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Physical Review A

Phase separation of a trapped Bose-Fermi gas mixture: Beyond the Thomas-Fermi approximation

X. X. Yi, C. P. Sun

Published Sep 1, 2001• 24 citations
Publisher

Abstract

Phase separation of a Bose-Fermi gas mixture in a trapping potential is strongly influenced by the interaction between the fermion and the boson. The stability condition for the mixture at zero temperature is deduced. It is found that mixture stability depends on the fermion-boson interaction, the total number of the bosons and the fermions, and the trapping frequencies. The stability conditions for the mixture at finite temperature are also derived and discussed.

DOI
10.1103/physreva.64.043608

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Phase separation of a Bose-Fermi gas mixture in a trapping potential is strongly influenced by the interaction between the fermion and the boson. The stability condition for the mixture at zero temperature is deduced. It is found that mixture stability depends on the fermion-boson interaction, the total number of the bosons and the fermions, and the trapping frequencies. The stability conditions for the mixture at finite temperature are also derived and discussed.
The stability of Bose-Fermi gases trapped in an isotropic potentials at ultracold temperature is strongly influenced by the interaction between the fermions and the bosons. At zero temperature, the stability criterion is given in this paper using variation method, the results show that whether a fermion-boson mixture is stable depends mainly on the interaction between the fermions and the bosons. For finite temperature, however, the stability is not only related to the coupling constants, but also to the temperature. The stability conditions for finite temperature are also derived and discuss in details in this paper.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.
In six different regimes for a spatial phase diagram of a trapped interacting Bose–Fermi gas mixture at low temperatures, we present the conditions for the spatial demixing and separation of bosons and fermions. Starting from a semiclassically thermodynamic model for the local density functional of thermal bosons and fermions, the explicit analytical expressions for the fugacities of bosons and fermions are derived in different regimes by means of a first-order perturbation method in a local-density approximation. The critical values of the fermion–boson interaction strength as a function of the fractional composition of fermions have a general feature: increase, extreme and decrease with increasing the fermionic composition slightly above Bose–Einstein critical temperature.
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.
We consider the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 ground state of mixtures of bosons and fermions. Applying the Thomas-Fermi approximation we show that, depending on the strength of boson-boson and boson-fermion interactions, the Fermi gas may constitute a ``shell'' around or a ``core'' inside the Bose condensate, or even both.