Effective Hamiltonian for fermions in an optical lattice across Feshbach resonance

TL;DR

This paper derives an effective Hamiltonian for cold fermionic atoms in optical lattices across Feshbach resonances, revealing tunable models that enable exploration of various quantum phase transitions.

Contribution

It introduces a simplified effective single-band Hamiltonian that captures complex multiband and neighboring-site effects across Feshbach resonances in optical lattices.

Findings

Derivation of an effective Hamiltonian across Feshbach resonance

Identification of a resonance between local dressed molecules and valence bond states

Demonstration of tunable parameters enabling phase transition observations

Abstract

We derive the Hamiltonian for cold fermionic atoms in an optical lattice across a broad Feshbach resonance, taking into account of both multiband occupations and neighboring-site collisions. Under typical configurations, the resulting Hamiltonian can be dramatically simplified to an effective single-band model, which describes a new type of resonance between the local dressed molecules and the valence bond states of fermionic atoms at neighboring sites. On different sides of such a resonance, the effective Hamiltonian is reduced to either a t-J model for the fermionic atoms or an XXZ model for the dressed molecules. The parameters in these models are experimentally tunable in the full range, which allows for observation of various phase transitions.