Symmetry breaking of solitons in two-component Gross-Pitaevskii equations

Abstract

We revisit the problem of the spontaneous symmetry breaking (SSB) of solitons in two-component linearly coupled nonlinear systems, adding the nonlinear interaction between the components. With this feature, the system may be realized in new physical settings, in terms of optics and the Bose-Einstein condensate (BEC). SSB bifurcation points are found analytically, for both symmetric and antisymmetric solitons (the symmetry between the two components is meant here). Asymmetric solitons, generated by the bifurcations, are described by means of the variational approximation (VA) and numerical methods, demonstrating good accuracy of the variational results. In the space of the self-phase-modulation (SPM) parameter and soliton's norm, a border separating stable symmetric and asymmetric solitons is identified. The nonlinear coupling may change the character of the SSB bifurcation, from subcritical to supercritical. Collisions between moving asymmetric and symmetric solitons are investigated too. Antisymmetric solitons are destabilized by a supercritical bifurcation, which gives rise to self-confined modes featuring Josephson oscillations, instead of stationary states with broken antisymmetry. An additional instability against delocalized perturbations is also found for the antisymmetric solitons.