Stability of dark solitons in a bubble Bose-Einstein condensate

TL;DR

This paper establishes stability criteria for dark solitons on spherical Bose-Einstein condensates, revealing a universal decay mechanism into vortex pairs beyond a critical nonlinear parameter.

Contribution

It analytically and numerically identifies the instability threshold and decay mechanism of dark solitons on curved surfaces, specifically on spherical BECs.

Findings

Dark solitons decay into vortex pairs beyond a critical nonlinear parameter.

Decay is governed by a single unstable mode for each angular momentum m ≥ 2.

The decay mechanism differs from 3D vortex ring formation, resulting in vortex pairs.

Abstract

The stability of nonlinear waves on curved surfaces is a problem of widespread interest across physics. Here, we establish the stability criteria for dark solitons on a spherical Bose-Einstein condensate. We demonstrate a sharp instability threshold in the nonlinear parameter, beyond which solitons decay into vortex dipoles via snake instabilities. Analytically and numerically, we prove this decay is dictated by a single unstable mode for each angular momentum $m \geq 2$, which is a universal mechanism that controls the resulting vortex state. Unlike in the full three-dimensional case, where snake instabilities lead to vortex rings, a dark soliton confined to the surface of a bubble can only decay into vortex pairs.