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

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.

16 pages, 8 figures

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• Relative dynamics of quantum vortices and massive cores in binary BECs
• "Capillary'' structures in transversely trapped nonlinear optical beams
• Systematic solitary waves from their linear limits in two-component Bose-Einstein condensates with unequal dispersion coefficients
• Nonuniformly Filled Vortex Rings in Nonlinear Optics
• Stability and dynamics of massive vortices in two-component Bose-Einstein condensates
• An Optical Analog for a Rotating Binary Bose-Einstein Condensate
• Direct and reverse precession of a massive vortex in a binary Bose--Einstein condensate