Polarizing the medium: Fermion-mediated interactions between bosons

We consider a homogeneous mixture of bosons and polarized fermions. find that long-range attractive fermion-mediated interactions between have dramatic effects on the properties bosons. construct phase diagram spanned by boson-fermion mass ratio scattering parameter. It consists stable region mixing unstable toward separation. In phase, collective long-wavelength excitations can either be well behaved with infinite lifetime or finite in suffered from Landau damping. examine induced interaction weakly interacting turns out not only enhances repulsion against collapse but also stability superfluid state suppressing quantum depletion.