Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices

TL;DR

This paper investigates the ground state properties and phase boundaries of inhomogeneous Bose-Fermi mixtures in cubic optical lattices, providing exact solutions and numerical methods to guide future experiments.

Contribution

It introduces a combined analytical and numerical approach to study inhomogeneous Bose-Fermi mixtures, including exact solutions in the ultradeep limit and a Gutzwiller-based numerical method.

Findings

Exact solutions for ultradeep lattices reveal domain structures.

Perturbation theory maps phase boundaries for finite hopping.

Numerical results align with experimental conditions for optical lattices.

Abstract

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices by studying the Bose-Fermi Hubbard model including parabolic confining potentials. We present the exact solution in the limit of vanishing hopping (ultradeep lattices) and study the resulting domain structure of composite particles. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimensionality within perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.