On Two-Component Dark-Bright Solitons in Three-dimensional Atomic Bose-Einstein Condensates

TL;DR

This paper investigates the stability and dynamics of two-component dark-bright solitons in three-dimensional Bose-Einstein condensates, revealing conditions for their stability and novel oscillatory behaviors.

Contribution

It extends the study of dark-bright solitons from 1D to fully 3D systems, analyzing stability and dynamics with numerical and theoretical methods.

Findings

Both planar and spherical shell solitons can be stable at low chemical potentials.

Unstable solitons evolve into more robust waveforms in simulations.

Multi-soliton configurations exhibit pairwise oscillatory motion.

Abstract

In the present work, we revisit two-component Bose-Einstein condensates in their fully three-dimensional (3d) form. Motivated by earlier studies of dark-bright solitons in the 1d case, we explore the stability of these structures in their fully 3d form in two variants. In one the dark soliton is planar and trapping a planar bright (disk) soliton. In the other case, a dark spherical shell soliton creates an effective potential in which a bright spherical shell of atoms is trapped in the second component. We identify these solutions as numerically exact states (up to a prescribed accuracy) and perform a Bogolyubov-de Gennes linearization analysis that illustrates that both structures can be dynamically stable in suitable intervals of sufficiently low chemical potentials. We corroborate this finding theoretically by analyzing the stability via degenerate perturbation theory near the linear limit of the system. When the solitary waves are found to be unstable, we explore their dynamical evolution via direct numerical simulations which, in turn, reveal novel waveforms that are more robust. Finally, using the SO$(2)$ symmetry of the model, we produce multi-dark-bright planar or shell solitons involved in pairwise oscillatory motion.