Quantized vortices and collective oscillations of a trapped Bose condensed gas

TL;DR

This paper uses a sum rule approach to analyze how quantized vortices affect the collective oscillation frequencies of a trapped Bose gas, providing analytic results across different interaction regimes and predicting vortex instability for negative scattering lengths.

Contribution

It introduces an analytic method to calculate frequency shifts caused by vortices in Bose gases, covering various interaction strengths and geometries.

Findings

Frequency shift proportional to vortex circulation and decreases with N^{-2/5}.

Predicted vortex instability for negative scattering lengths.

Discussed frequency splitting in toroidal Bose gas configurations.

Abstract

Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large N where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as N^{-2/5}. Results are also given for smaller values of N covering the transition between the ideal gas and the Thomas-Fermi limit. For negative scattering lengths we predict a macroscopic instability of the vortex. The splitting of the collective frequencies in toroidal configurations is also discussed.