Fermions in optical lattices near a Feshbach resonance: from band insulator to Mott insulator

TL;DR

This paper investigates a system of two-species fermions in an optical lattice, showing a transition from a band insulator to a Mott insulator as interaction strength varies, with implications for experimental detection.

Contribution

It introduces a model describing the transition from band to Mott insulator in fermionic optical lattices near a Feshbach resonance, highlighting the effective spin-1 Heisenberg antiferromagnet behavior.

Findings

Weak interactions produce a band insulator.

Strong interactions lead to a Mott insulator with spin-1 Heisenberg behavior.

Experimental signatures distinguish the two insulator types.

Abstract

We study a model of an equal mixture of two species of fermions in a deep optical lattice at a filling of two fermions per site. At weak inter-species interaction, the system is a band insulator. When the inter-species interaction is tuned via a Feshbach resonance to be larger than an energy related to the energy separation of the first and second Bloch band, atoms populate equally the two Bloch bands. With weak tunneling between sites of the optical lattice, the system becomes a Mott insulator with the low energy effective Hamiltonian of a spin-1 Heisenberg antiferromagnet, because of a Hund's rule like coupling between the two bands. We discuss experimental signatures of these two types of insulators.