Strongly interacting Bose-Fermi mixture: mediated interaction, phase diagram and sound propagation

TL;DR

This paper develops a strong-coupling theory for Bose-Fermi mixtures that accurately predicts stability and sound propagation near resonance, aligning well with recent experimental results and revealing hybridized sound modes.

Contribution

It introduces a non-perturbative approach for resonant Bose-Fermi interactions, extending mediated interaction concepts to strong coupling and finite frequencies.

Findings

Mixture remains stable at large interactions near resonance.

Calculated sound velocity matches experimental data.

Predicted hybridization of Bose and Fermi sound modes.

Abstract

Motivated by recent surprising experimental findings, we develop a strong-coupling theory for Bose-Fermi mixtures capable of treating resonant inter-species interactions while satisfying the compressibility sum rule. We show that the mixture can be stable at large interaction strengths close to resonance, in agreement with the experiment but at odds with the widely used perturbation theory. We also calculate the sound velocity of the Bose gas in the $^{133}$Cs-$^6$Li mixture, again finding good agreement with the experimental observations both at weak and strong interactions. A central ingredient of our theory is the generalization of a fermion mediated interaction to strong Bose-Fermi scatterings and to finite frequencies. This further leads to a predicted hybridization of the sound modes of the Bose and Fermi gases, which can be directly observed using Bragg spectroscopy.