Gapless finite-$T$ theory of collective modes of a trapped gas

TL;DR

This paper introduces a gapless finite-temperature theory for collective modes in trapped Bose-Einstein condensates, accurately predicting frequency shifts observed experimentally near the critical temperature.

Contribution

It provides the first self-consistent, gapless calculation of collective mode frequencies in trapped Bose gases at finite temperature, including mean-field and anomalous averages.

Findings

Quantitative agreement with experimental frequency shifts near critical temperature

First gapless finite-temperature calculation for trapped Bose gases

Accurate modeling of collective mode behavior as temperature approaches critical point

Abstract

We present predictions for the frequencies of collective modes of trapped Bose-condensed $^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.