Single-particle excitations and effects of hetero-pairing fluctuations in a Bose–Fermi mixture with a Feshbach resonance

We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green’s function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz–Pines relation at the Bose–Einstein condensation (BEC) temperature T_BEC. In the unitary regime at T_BEC, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose–Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight. We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose–Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas.