Quasiparticle excitations in Bose-Fermi mixtures

Abstract

We analyze the excitation spectrum of a three-dimensional Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a three-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 $1/{N}_{\ensuremath{\psi}}$ expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) ${N}_{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\infty}$. 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.