Excitation spectrum in a cylindrical Bose-Einstein gas

TL;DR

This paper calculates the excitation spectrum of a cylindrical Bose-Einstein condensate using the Popov approximation, analyzing the dispersion relation and temperature effects on the zero sound mode, and compares findings with recent experiments.

Contribution

It provides a detailed theoretical analysis of the excitation spectrum and sound velocity in a cylindrically trapped Bose-Einstein gas, including temperature dependence and experimental comparison.

Findings

The dispersion relation and zero sound mode are characterized within the Popov approximation.

Sound velocity depends on both peak density and axial area density.

Theoretical results are discussed in relation to recent Na atom gas experiments.

Abstract

Whole excitation spectrum is calculated within the Popov approximation of the Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped radially by a harmonic potential. The full dispersion relation and its temperature dependence of the zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, but also on the axial area density. Recent sound velocity experiment on Na atom gas is discussed in light of the present theory.