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arXiv:cond-mat/9712122 · Journal of the Physical Society of Japan

Excitation Spectrum in a Cylindrical Bose-Einstein Condensate

Tomoya Isoshima, Kazushige Machida

Published Jun 15, 1998• 8 citations
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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.

DOI
10.1143/jpsj.67.1840

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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.
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 quantities are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a relatively 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 trapped gas in the high temperature limit.
We study the excitation spectrum of a spatially homogeneous Bose-condensed gas. Using finite-temperature field theory, we derive the dependence of the excitation spectrum on both the gaseous parameter and the temperature. In particular, we derive the asymptotic forms of the spectral weight at finite temperature. We then discuss the effects of the interaction between the excitations on the dispersion relation, in particular on its curvature for small momentum. From the gaseous parameter dependence of the curvature at zero temperature, we find that there exists a threshold for the gaseous parameter, above which the spectrum becomes stable and no damping processes occur. The excitation stability is analyzed at finite temperature, and it is found that the effect of the finite temperature is to increase the stability of the excitation. We numerically calculated the ratio of the critical velocity to the sound velocity, finding that the critical velocity is small compared to the sound velocity for specific gaseous parameters and temperatures.
We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of 87Rb{}^{87}\mathrm{Rb}87Rb atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.