Symmetry breaking in a two-component system with repulsive interactions and linear coupling
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 (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.
- Publication:
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Communications in Nonlinear Science and Numerical Simulations
- Pub Date:
- January 2021
- DOI:
- 10.1016/j.cnsns.2020.105496
- arXiv:
- arXiv:2008.04610
- Bibcode:
- 2021CNSNS..9205496S
- Keywords:
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- Coupled Gross-Pitaevskii equations;
- Bose-Einstein condensates;
- Soliton and vortex;
- Symmetry-breaking;
- Nonlinear Sciences - Pattern Formation and Solitons;
- Condensed Matter - Quantum Gases;
- Physics - Optics
- E-Print:
- to be published in CNSNS (Communications in Nonlinear Science and Numerical Simulation)