Polarizing the Medium: Fermion-Mediated Interactions between Bosons

TL;DR

This paper investigates how fermion-mediated interactions influence the phase behavior and stability of a boson-fermion mixture, revealing conditions for stable mixing and effects on bosonic excitations and superfluidity.

Contribution

It introduces a phase diagram for boson-fermion mixtures considering fermion-mediated interactions and analyzes their impact on bosonic properties and stability.

Findings

Fermion-mediated interactions can stabilize bosonic mixtures against collapse.

The phase diagram includes stable mixing and phase separation regions.

Induced interactions affect collective excitations and superfluid stability.

Abstract

We consider a homogeneous mixture of bosons and polarized fermions. We find that long-range and attractive fermion-mediated interactions between bosons have dramatic effects on the properties of the bosons. We construct the phase diagram spanned by boson-fermion mass ratio and boson-fermion scattering parameter. It consists of stable region of mixing and unstable region toward phase separation. In stable mixing phase, the collective long-wavelength excitations can either be well-behaved with infinite lifetime or be finite in lifetime suffered from the Landau damping. We examine the effects of the induced interaction on the properties of weakly interacting bosons. It turns out that the induced interaction not only enhances the repulsion between the bosons against collapse but also enhances the stability of the superfluid state by suppressing quantum depletion.