Statistical mechanics of a Feshbach coupled Bose-Fermi gas in an optical lattice

TL;DR

This paper investigates the thermodynamics of a Feshbach-resonant Bose-Fermi mixture in an optical lattice, revealing how lattice depth influences atom-molecule conversion and dissociation energy.

Contribution

It provides a numerical phase diagram and analytical results for thermodynamic quantities in a Feshbach-coupled Bose-Fermi gas in an optical lattice, highlighting non-monotonic behavior of dissociation energy.

Findings

Dissociation energy varies non-monotonically with lattice depth.

Analytical expressions derived for limiting cases of lattice depth.

Numerical phase diagram of atom-molecule mixture established.

Abstract

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibrium is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular energy spectrum with respect to the atomic one for which half of the atoms have been converted into dimers. Importantly we find that the dissociation energy has a non-monotonic dependence on lattice depth.