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Physical Review A

Low-energy excitations of trapped Bose condensates

Li You, William Hoston, Maciej Lewenstein

Published Mar 1, 1997• 79 citations
Publisher

Abstract

We use the Bogoliubov-Hartree theory to describe low-energy excitations of trapped Bose condensates. We construct the quasiparticle spectrum and the quasiparticle operators explicitly in terms of the bare atomic operators. Our results reveal interesting properties of spatially confined Bose condensates and are in excellent agreement with recent experiments.

DOI
10.1103/physreva.55.r1581

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We use the Bogoliubov-Hartree theory to describe low-energy excitations of trapped Bose condensates. We construct the quasiparticle spectrum and the quasiparticle operators explicitly in terms of the bare atomic operators. Our results reveal interesting properties of spatially confined Bose condensates and are in excellent agreement with recent experiments.
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The paper deals with the properties of Bose-gases in inhomogeneous external fields at very low temperatures, when a Bose–Einstein condensation occurs. This particularly refers to trapped alkali gases, which are of great experimental and theoretical interest. The system is considered here in the frame of the developed approach close to the Bogoliubov one with necessary modifications. In particular the generalization of Bogoliubov transformations made it possible to find the spectrum of quasiparticles (low-energy thermal excitations) with account of purely quantum parts of ψ-operators in first order.
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 compute structures of vortex configurations in a harmonically trapped Bose-Einstein condensed atom gas within three different gapless self-consistent mean-field theories. Outside the vortex core region, the density profiles for the condensate and the thermal gas derived from the Hartree-Fock-Bogoliubov-Popov theory are found to differ by only a few per cent from those derived from two of its recently proposed gapless extensions. In the core region, however, the differences between the density profiles are substantial. The structural differences are reflected in the energies of the quasiparticle states localized near the vortex core. In particular, the predictions for the energy of the lowest quasiparticle excitation derived from the theoretical models investigated differ considerably.