Stability of vortices in rotating taps: a 3d analysis

TL;DR

This paper investigates the stability of vortex lines in rotating trapped Bose-Einstein condensates using 3D numerical solutions of the Gross-Pitaevskii and Bogoliubov equations, revealing that only singly charged vortices can be stabilized by rotation.

Contribution

It provides a detailed 3D analysis of vortex stability in rotating condensates, showing that multicharged vortices are inherently unstable and only single-charged vortices can be stabilized by rotation.

Findings

Single-charged vortices can be stabilized by rotation.

Multicharged vortices are energetically unstable.

The energy minimum is not an eigenstate of angular momentum at high rotation speeds.

Abstract

We study the stability of vortex-lines in trapped dilute gases subject to rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a 3d condensate in spherically and cilyndrically symmetric stationary traps, from small to very large nonlinearities. In the stationary case it is found that the vortex states with unit and $m=2$ charge are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1$ vortex-line, and that the multicharged vortices are never a local minimum of the energy functional, which implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value, $\Omega > \Omega_2$.