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Acta Physica Polonica A

Low Energy Excitation Spectra of Trapped Bose Condensates

Li You, William Hoston, Maciej Lewenstein, M. Marinescu

Published Jan 1, 1998• 6 citations
Publisher

Abstract

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.

DOI
10.12693/aphyspola.93.211

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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.
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The mode frequencies of a weakly interacting Bose gas in a magnetic trap are studied as a function of the anisotropy of the trap. As in earlier works, the generalized Hartree-Fock-Bogoliubov equations within the Popov approximation are used for our calculations. A feature of our work is the combined use of a mode expansion in a finite basis and a semiclassical approximation of the highly excited states. The results are applied to check the accuracy of the recently suggested equivalent zero temperature condensate approximation, which involves a much simpler model.
We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random-phase approximation and linear-response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.