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Journal of Low Temperature Physics

Collective Excitations of a Trapped Bose–Einstein Condensate at Finite Large Atom Numbers

Yong-li Ma, S. T. Chui, John C. Kimball

Published Oct 1, 2002• 9 citations
Publisher
DOI
10.1023/a:1020001519190

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The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose–Einstein condensation (BEC) with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree–Fock–Bogoliubov (HFB) approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.
The breathing mode collective-excitation frequency of a Bose-Einstein condensate is studied in a highly asymmetric (two- or one-dimensional) trap by using a sum-rule method and a time-dependent variational method. The collective-excitation frequency of the breathing mode in the Thomas-Fermi limit for a purely two- or one-dimensional trap is reproduced by a general result for a three-dimensional trap. In the case of a two- or one-dimensional trap, we obtain the lowest-order correction for the excitation frequency due to the finiteness of the trap frequency in the tightly trapped direction or the finiteness of the number of atoms.
We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas-Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a Gaussian ansatz.