Characteristic features of symmetry breaking in two-component Bose-Einstein condensates

We examine the stability properties of the ground state of two-component Bose-Einstein condensates as a function of the interspecies interactions. A stability criterion is identified from the curvature matrix of the Gross-Pitaevskii energy functional subject to the normalization conditions. By analyzing the stability signature, the characteristic features of the spontaneous spatial symmetry breaking are verified in various types of traps. The details of the differences between the continuous symmetry breaking and discrete symmetry breaking are discussed.