Stability condition of a strongly interacting boson-fermion mixture across an interspecies Feshbach resonance

We study the properties of dilute bosons immersed in a single-component Fermi sea across a broad boson-fermion Feshbach resonance. The stability of the mixture requires that the bare interaction between bosons exceeds a critical value, which is a universal function of the boson-fermion scattering length, and exhibits a maximum in the unitary region. We calculate the quantum depletion, momentum distribution, and the boson contact parameter across the resonance. The transition from condensate to molecular Fermi gas is also discussed.