We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons an
d fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the indirect Pauli exclusion effect on the boson momentum distribution function. For the homogeneous system, we present finally a Diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion c
omponent. We focus on the case where the boson density $n_B$ is smaller than the fermion density $n_F$, for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing $n_B$.
