Fermions Trapped in Boson Gas

Bess Fang, Patrizia Vignolo, Christian Miniatura +1 more

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

H. A. Buchdahl

X. X. Yi, C. P. Sun

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.

Krutik Patel, Geyue Cai, B. J. DeSalvo +1 more

Yong-li Ma, S. T. Chui

We calculate the critical temperature of a trapped interacting Bose-Fermi gas mixture by means of a first-order perturbation method in a local-density approximation. An explicit analytical expression is derived for the dependence of the critical temperature on the numbers of bosons and fermions, the strengths of boson-boson and boson-fermion interactions, and the trapping frequencies.