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

TL;DR

This paper investigates how phonon exchange in dilute Fermi-Bose mixtures influences fermionic interactions, revealing sensitivity to condensate density and effects on collective modes, with implications for stability and superfluidity.

Contribution

It provides a detailed calculation of phonon-mediated interactions and their impact on effective scattering lengths and collective excitations in Fermi-Bose mixtures.

Findings

Effective scattering length is highly sensitive to condensate density.

Interaction potential becomes strongly energy dependent.

Mixture stability and collective mode behavior are analyzed.

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.