Thermal suppression of phase separation in condensate mixtures

Abstract

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...

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