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arXiv:1406.1242 · Physical Review A

Atom-dimer scattering and stability of Bose and Fermi mixtures

Xiaoling Cui

Published Oct 21, 2014• 27 citations
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Abstract

Motivated by a recent experiment by the Ecole Normale Sup\'erieure de Lyon (ENS) group on the mixture of Bose and Fermi superfluids [I. Ferrier-Barbut et al., Science 345, 1035 (2014)], we investigate the effective scattering between a bosonic atom and a molecule (dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length $({a}_{\mathrm{ad}})$, as simply given by the boson-fermion scattering length $({a}_{\mathrm{bf}})$, generically fails. Instead, ${a}_{\mathrm{ad}}$ crucially depends on the ratio between ${a}_{\mathrm{bf}}$ and ${a}_{\mathrm{ff}}$ (the fermion-fermion scattering length), and in addition it log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing ${a}_{\mathrm{ad}}$ for a wide range of ${a}_{\mathrm{ff}}$ in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning ${a}_{\mathrm{ff}}$. Our results have some implications for the ENS experiment.

DOI
10.1103/physreva.90.041603

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The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.
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