Fermi-Bose mixture across a Feshbach resonance

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.

9 pages, 5 figures, to be published in Phys. Rev. A

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• Effects of Axial Vorticity in Elongated Mixtures of Bose-Einstein Condensates
• Collective Modes and Stability of Bose-Fermi Mixtures with a BCS-BEC Crossover
• How the effective boson-boson interaction works in Bose-Fermi mixtures in periodic geometries