Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates

TL;DR

This paper investigates the stability of vortex-ring-bright solitons in trapped binary 3D Bose-Einstein condensates, revealing new instability mechanisms and the impact of bright components on vortex stability.

Contribution

It provides the first detailed analysis of linear and nonlinear instabilities of vortex-ring-bright solitons in 3D BECs, including novel instability modes.

Findings

Filled vortex cores with bright components reduce stability intervals.

Identified new azimuthal instability modes ($m=0$ and $m=1$).

Discovered nonlinear parametric resonance between modes.

Abstract

Instabilities of vortex-ring-bright coherent structures in harmonically trapped two-component three-dimensional Bose-Einstein condensates are studied numerically within the coupled Gross-Pitaevskii equations and interpreted analytically. Interestingly, the filled vortex core with a sufficiently large amount of the bright component is observed to reduce the parametric interval of stability of the vortex ring. We have identified the mechanisms of several linear instabilities and one nonlinear parametric instability in this connection. Two of the linear instabilities are qualitatively different from ones reported earlier, to our knowledge, and are associated with azimuthal modes of $m=0$ and $m=1$, i.e., deviations of the vortex from the stationary ring shape. Our nonlinear parametric resonance instability occurs between the $m=0$ and $m=2$ modes and signals the exchange of energy between them.