Cusp catastrophe of symmetry breaking in two-component Bose-Einstein condensates

Abstract

Bifurcation analysis is. applied to the spontaneous spatial symmetry breaking occurring in the ground state of two-component Bose-Einstein condensates. The cusp catastrophe describing the supercritical pitchfork bifurcation associated with the symmetry breaking is derived via the identification of the local curvature of the Gross-Pitaevskii energy functional. The bifurcation diagram and universal scaling laws for the eigenvalue and energy are obtained 9 from the catastrophe function.