Collective Modes and Stability of Bose-Fermi Mixtures with a BCS-BEC Crossover

TL;DR

This paper analyzes the collective excitations and stability of ultracold Bose-Fermi mixtures across the BCS-BEC crossover, deriving a unified stability criterion and exploring phase separation and collapse phenomena.

Contribution

It introduces a comprehensive stability condition valid throughout the BCS-BEC crossover and examines the effects of fermion-boson interactions on phase behavior.

Findings

Strong FB interactions can destabilize the mixture.

FB repulsion leads to phase separation.

FB attraction can cause collapse.

Abstract

We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion-pairs and bosons in a superfluid phase. We derive a stability condition of the mixtures, which is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and BEC limits, shows that sufficiently strong FB interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground state energy of both the uniformly mixed and the phase-separated states. We find that the FB repulsion induces a phase separation, whereas the FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.