Dynamical stability of a doubly quantized vortex in a three-dimensional condensate

TL;DR

This paper investigates the dynamical stability of doubly quantized vortices in three-dimensional Bose-Einstein condensates, revealing stability windows that depend on condensate shape and matching experimental observations.

Contribution

It provides a detailed analysis of stability windows for doubly quantized vortices using Bogoliubov equations, variational calculus, and numerical methods, highlighting shape-dependent stability.

Findings

Stability windows are smaller in cigar-shaped condensates.

Complex frequencies indicate dynamical instability in certain parameter ranges.

Stability and instability alternate as parameters vary.

Abstract

The Bogoliubov equations are solved for a three-dimensional Bose-Einstein condensate containing a doubly quantized vortex, trapped in a harmonic potential. Complex frequencies, signifying dynamical instability, are found for certain ranges of parameter values. The existence of alternating windows of stability and instability, respectively, is explained qualitatively and quantitatively using variational calculus and direct numerical solution. It is seen that the windows of stability are much smaller for a cigar shaped condensate than for a pancake shaped one, which is consistent with the findings of recent experiments.