Frequency shift and mode coupling in the nonlinear dynamics of a Bose condensed gas

TL;DR

This paper analyzes how nonlinear interactions in a Bose-condensed gas cause frequency shifts and mode coupling, highlighting the effects of trap anisotropy on collective oscillations at zero temperature.

Contribution

It provides analytic expressions for frequency shifts and explores the impact of anisotropy on mode coupling in a Bose-condensed gas.

Findings

Frequency shifts depend on trap anisotropy.

Mode coupling is strongest at specific anisotropy values.

Large frequency shifts influence collapse and revival phenomena.

Abstract

We investigate the behavior of large amplitude oscillations of a trapped Bose-condensed gas of alkali atoms at zero temperature, by solving the equations of hydrodynamics for collective modes. Due to the atom-atom interaction, the equations of motion are nonlinear and give rise to significant frequency shift and mode coupling. We provide analytic expressions for the frequency shift, pointing out the crucial role played by the anisotropy of the confining potential. For special values of the anisotropy parameter the mode coupling is particularly strong and the frequency shift becomes large, revealing a peculiar behavior of the Bose-condensed gas. Consequences on the theory of collapse and revival of collective excitations are also discussed.