Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates

TL;DR

This paper investigates nonlinear interactions among collective modes in a trapped Bose-Einstein condensate, revealing mode mixing phenomena and matching spectral predictions with numerical simulations.

Contribution

It introduces a perturbative and variational method to analyze nonlinear mode coupling in BECs, explaining experimental observations and predicting spectral features.

Findings

Mode mixing occurs selectively among quadrupole and scissors modes.

The approach explains experimental beating and modulation phenomena.

Spectral peaks from the theory match numerical simulations.

Abstract

We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing selectively occurs. Our perturbative approach is useful in gaining qualitative understanding of the recent experiment [Yamazaki et al., J. Phys. Soc. Japan 84, 44001 (2015)], exhibiting a beating phenomenon of the scissors mode as well as a modulation phenomenon of the low-lying quadrupole mode by the high-lying quadrupole mode frequency. Within the second-order treatment of the nonlinear mode coupling terms, our approach predicts all the spectral peaks obtained by the numerical simulation of the Gross-Pitaevskii equation.