Shifts and widths of collective excitations in trapped Bose gases by the dielectric formalism

TL;DR

This paper predicts how collective excitation frequencies and damping rates in trapped Bose gases change with temperature using the dielectric formalism, showing good agreement with experiments for some modes but highlighting the need for non-perturbative methods for others.

Contribution

It introduces a perturbative approach based on the dielectric formalism to calculate temperature-dependent shifts and damping rates in trapped Bose gases, extending previous theoretical models.

Findings

Good agreement with experimental data for the m=2 mode

Discrepancies in the m=0 mode shifts suggest non-perturbative effects are important

Numerical results detail the temperature dependence of collective excitations

Abstract

We present predictions for the temperature dependent shifts and damping rates. They are obtained by applying the dielectric formalism to a simple model of a trapped Bose gas. Within the framework of the model we use lowest order perturbation theory to determine the first order correction to the results of Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation frequencies, and present numerical results for the temperature dependence of the damping rates and the frequency shifts. Good agreement with the experimental values measured at JILA are found for the m=2 mode, while we find disagreements in the shifts for m=0. The latter point to the necessity of a non-perturbative treatment for an explanation of the temperature-dependence of the m=0 shifts.