Quantum and thermal fluctuations in two-component Bose gases

We study the effects of quantum and thermal fluctuations on Bose-Bose mixtures at finite temperature employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The theory governs self-consistently the motion of the condensates, the noncondensates, and of the anomalous components on an equal footing. The finite temperature criterion for the phase separation is established. We numerically analyze the temperature dependence of different densities for both miscible and immiscible mixtures. We show that the degree of the overlap between the two condensates and the thermal clouds is lowered and the relative motion of the centers of mass of the condensed and thermal components is strongly damped due to the presence of the pair anomalous fluctuations. Our results are compared with previous theoretical and experimental findings. On the other hand, starting from our TDHFB equations, we develop a random-phase theory for the elementary excitations in a homogeneous mixture. We find that the normal and anomalous fluctuations may lead to enhance the excitations and the thermodynamics of the system.