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arXiv:cond-mat/9911084 · Physical Review A

Phonon exchange in dilute Fermi-Bose mixtures: Tailoring the Fermi-Fermi interaction

Michiel J. Bijlsma, B. A. Heringa, Henk T. C. Stoof

Published Apr 5, 2000• 206 citations
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Abstract

We consider a mixture of a single-component Bose gas and a two-component Fermi gas at temperatures where the Bose gas is almost fully condensed. In such a mixture, two fermionic atoms can interact with each other by exchanging a phonon that propagates through the Bose condensate. We calculate the interaction potential due to this mechanism, and determine the effective s-wave scattering length for two fermions that interact, both directly by the interatomic potentials as well as by the above-mentioned exchange mechanism. We find that the effective scattering length is quite sensitive to changes in the condensate density, and becomes strongly energy dependent. In addition, we consider the mechanical stability of these mixtures, and also calculate the dispersion and the damping of the various collisionless collective modes of the gas.

DOI
10.1103/physreva.61.053601

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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{m}_{b}∕{m}_{f}mb​∕mf​ and the number ratio Nb∕Nf{N}_{b}∕{N}_{f}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{N}_{b}∕{N}_{f}Nb​∕Nf​.
We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-lll channels. It has been found that the onset of the superconducting phase can occur at temperatures (>100nK)(>100\mathrm{nK})(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.