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.

We examine the role of thermal fluctuations in two-species Bose-Einstein condensates confined in quasi-twodimensional (quasi-2D) optical lattices using the Hartree-Fock-Bogoliubov theory with the Popov approximation. The method, in particular, is ideal to probe the evolution of quasiparticle modes at finite temperatures. Our studies show that the quasiparticle spectrum in the phase-separated domain of the two-species Bose-Einstein condensate has a discontinuity at some critical value of the temperature. Furthermore, the low-lying modes like the slosh mode becomes degenerate at this critical temperature, and this is associated with the transition from the immiscible side-by-side density profile to the miscible phase. Hence, the rotational symmetry of the condensate density profiles are restored, and so is the degeneracy of quasiparticle modes.

We study numerically the dynamical instabilities and splitting of singly and doubly quantized composite vortices in nonrotated two-component Bose-Einstein condensates harmonically confined to quasi two dimensions. In this system, the vortices become pointlike composite defects that can be classified in terms of an integer pair (κ 1 ,κ 2 ) of phase-winding numbers. Our numerical simulations based on zero-temperature mean-field theory reveal several vortex splitting behaviors that stem from the multicomponent nature of the system and do not have direct counterparts in single-component condensates. By calculating the Bogoliubov quasiparticle excitations of stationary axisymmetric composite vortices, we find complex-frequency excitations (dynamical instabilities) for the singly quantized (1,1) and (1,−1) vortices and for all variants of doubly quantized vortices, which we define by max j=1,2 |κ j | = 2. While the predictions of the linear Bogoliubov analysis are confirmed by direct time integration of the Gross-Pitaevskii equations of motion, the latter also reveals intricate long-time decay behavior not captured by the linearized dynamics. Firstly, the (1,±1) vortex is found to be unstable against splitting into a (1,0) and a (0,±1) vortex. Secondly, the (2,1) vortex exhibits a two-step decay process by splitting first into a (2,0) and a (0,1) vortex followed by the off-axis splitting of the (2,0) vortex into two (1,0) vortices. Thirdly, the (2,−2) vortex is observed to split into a (−1,1) vortex, three (1,0) vortices, and three (0,−1) vortices. Each of these exotic splitting modes is the dominant dynamical instability of the respective stationary vortex in a wide range of intercomponent interaction strengths and relative populations of the two condensate components and should be amenable to experimental detection. Our results contribute to a better understanding of vortex physics, hydrodynamic instabilities, and two-dimensional quantum turbulence in multicomponent superfluids.The aforementioned studies of vortex splitting [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] were conducted for a solitary scalar BEC, which is described by a single C-valued order parameter. However, vortex physics becomes much more diverse when multiple, say K ∈ N, scalar condensates come into contact, interact with one another, and thereby constitute an K-component BEC described by a C K -valued vectorial order parameter. Already the simplest multicomponent system, the two-component BEC corresponding to K = 2, has been found to exhibit many stable vortex structures not encountered in single-component BECs, such as coreless vortices [6], square vortex lattices [47][48][49], serpentine vortex sheets [50], triangular lattices of vortex pairs [49], skyrmions [51][52][53], and meron pairs [54,55]. Although presently only the coreless vortices [6] and square vortex lattices [48] from this list have been verified experimentally, studies of exotic vortex configurations in twocomponent BECs are becoming more and more within reach ...

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We show that the presence of a soliton in a single-species condensate, at zero temperature, enhances the quantum depletion sufficiently enough to induce dynamical instability of the system. We also predict that for two-species condensates, two Goldstone modes emerge in the excitation spectrum at phase separation. Of these, one is due to the presence of the soliton. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution, and demonstrate that when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also report a soliton-induced change in the topology of the density profiles of the two-species condensates at phase separation.