We examine the role of thermal fluctuations in binary condensate mixtures of dilute atomic gases. In particular, we use Hartree-Fock-Bogoliubov with Popov approximation to probe the impact of non-condensate atoms to the phenomenon of phase-separation in two-component Bose-Einstein condensates. We demonstrate that, in comparison to T = 0, there is a suppression in the phase-separation of the binary condensates at T = 0. This arises from the interaction of the condensate atoms with the thermal cloud. We also show that, when T = 0 it is possible to distinguish the phase-separated case from miscible from the trends in the correlation function. However, this is not the case at T = 0. [15], is that the intra-(U 11 , U 22 ) and inter-species interaction (U 12 ) strengths, must satisfy the inequality U 2 12 > U 11 U 22 . However, experiments are conducted at finite temperatures, and therefore, deviations from the criterion is to be expected. Theoretical studies on effects of thermal cloud on phase-separation have been carried out for homogeneous binary Bose gases using HartreeFock theory [16] and large-N approximation [17]. Phaseseparation of trapped binary mixtures at finite temperature has also been examined using local-density approximation [18]. In this Letter we address this issue by using Hartree-FockBogoliubov theory with Popov approximation (HFB-Popov) [19] to account for the thermal fluctuations. It is a gapless formalism satisfying Hugenholtz-Pines theorem [20] and can be employed to compute the energy eigenspectra of the quasiparticle excitations of the condensates.The method has been validated extensively in single species BEC, and we have used it in our recent works to examine the effect of quantum fluctuations in TBECs [21]. In the present work, we systematically study the role of thermal fluctuations in the phenomenon of phase-separation in trapped TBECs. Our studies reveal that at T = 0, the constituent species in the TBEC undergo phase-separation at a higher U 12 than the value predicted based on the TF-approximation at T = 0. Consistent with experimental observations of dual species condensate of 87 Rb and 133 Cs [7], our theoretical investigations show that even when the phase-separation condition is met, there is a sizable overlap between the two species. We attribute this to the presence of the thermal cloud, which have profound affects on the miscibility-immiscibility transition. At T = 0, the TBECs are coherent throughout the spatial extent of the condensate, however, when T = 0 coherence decays and is reflected in the correlation function. This implies that at T = 0, the miscible or immiscible phases are indistinguishable from the trends in the correlation function. But, for T = 0 the miscible-immiscible transition and the associated changes in the density profiles have a characteristic signature in the form of the correlation functions. There is a smooth cross-over between the correlations functions when the transition occurs. Interspecies Feshbach resonances of ultracold bosons have been exper...

We show that the third Goldstone mode, which emerges in binary condensates at phase-separation, persists to higher inter-species interaction for density profiles where one component is surrounded on both sides by the other component. This is not the case with symmetry-broken density profiles where one species is to entirely to the left and the other is entirely to the right. We, then, use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution at T = 0 and demonstrate the existence of mode bifurcation near the critical temperature. The Kohn mode, however, exhibits deviation from the natural frequency at finite temperatures after the phase separation. This is due to the exclusion of the non-condensate atoms in the dynamics.

We study the dynamics of a single and a pair of vortices in quasi two-dimensional Bose-Einstein condensates at finite temperatures. We use the stochastic Gross-Pitaevskii equation, which is the Langevin equation for the Bose-Einstein condensate, to this end. For a pair of vortices, we study the dynamics of both the vortex-vortex and vortex-antivortex pairs, which are generated by rotating the trap and moving the Gaussian obstacle potential, respectively. Due to thermal fluctuations, the constituent vortices are not symmetrically generated with respect to each other at finite temperatures. This initial asymmetry coupled with the presence of random thermal fluctuations in the system can lead to different decay rates for the component vortices of the pair, especially in the case of two corotating vortices.

We examine the dynamics associated with the miscibility-immiscibility transition of trapped two-component Bose-Einstein condensates (TBECs) of dilute atomic gases in presence of vortices. In particular, we consider TBECs of Rb hyperfine states, and Rb-Cs mixture. There is an enhancement of the phase-separation when the vortex is present in both condensates. In the case of a singly charged vortex in only one of the condensates, there is enhancement when the vortex is present in the species which occupy the edges at phase-separation. But, suppression occurs when the vortex is in the species which occupies the core region. To examine the role of the vortex, we quench the inter-species interactions to propel the TBEC from miscible to immiscible phase, and use the time dependent Gross-Pitaevskii equation to probe the phenomenon of phase-separation. We also examine the effect of higher charged vortex.