Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate

TL;DR

This paper uses hydrodynamic and Bogoliubov approaches to analyze the normal modes of a vortex in a trapped Bose-Einstein condensate, demonstrating vortex stability and characterizing wave behaviors in different limits.

Contribution

It provides a detailed analysis of vortex normal modes in trapped BECs, including frequency shifts and stability, using both hydrodynamic and Bogoliubov methods, which was not previously fully explored.

Findings

Vortex induces small frequency shifts in normal modes.

Vortex stability is supported by negligible frequency shifts.

Helical wave solutions are confirmed by Bogoliubov equations.

Abstract

A hydrodynamic description is used to study the normal modes of a vortex in a zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the circulating superfluid velocity far from the vortex core provides a small perturbation that splits the originally degenerate normal modes of a vortex-free condensate. The relative frequency shifts are small in all cases considered (they vanish for the lowest dipole mode with |m|=1), suggesting that the vortex is stable. The Bogoliubov equations serve to verify the existence of helical waves, similar to those of a vortex line in an unbounded weakly interacting Bose gas. In the large-condensate (small-core) limit, the condensate wave function reduces to that of a straight vortex in an unbounded condensate; the corresponding Bogoliubov equations have no bound-state solutions that are uniform along the symmetry axis and decay exponentially far from the vortex core.