Temperature-Dependent Frequency Shifts in Collective Excitations of a Bose-Einstein Condensate

TL;DR

This paper develops a theoretical model to analyze how temperature affects collective excitation frequencies in a Bose-Einstein condensate by incorporating the thermal cloud's contribution, extending zero-temperature methods.

Contribution

It introduces a temperature-dependent variational approach that accounts for the thermal cloud, providing analytical expressions for excitation frequencies in Bose-Einstein condensates.

Findings

Theoretical predictions match experimental measurements from JILA and MIT.

Analytical formulas for excitation frequencies as functions of temperature.

Extension of zero-temperature models to finite-temperature scenarios.

Abstract

By including the contribution of the thermal cloud to the Lagrangian of the condensate of a Bose gas, we extend the time-dependent variational method at zero temperature to study temperature-dependent low collective excitation modes. A Gaussian trial wave function of the condensate and a static distribution density of the thermal cloud are used, and analytical expressions for temperature-dependent excitation frequencies obtained. Theoretical results are compared with measurements in the JILA and MIT experiments.