Quasiparticle excitations in Bose-Fermi mixtures

We analyze the excitation spectrum of a three-dimensional(3D) Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a 3-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low lying excitations of the mean-field theory are described by the Fermi liquid picture with a quasiparticle weight and charge which is justified by a $1/N_\psi$ expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) $N_\psi \to \infty$. Our emphasis is placed on the novel conditions for chemical equilibrium and how many-body chemical reactions renormalize the bosonic chemical potential, modifying condensation and superfluid-insulator transitions.