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

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 (HO) 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 than 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. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study extends the theoretical treatment of spontaneous symmetry breaking in two-component systems to a system with competing linear coupling and repulsive interactions. It explores ground-state solutions, vortex states, and gap solitons in various conditions, showing that spontaneous symmetry breaking occurs when the cross-component repulsion is stronger than the self-repulsion. The symmetry breaking transition is categorized as a supercritical bifurcation, leading to broken symmetry states in the inner area and intact symmetry in the surrounding layer.