Semiclassical Corrections to the Oscillation Frequencies of a Trapped Bose-Enstein Condensate

Details Semiclassical Corrections to the Oscillation Frequencies of a Trapped Bose-Enstein Condensate Semiclassical Corrections to the Oscillation Frequencies of a Trapped Bose-Enstein Condensate

1998-08-09

arxiv.org/abs/cond-mat/9808088v3

Physics

Condensed Matter

Statistical Mechanics

v3, 11 pages, REVTeX, details added in derivation of (9)

Scientific paper

10.1103/PhysRevLett.82.255

The oscillation frequencies of collective excitations of a trapped Bose-Einstein condensate, when calculated in the mean-field approximation and in the Thomas-Fermi limit, are independent of the scattering length $a$. We calculate the leading corrections to the frequencies from quantum fluctuations around the mean field. The semiclassical correction is proportional to $N^{1/5} a^{6/5}$, where $N$ is the number of atoms in the condensate. The correction is positive semidefinite and is zero for surface modes whose eigenfunctions have a vanishing laplacian. The shift in the frequency of the lowest quadrupole mode for an axially symmetric trap is large enough that it should be measurable in future experiments.

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