Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

TL;DR

This paper analyzes the small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate using a variational approach, confirming the existence of specific dipole and anomalous modes.

Contribution

It introduces a variational Lagrangian method to derive the coupled normal modes of a vortex in a BEC, providing an alternative to Bogoliubov analysis.

Findings

Identification of two rigid dipole modes.

Confirmation of an anomalous mode with negative frequency.

Agreement with previous Bogoliubov results.

Abstract

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.