Mean-field theory of Bose-Fermi mixtures in optical lattices

TL;DR

This paper develops a mean-field theoretical framework to analyze the phase diagram of ultracold Bose-Fermi mixtures in optical lattices, revealing quantum phases involving fermion-boson pairing and bosonic holes, with analytical phase boundaries and experimental relevance.

Contribution

It introduces an analytic mean-field approach to identify phase boundaries in strongly interacting Bose-Fermi mixtures, including novel fermion-boson paired phases.

Findings

Identification of quantum phases with fermion-boson pairing and bosonic holes.

Analytic expressions for phase boundaries between phases.

Comparison with numerical simulations confirming the phase diagram.

Abstract

We determine the phase diagram of a mixture of ultracold bosons and polarized fermions placed in an optical lattice using mean field theory. In the limit of strong atom-atom interactions, there exist quantum phases that involve pairing of fermions with one or more bosons, or bosonic holes, respectively. We obtain the analytic form of the phase boundaries separating these composite fermion phases from the bosonic superfluid coexisting with Fermi liquid. We compare the results with numerical simulations and discuss their validity and relevance for current experiments.