Evolution of Goldstone mode in binary condensate mixtures

We show that the third Goldstone mode in the two-species condensate mixtures, which emerges at phase-separation, gets hardened when the confining potentials have separated trap centers. The sandwich type condensate density profiles, in this case, acquire a side-by-side density profile configuration. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution and density profiles for these phase transitions at T = 0.