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

Abstract

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.

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

References in corpus (5)

• Low-energy elementary excitations of a trapped Bose-condensed gas
• Hydrodynamic excitations of Bose condensates in anisotropic traps
• Frequency shift and mode coupling in the nonlinear dynamics of a Bose condensed gas
• Quantum Corrections to the Ground State of a Trapped Bose-Einstein Condensate
• Excitations of a Bose-condensed gas in anisotropic traps

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