E. Braaten et J. Pearson, Semiclassical corrections to the oscillation frequencies of a trapped Bose-Einstein condensate, PHYS REV L, 82(2), 1999, pp. 255-258
The oscillation frequencies of collective excitations of a trapped Bose-Ein
stein condensate, when calculated in the mean-field approximation and in th
e Thomas-Fermi limit, are independent of the scattering length a. We calcul
ate the leading corrections to the frequencies from quantum fluctuations ar
ound 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 h
ave a vanishing Laplacian. The shift in the frequency of the lowest quadrup
ole mode for an axially symmetric trap is large enough that it should be me
asurable in future experiments.