Characteristic temperature for the immiscible-miscible transition of binary condensates in optical lattices

We study a two-species Bose-Einstein condensates confined in quasi-two-dimensional (quasi-2D) optical lattices at finite temperatures, employing the Hartree-Fock-Bogoliubov theory with the Popov approximation. We examine the role of thermal fluctuations on the ground-state density distributions, and the quasiparticle mode evolution. At zero temperature, the geometry of the ground-state in the immiscible domain is side-by-side. Our results show that the thermal fluctuations enhance the miscibility of the condensates, and at a characteristic temperature the system becomes miscible with rotationally symmetric overlapping density profiles. This immiscible-miscible transition is accompanied by a discontinuity in the excitation spectrum, and the low-lying quasiparticle modes such as slosh mode becomes degenerate at the characteristic temperature.