited levels thermalize much faster with the cooling agent than the other levels. Evaporation of particles, know to be important in the initial stages of the cooling process, is explicitly included.