Finite temperature excitations of a trapped Bose gas

TL;DR

This paper investigates how the density profiles and excitation frequencies of a trapped Bose gas change with temperature, revealing weak frequency dependence below transition and significant shifts near the transition point.

Contribution

It provides a self-consistent calculation of density profiles and excitation frequencies across temperatures using the Hartree-Fock-Bogoliubov framework within the Popov approximation.

Findings

Excitation frequencies are weakly dependent on temperature below the transition.

Condensate density decreases significantly as temperature approaches the transition.

Frequencies approach noninteracting gas values at high temperatures.

Abstract

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantitites are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a realtively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting gas in the high temperature limit.