Spontaneous symmetry breaking of gap solitons in double-well traps

TL;DR

This paper investigates symmetry-breaking bifurcations of gap solitons in a 2D Bose-Einstein condensate model with a double-well potential and optical lattice, revealing how nonlinearities influence bifurcation types.

Contribution

It introduces a 2D model combining double-well potential and optical lattice, analyzing symmetry-breaking bifurcations of gap solitons with variational and numerical methods.

Findings

Supercritical bifurcation in repulsive case.

Transition from subcritical to supercritical bifurcation with increasing lattice strength.

Verification of variational approximation by numerical results.

Abstract

We introduce a two dimensional model for the Bose-Einstein condensate with both attractive and repulsive nonlinearities. We assume a combination of a double well potential in one direction, and an optical lattice along the perpendicular coordinate. We look for dual core solitons in this model, focusing on their symmetry-breaking bifurcations. The analysis employs a variational approximation, which is verified by numerical results. The bifurcation which transforms antisymmetric gap solitons into asymmetric ones is of supercritical type in the case of repulsion; in the attraction model, increase of the optical latttice strength leads to a gradual transition from subcritical bifurcation (for symmetric solitons) to a supercritical one.