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arXiv:1207.2391 · Physical Review A

Large- N approximation for one- and two-component dilute Bose gases

Chih-Chun Chien, Fred Cooper, Eddy Timmermans

Published Aug 29, 2012• 15 citations
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Abstract

We discuss the mean-field theories obtained from the leading order in a large-$N$ approximation for one- and two-component dilute Bose gases. For a one-component Bose gas, this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature ${T}_{c}$ is not shifted from the noninteracting gas value ${T}_{0}$. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intraspecies interactions and focus on the stability of the mixture state above ${T}_{c}$. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the interspecies interaction strength to the intraspecies interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.

DOI
10.1103/physreva.86.023634

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We discuss the mean-field theories obtained from the leading order in a large-NNN approximation for one- and two-component dilute Bose gases. For a one-component Bose gas, this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature Tc{T}_{c}Tc​ is not shifted from the noninteracting gas value T0{T}_{0}T0​. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intraspecies interactions and focus on the stability of the mixture state above Tc{T}_{c}Tc​. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the interspecies interaction strength to the intraspecies interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.
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We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the interspecies interactions. The dynamics above the critical temperature Tc{T}_{c}Tc​ is studied using a leading-order large-NNN approximation that predicted a phase transition from mixing to phase separation as a function of the interspecies coupling. Here, we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above Tc{T}_{c}Tc​ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to those found at zero temperature where only the condensates contribute to the densities. When the interspecies interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above Tc{T}_{c}Tc​ where no condensate is present this dynamical transition should still be observable in experiments.
Abstract We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose–Einstein condensates. Inter alia we analytically demonstrate that for sufficiently weak interspecies interactions a 12 the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials µ 1, µ 2 and temperature T. In contrast, for sufficiently large, positive values of a 12, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid–gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.
We study the thermodynamic properties of binary Bose mixtures by developing a beyond mean-field Popov theory which properly includes the effects of quantum and thermal fluctuations in both the density and spin channels. Results for key thermodynamic quantities, such as the isothermal compressibility and the magnetic susceptibility, are derived from a perturbative calculation of the grand-canonical potential. We find that thermal fluctuations can play a crucial role on the miscibility condition of a binary mixture, favoring phase separation at finite temperature even if the mixture is soluble at zero temperature, as already anticipated in a previous work [M. Ota et al., Phys. Rev. Lett. 123, 075301 (2019)]. We further investigate the miscibility condition for binary mixtures in the presence of asymmetry in the intraspecies interactions, as well as in the masses of the two components. Furthermore, we discuss the superfluid behavior of the mixture and the temperature dependence of the Andreev-Bashkin effect.
Atomic interactions play an important role in the properties of ultracold atomic gases. In single-component bosonic systems, its effect is already present at the critical point for the Bose-Einstein condensate phase transition by shifting it to lower temperatures as a consequence of effective repulsion between the atoms. When considering atomic bosonic mixtures, interesting effects arise from the competition between intra- and interspecies interactions such as the miscible-immiscible phase transition and the particular case of self-bounded quantum droplets. In such a scenario, it is natural to expect that these interactions will also affect the critical point of each species composing the mixture. In this paper, we obtain semianalytical expressions for the critical temperature shift of the phase transition to a Bose-Einstein condensate in the presence of a second species considering the mean-field framework. We treat differently the cases in which the second species is above or below its own critical temperature and apply the obtained relations to the case of a Na 23 − K 39 bosonic mixture that can be realized in current running experimental setups. Our findings can be easily extended to other atomic mixtures.
We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein-condensed phases may be either continuous or first order. The phase diagram hosts lines of triple points, tricritical points, and quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intraspecies interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas-type transition between noncondensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points.