Abstract
We examine the role of thermal fluctuations in uniform two-dimensional binary Bose mixtures of dilute ultracold atomic gases. We use a mean-field Hartree-Fock theory to derive analytical predictions for the miscible-immiscible transition. A nontrivial result of this theory is that a fully miscible phase at $T=0$ may become unstable at $T\neq0$, as a consequence of a divergent behaviour in the spin susceptibility. We test this prediction by performing numerical simulations with the Stochastic (Projected) Gross-Pitaevskii equation, which includes beyond mean-field effects. We calculate the equilibrium configurations at different temperatures and interaction strengths and we simulate spin oscillations produced by a weak external perturbation. Despite some qualitative agreement, the comparison between the two theories shows that the mean-field approximation is not able to properly describe the behavior of the two-dimensional mixture near the miscible-immiscible transition, as thermal fluctuations smoothen all sharp features both in the phase diagram and in spin dynamics, except for temperature well below the critical temperature for superfluidity.
Highlights
The study of phase-separation in two-component classical fluids is of paramount importance and the role of temperature can be rather nontrivial
In random phase approximation (RPA), the oscillation frequency at T 0 is given by the spin m√ode of the Bogoliubov sound as ω = csq0, with cs(T = 0) = (g − g12)n/(2m) where n = n1 + n2 is the total density of atoms, and we find a good agreement with stochastic (projected) GrossPitaevskii (SGPE) simulation
A remarkable result predicted by the meanfield theory is the existence of phase-separation induced by thermal fluctuations, occurring even for mixtures which are miscible at zero temperature (g12 < g)
Summary
The study of phase-separation in two-component classical fluids is of paramount importance and the role of temperature can be rather nontrivial. Superfluidity still exists below the critical temperature TBKT for the Berezinskii-Kosterlitz-Thouless (BKT) phase transition [38,39,40,41]; the transition from normal gas to superfluid follows from the binding and unbinding of vortexantivortex pairs at TBKT [42] Observation of such transition in the domain of ultracold quantum gases has been possible with quasiuniform box traps [43,44]. Our goal is to extend the investigation to the beyond mean-field level and explore the case of a uniform 2D Bose-Bose mixture occupying two different hyperfine states and satisfying the miscibility condition at zero temperature. We use the stochastic (projected) GrossPitaevskii (SGPE) [46,47] theory for the same mixtures This formalism describes the system and its fluctuations by using noisy classical fields coupled to a thermal bath, and includes effects of thermal fluctuations both in the density and spin channels, going beyond the HF description. For temperature T 0.5TBKT, the two theories provide consistent results
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