Atom-Dimer Scattering and Stability of Bose and Fermi Mixtures

TL;DR

This paper studies the interactions between bosonic atoms and fermionic dimers, revealing complex dependencies on scattering lengths and three-body parameters, and discusses stability conditions relevant to recent experiments.

Contribution

It provides a detailed analysis of atom-dimer scattering lengths beyond mean-field predictions, incorporating dependence on scattering length ratios and three-body parameters.

Findings

$a_{ad}$ depends on $a_{bf}$, $a_{ff}$, and the three-body parameter

Universal parameters characterize $a_{ad}$ across a range of $a_{ff}$

System stability can be compromised by tuning $a_{ff}$ leading to phase separation or collapse

Abstract

Motivated by a recent experiment by ENS group on the mixture of Bose and Fermi superfluids (arxiv:1404.2548), 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 ($a_{ad}$), as simply given by the boson-fermion scattering length ($a_{bf}$), generically fails. Instead, $a_{ad}$ crucially depends on the ratio between $a_{bf}$ and $a_{ff}$ (the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing $a_{ad}$ for a wide range of $a_{ff}$ 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 $a_{ff}$. Our results have some implications to the ENS experiment.