Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability and dynamics

TL;DR

This paper investigates the existence, stability, and dynamics of spherical shell dark solitons in three-dimensional Bose-Einstein condensates, using analytical and numerical methods to identify stable configurations and their instabilities.

Contribution

It introduces a comprehensive analysis of spherical shell dark solitons, including stability spectra, instabilities, and effective particle models, extending understanding of topological solitons in 3D BECs.

Findings

Spherical shell dark solitons can be stable near the linear limit.

Identified instabilities lead to vortex line and ring cage formations.

Effective particle models accurately predict equilibrium radius and dynamics.

Abstract

In this work we study spherical shell dark soliton states in three-dimensional atomic Bose-Einstein condensates. Their symmetry is exploited in order to analyze their existence, as well as that of topologically charged variants of the structures, and, importantly, to identify their linear stability Bogolyubov-de Gennes spectrum. We compare our effective 1D spherical and 2D cylindrical computations with the full 3D numerics. An important conclusion is that such spherical shell solitons can be stable sufficiently close to the linear limit of the isotropic condensates considered herein. We have also identified their instabilities leading to the emergence of vortex line and vortex ring cages. In addition, we generalize effective particle pictures of lower dimensional dark solitons and ring dark solitons to the spherical shell solitons concerning their equilibrium radius and effective dynamics around it. In this case too, we favorably compare the resulting predictions such as the shell equilibrium radius, qualitatively and quantitatively, with full numerical solutions in 3D.