Symmetry breaking in a two-component system with repulsive interactions and linear coupling

TL;DR

This paper investigates symmetry breaking in a two-component system with competing linear coupling and repulsive interactions, revealing conditions for symmetry breaking in ground states and vortices in BEC and optics.

Contribution

It extends the theoretical framework of spontaneous symmetry breaking to systems with repulsive interactions and linear coupling, analyzing both ground states and vortex solutions in 1D and 2D.

Findings

SSB occurs when cross-component repulsion exceeds self-repulsion in GSs and vortices.

SSB transition is a supercritical bifurcation with broken symmetry regions.

States with S=2 vortices are unstable against splitting.

Abstract

We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive interactions. First, we address one- and two-dimensional (1D and 2D) ground-state (GS) solutions and 2D vortex states with topological charges S=1 and 2, maintained by a confining harmonic-oscillator potential. The system can be implemented in BEC and optics. By means of the Thomas-Fermi approximation and numerical solution of the underlying coupled Gross-Pitaevskii equations, we demonstrate that SSB takes place, in the GSs and vortices alike, when the cross-component repulsion is stronger that the self-repulsion in each component. The SSB transition is categorized as a supercritical bifurcation, which gives rise to states featuring broken symmetry in an inner area, and intact symmetry in a surrounding layer. Unlike stable GSs and vortices with S=1, the states with S=2 are unstable against splitting. We also address SSB for 1D gap solitons in the system including a lattice potential. In this case, SSB takes place under the opposite condition, i.e., the cross-component repulsion must be weaker than the self-repulsion, and SSB is exhibited by antisymmetric solitons.