Faraday waves on a bubble Bose-Einstein condensed binary mixture

TL;DR

This paper investigates how Rabi coupling influences Faraday wave formation and phase separation in a spherical bubble Bose-Einstein condensate binary mixture, combining analytical and numerical stability analyses.

Contribution

It introduces a novel study of Faraday waves on a spherical bubble BEC mixture, highlighting the role of Rabi coupling and discrete spectrum in pattern formation.

Findings

Faraday waves coexist with immiscible phases in bubble BECs.

Rabi coupling and contact interactions are key parameters for wave emergence.

Analytical and numerical methods confirm stability predictions.

Abstract

By studying the dynamic stability of Bose-Einstein condensed binary mixtures trapped on the surface of an ideal two-dimensional spherical bubble, we show how the Rabi coupling between the species can modulate the interactions leading to parametric resonances. In this spherical geometry, the discrete unstable angular modes drive both phase separations and spatial patterns, with Faraday waves emerging and coexisting with an immiscible phase. Noticeable is the fact that, in the context of discrete kinetic energy spectrum, the only parameters to drive the emergence of Faraday waves are the $s-wave$ contact interactions and the Rabi coupling. Once analytical solutions for population dynamics are obtained, the stability of homogeneous miscible species is investigated through Bogoliubov-de Gennes and Floquet methods, with predictions being analysed by full numerical solutions applied to the corresponding time-dependent coupled formalism.