Mass imbalance effect in resonant Bose-Fermi mixtures

TL;DR

This paper investigates how mass and density imbalances affect the phase diagram and quantum phase transition in resonant Bose-Fermi mixtures, revealing critical coupling dependencies and momentum distribution effects.

Contribution

It provides a detailed analysis of the mass imbalance effect on the phase transition and critical coupling in Bose-Fermi mixtures using many-body diagrammatic methods.

Findings

Critical coupling depends strongly on mass ratio.

Weak dependence of critical coupling on density imbalance.

Distinct momentum distribution features due to composite and unpaired fermions.

Abstract

We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture $^{87}$Rb $-^{40}$K for different values of the density imbalance. We then analyse the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.