Bose-Fermi pair correlations in attractively interacting Bose-Fermi atomic mixtures

摘要

We study static properties of attractively interacting Bose-Fermi mixtures of uniform atomic gases at zero temperature. Using the Green's function formalism, we calculate the boson-fermion scattering amplitude and the fermion self-energy in the medium to lowest order of the hole-line expansion. We study the ground-state energy and pressure as a function of the scattering length for a few values of the boson-fermion mass ratio mb/mf and the number ratio Nb/Nf. We find that the attractive contribution to the energy is greatly enhanced for small values of the mass ratio. We study the role of Bose-Fermi pair correlations in the mixture by calculating the pole of the boson-fermion scattering amplitude in the medium. The pole shows a standard quasiparticle dispersion for a Bose-Fermi pair. In addition, we also study the fermion dispersion relation. We find two dispersion branches with the possibility of avoided crossings. This strongly depends on the number ratio Nb/Nf.