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arXiv:cond-mat/9708139 · Physical Review A

Collective excitations of Bose-Einstein-condensed gases at finite temperatures

R. J. Dodd, Mark Edwards, Charles W. Clark, Keith R. Burnett

Published Jan 1, 1998• 119 citations
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Abstract

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 ${}^{87}\mathrm{Rb}$ 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.

DOI
10.1103/physreva.57.r32

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We derive and discuss the temperature dependence of the condensate and noncondensate density profile of a Bose-Einstein condensate gas with Feshbach resonance in a parabolic trap. These quantities are calculated self-consistently using the generalized Hartree-Fock-Bogoliubov (HFB) equations within the Bogoliubov approximation. At zero temperature, the HFB equation can be solved by means of a variation method that gives the low-excitation spectrum. Moreover, within the two-body collision theory, we estimate the relationship between the number of atoms in the condensate and the external magnetic field B . The result is in good agreement with data from recent experiments.
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We discuss our numerical studies of the low energy excitations of trapped Bose condensates using a Bogoliubov-Hartree treatment.In the zero temperature limit, the lowest few excitation frequencies calculated within the Bogoliubov approximation agree well with the experimental data.Finite temperature results obtained using the Popov approximation display qualitative differences from the experimental data close to the critical temperature region.Details of our numerical approach are presented and comparison with other results is discussed.
We present a topical review of the development of finite-temperature field theories of Bose-Einstein condensation in weakly interacting atomic gases. We highlight the difficulties in obtaining a consistent finite-temperature theory that has a gapless excitation spectrum in accordance with Goldstone's theorem and which is free from both ultraviolet and infrared divergences. We present results from the two consistent theories developed so far. These are the Hartree-Fock-Bogoliubov theory within the Popov approximation and a many-body T -matrix approach which we have termed gapless-Hartree-Fock-Bogoliubov (GHFB). Comparison with the available experimental results is made and the remaining difficulties are highlighted.