On the Bifurcation and Stability of Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates

TL;DR

This paper investigates the emergence, bifurcation, and stability of vortex rings in three-dimensional Bose-Einstein condensates, combining analytical and numerical methods to understand their spectral properties and stability regimes.

Contribution

It introduces a systematic approach to analyze bifurcations and stability of vortex rings in 3D BECs, with quantitative agreement between analytical and numerical results.

Findings

Vortex rings can emerge from dark solitons via bifurcations.

Stability of vortex rings improves with larger chemical potentials.

Analytical methods accurately predict BdG spectra and stability regimes.

Abstract

In the present work, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach, and find good qualitative and quantitative agreement with our Bogoliubov-de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortex-ring states. We systematically capture these as stationary states of the system and quantify their BdG spectra numerically. We find that although the vortex ring may be unstable when bifurcating, its instabilities weaken and may even eventually disappear, for sufficiently large chemical potentials and suitable trap settings. For instance, we demonstrate the stability of the vortex ring for an isotropic trap in the large chemical potential regime.