Mixtures of Bosonic and Fermionic Atoms in Optical Lattices

TL;DR

This paper develops a theoretical framework for understanding mixtures of Bosonic and Fermionic atoms in optical lattices, analyzing their stability, phase transitions, and ground state properties at zero temperature.

Contribution

It derives a Bose--Fermi Hubbard model for such mixtures and explores their phase behavior using mean field theory and numerical simulations.

Findings

Predicted conditions for superfluid transition and phase separation.

Identified a disordered phase with degenerate ground states in deep lattices.

Analyzed density distributions and quantum phase transitions.

Abstract

We discuss the theory of mixtures of Bosonic and Fermionic atoms in periodic potentials at zero temperature. We derive a general Bose--Fermi Hubbard Hamiltonian in a one--dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean field criterion for the onset of a Bosonic superfluid transition. We investigate the ground state properties of the mixture in the Gutzwiller formulation of mean field theory, and present numerical studies of finite systems. The Bosonic and Fermionic density distributions and the onset of quantum phase transitions to demixing and to a Bosonic Mott--insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasi--degenerate ground states is related to a breaking of the mirror symmetry in the lattice.