Fermion-mediated interactions in a dilute Bose-Einstein condensate

TL;DR

This paper develops a diagrammatic perturbation approach to analyze the equation of state of a dilute Bose-Einstein condensate mixed with a Fermi gas, revealing a fermion-mediated instability that leads to phase separation.

Contribution

It introduces a novel diagrammatic perturbation method to study fermion-mediated interactions in a BEC-Fermi mixture, highlighting the breakdown of mean-field theory near instability.

Findings

Identifies fermion-mediated interactions causing instability.

Shows divergence of boson compressibility near phase separation.

Simplifies analysis in low BEC-density limit.

Abstract

We develop a diagrammatic perturbation treatment to calculate the zero-temperature equation of state of the dilute gas mixture of a single spin component Bose-Einstein condensate (BEC) and a normal Fermi gas of indistinguishable (single spin) fermion particles. We find that the mean-field description breaks down near the mechanical instability related to the phase separation phenomenon. Our analysis shows that the instability is caused by the competition of the usual short-range and fermion-mediated boson-boson interactions, which result in a boson compressibility that diverges. In the low BEC-density limit, we show that the diagrammatic analysis simplifies, we sum part of the higher order diagrams, and we discuss the effects of other higher-order contributions.