Beliaev Damping and Kelvin Mode Spectroscopy of a Condensate in the Presence of a Vortex Line

TL;DR

This paper theoretically demonstrates that Beliaev damping causes decay of quadrupole modes into Kelvin waves in a Bose-Einstein condensate with a vortex, matching experimental observations and identifying Kelvin modes via spectral analysis.

Contribution

It provides a theoretical analysis of Beliaev damping leading to Kelvin mode excitation in vortex-containing condensates, aligning with experimental data.

Findings

Quadrupole mode decays into Kelvin modes via Beliaev process.

Spectral weight calculations match experimental results.

Kelvin waves are identified as the decayed mode.

Abstract

It is demonstrated theoretically that the counter-rotating quadrupole mode in a vortex of Bose-Einstein condensates can decay into a pair of Kelvin modes via Beliaev process. We calculate the spectral weight of density-response function within Bogoliubov framework, taking account of both Beliaev and Landau processes. Good agreement with experiment on $^{87}$Rb by Bretin et al. [cond-mat/0211101] allows us to unambigiously identify the decayed mode as the Kelvin wave propagating along a vortex line.