Fermi-Bose mixture across a Feshbach resonance

TL;DR

This paper investigates the phase behavior of a dilute boson-fermion mixture across a Feshbach resonance, revealing phase separation, molecule formation, and collapse conditions with experimental relevance.

Contribution

It provides a detailed analysis of the phase diagram and stability conditions of boson-fermion mixtures across a Feshbach resonance, including effects of interactions and trapping.

Findings

Identification of three possible phases in the mixture.

Determination of conditions for phase separation and collapse.

Analysis of molecule formation and spatial separation.

Abstract

We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length $a_F$. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: a single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As $1/a_F$ is increased from a negative value to the Feshbach resonance ($1/a_F=0$) the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance ($1/a_F>0$), pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when $1/a_F$ exceedes a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^6$Li--$^{23}$Na and $^{40}$K--$^{87}$Rb atoms.