Symmetry-Breaking Bifurcation in Nonlinear Schrödinger/Gross-Pitaevskii Equations

We consider a class of nonlinear Schrödinger / Gross-Pitaveskii (NLS-GP) equations, i.e. NLS with a linear potential. We obtain conditions for a symmetry breaking bifurcation in a symmetric family of states asN , the squared L2 norm (particle number, optical power), is increased. In the special case where the linear potential is a doublewell with well separation L, we estimate Ncr(L), the symmetry breaking threshold. Along the “lowest energy” symmetric branch, there is an exchange of stability from the symmetric to asymmetric branch as N is increased beyond Ncr.