Stability of a Bose condensed mixture on a bubble trap

TL;DR

This paper investigates the stability and dynamics of binary Bose-Einstein condensates on a spherical shell, analyzing miscibility, vortex effects, and interactions through theoretical and numerical methods.

Contribution

It provides a comprehensive stability diagram considering vortex charges and interactions, and explores dynamics beyond small perturbations using numerical simulations.

Findings

Stability depends on intra- and inter-species interactions.

Vortex charges influence the stability and miscibility.

Numerical simulations reveal complex dynamical behaviors.

Abstract

Stability and dynamical behavior of binary Bose-Einstein condensed mixtures trapped on the surface of a rigid spherical shell are investigated in the mean-field level, exploring the miscibility with and without vortex charges, considering repulsive and attractive interactions. In order to compute the critical points for the stability, we follow the Bogoliubov-de Gennes method for the analysis of perturbed solutions, with the constraint that initially the stationary states are in a complete miscible configuration. For the perturbed equal density mixture, of a homogeneous uniform gas and when hidden vorticity is verified, with the species having opposite azimuthal circulation, we consider small perturbation analysis for each unstable mode, providing a complete diagram with the intra- and inter-species interaction role on the stability of the miscible system. Finally, beyond small perturbation analysis, we explore the dynamics of some repulsive and attractive inter-species states by full numerical solutions of the time-dependent Gross-Pitaevskii equation.