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arXiv:1709.09698 · Phase Transitions

Bose–Einstein condensation in a mixture of interacting Bose and Fermi particles

Yu. M. Poluéktov, A. A. Soroka

Published May 12, 2020• 1 citation
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Abstract

A self-consistent field model for a mixture of Bose and Fermi particles is formulated. There is explored in detail the case of a delta-like interaction, for which the thermodynamic functions are obtained, and Bose–Einstein condensation of interacting particles in the presence of the admixture of fermions is studied. It is shown that at a fixed total density, the admixture of Fermi particles leads to reducing of the temperature of Bose–Einstein condensation and smoothing of features of thermodynamic quantities at the transition temperature. The regions of stability of the spatially uniform states of a mixture are found. As in the case of a pure Bose system, in the state of a mixture with condensate the dependence of the thermodynamic potential on the interaction constant between Bose particles has a nonanalytic character, so that it proves impossible to develop the perturbation theory in the magnitude of interaction of Bose particles.

DOI
10.1080/01411594.2020.1761366

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A self-consistent field model for a mixture of Bose and Fermi particles is formulated. There is explored in detail the case of a delta-like interaction, for which the thermodynamic functions are obtained, and Bose–Einstein condensation of interacting particles in the presence of the admixture of fermions is studied. It is shown that at a fixed total density, the admixture of Fermi particles leads to reducing of the temperature of Bose–Einstein condensation and smoothing of features of thermodynamic quantities at the transition temperature. The regions of stability of the spatially uniform states of a mixture are found. As in the case of a pure Bose system, in the state of a mixture with condensate the dependence of the thermodynamic potential on the interaction constant between Bose particles has a nonanalytic character, so that it proves impossible to develop the perturbation theory in the magnitude of interaction of Bose particles.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.
We calculate the shift in the critical temperature of Bose–Einstein condensation for a dilute Bose–Fermi mixture confined by a harmonic potential, to lowest order in both the Bose–Bose and Bose–Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson–boson and boson–fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose–Fermi mixtures is discussed.
We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction ${U}_{\mathrm{BB}}\ensuremath{\ge}0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent TTT-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $\ensuremath{-}{U}_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature Tclp{T}_{\mathrm{clp}}Tclp​ (leading to density collapse). When UBB=0,Tclp{U}_{\mathrm{BB}}=0, {T}_{\mathrm{clp}}UBB​=0,Tclp​ is always higher than the Bose-Einstein condensation (BEC) temperature Tc{T}_{\mathrm{c}}Tc​. When UBB>0{U}_{\mathrm{BB}}>0UBB​>0, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.
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.
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.
We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.