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

TL;DR

This paper calculates quantum fluctuation corrections to the oscillation frequencies of a trapped Bose-Einstein condensate, revealing measurable shifts especially in the quadrupole mode, beyond mean-field predictions.

Contribution

It introduces the leading semiclassical corrections to collective excitation frequencies, accounting for quantum fluctuations around the mean field in Bose-Einstein condensates.

Findings

Corrections are proportional to N^{1/5} a^{6/5}.

Frequency shifts are positive and measurable for certain modes.

Surface modes with zero Laplacian are unaffected.

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.