Ring dark solitons in three-dimensional Bose-Einstein condensates

TL;DR

This paper systematically studies three-dimensional ring dark solitons in Bose-Einstein condensates, analyzing their stability, dynamics, and spectral properties, and introduces a semi-analytical method for spectral analysis near the linear limit.

Contribution

It develops a modified degenerate perturbation theory for spectral analysis of solitons with a linear limit, validated against numerical spectra, and explores stabilization via external potentials.

Findings

Ring dark solitons are unstable when detuned from the linear limit but can be stabilized with external potentials.

Spectral stability analysis reveals multiple unstable modes and dynamical destabilization scenarios.

The semi-analytical method accurately predicts spectral properties and applies to complex soliton structures.

Abstract

In this work we present a systematic study of the three-dimensional extension of the ring dark soliton examining its existence, stability, and dynamics in isotropic harmonically trapped Bose-Einstein condensates. Detuning the chemical potential from the linear limit, the ring dark soliton becomes unstable immediately, but can be fully stabilized by an external cylindrical potential. The ring has a large number of unstable modes which are analyzed through spectral stability analysis. Furthermore, a few typical destabilization dynamical scenarios are revealed with a number of interesting vortical structures emerging such as the two or four coaxial parallel vortex rings. In the process of considering the stability of the structure, we also develop a modified version of the degenerate perturbation theory method for characterizing the spectra of the coherent structure. This semi-analytical method can be reliably applied to any soliton with a linear limit to explore its spectral properties near this limit. The good agreement of the resulting spectrum is illustrated via a comparison with the full numerical Bogolyubov-de Gennes spectrum. The application of the method to the two-component ring dark-bright soliton is also discussed.