Quantum phases in a resonantly-interacting Bose-Fermi mixture

TL;DR

This paper models a resonantly-interacting Bose-Fermi mixture in an optical lattice, predicting a quantum phase transition at low filling fractions and providing a detailed phase diagram based on microscopic parameters.

Contribution

It introduces a generalized Hubbard model for the mixture, incorporating molecules, and predicts quantum phase transitions using microscopic parameters derived from the optical lattice and Feshbach resonance.

Findings

Prediction of a quantum phase transition at low filling fractions.

Development of a detailed phase diagram as a function of temperature and magnetic field.

Derivation of microscopic parameters from the optical lattice and Feshbach resonance.

Abstract

We consider a resonantly-interacting Bose-Fermi mixture of $^{40}$K and $^{87}$Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for $^{40}$K and $^{87}$Rb atoms, and $^{40}$K-$^{87}$Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.