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arXiv:cond-mat/9901160 · Physical Review A

Component separation in harmonically trapped boson-fermion mixtures

Nicolai Gayle Nygaard, Klaus Mølmer

Published Apr 1, 1999• 80 citations
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Abstract

We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anisotropic harmonic traps. We investigate the phenomenon of component separation as a function of the strength of the interparticle interaction. While solving a Gross-Pitaevskii mean-field equation for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum-mechanical Slater determinant Schr\"odinger equation.

DOI
10.1103/physreva.59.2974

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The influence of boson-boson and boson-fermion interactions on the stability of a binary mixture of bosonic and fermionic atoms is investigated. The density profiles of the trapped mixture are obtained from direct numerical solution of a modified Gross-Pitaevskii equation that is self-consistently coupled to the mean field generated by the interaction with the fermionic species, the fermions which in turn feel the mean field created by the bosons are treated in the Thomas-Fermi approximation. We study the effects of different combinations of signs of the boson-boson and the boson-fermion scattering lengths and determine explicit expressions for critical particle numbers as a function of these scattering lengths.
We consider a mixture of two-component Fermi gases at low temperature. The density profile of this degenerate Fermi gas is calculated under the semiclassical approximation. The results show that the fermion-fermion interactions make a large correction to the density profile at low temperature. The phase separation of such a mixture is also discussed for both attractive and repulsive interatomic interactions, and the numerical calculations demonstrate the existance of a stable temperature region T c1 < T < T c2 for the mixture. In addition, we give the critical temperature of the BCS-type transition in this system beyond the semiclassical approximation.
By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state energy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between two components when the interaction is strong enough but finite. While in the infinite interaction limit both bosons and fermions display the completely same Fermi-like distributions and phase separation disappears.
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We present a density-functional theory for the one-dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground-state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the local density approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for sufficiently strong interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves, reflecting the strong correlation with fermions. For infinitely strong interaction, the ground-state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.