Bose-Fermi Mixtures Near an Interspecies Feshbach Resonance: Testing a Non Equilibrium Approach

TL;DR

This paper evaluates a non-equilibrium theoretical approach to Bose-Fermi mixtures near a Feshbach resonance, revealing limitations of the Hartree-Fock-Bogoliubov method and emphasizing the importance of higher-order correlations in molecular formation.

Contribution

The study demonstrates that standard HFB theory fails for Bose-Fermi mixtures and highlights the need to consider three-point and higher correlations for accurate modeling.

Findings

HFB theory does not accurately predict molecular binding energies in Bose-Fermi mixtures.

Molecular formation is primarily driven by higher-order correlations, not just pair correlations.

Standard resonant system models are insufficient for Bose-Fermi mixtures due to bosonic depletion effects.

Abstract

We test a non equilibrium approach to study the behavior of a Bose-Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree-Fock-Bogoliubov (HFB) equations of motion for, the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose-Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that bosonic depletion plays in the Bose-Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose-Fermi mixtures is driven by three point and higher order correlations in the gas, unlike any other resonant system studied in the context of ultra-cold atomic physics.