Phase transition of a Bose gas in a harmonic potential

TL;DR

This paper studies the phase transition of a dilute Bose gas in a harmonic trap, defining a thermodynamic limit, analyzing phase properties, and exploring non-equilibrium dynamics, highlighting differences from uniform systems.

Contribution

It introduces a thermodynamic limit for trapped Bose gases and analyzes phase transition properties and dynamics, extending understanding beyond translationally invariant cases.

Findings

Critical properties differ from uniform Bose gases but are related.

The thermodynamic limit accurately describes experimental gases except near the critical temperature.

Universal scaling describes late-time dynamics after a quench.

Abstract

We consider a dilute Bose gas confined by a harmonic potential. We define an appropriate thermodynamic limit and analyze the properties of the phases and phase transition in this limit. Critical properties in the presence of the potential are found to be different from, though simply related, to those in the usual translationally invariant case. We argue that the properties of magnetically trapped rubidium\cite{Wieman} and sodium\cite{ketterle} gases (in which Bose-Einstein condensation has been recently observed) are well approximated by our thermodynamic limit except in a narrow window of temperature around the critical temperature. We also consider the effect of the confining potential on the non-equilibrium dynamics following a rapid quench to the ordered side and give a scaling description of the late time universal dynamics.