Strongly interacting fermions in an optical lattice

TL;DR

This paper develops a detailed two-channel model for strongly interacting two-component fermions in an optical lattice, deriving an effective Hamiltonian that accurately describes the BEC-BCS crossover across various interaction regimes.

Contribution

It introduces the Fermi resonance Hamiltonian (FRH), a new effective model incorporating dressed molecules, valid for arbitrary s-wave scattering lengths and resonance widths.

Findings

Derived nonlinear eigenvalue equation for two-particle bound states.

Presented numerical methods and renormalization for the two-channel lattice model.

Established the FRH as an accurate many-body description of fermions in optical lattices.

Abstract

We analyze a system of two-component fermions which interact via a Feshbach resonance in the presence of a three-dimensional lattice potential. By expressing a two-channel model of the resonance in the basis of Bloch states appropriate for the lattice, we derive an eigenvalue equation for the two-particle bound states which is nonlinear in the energy eigenvalue. Compact expressions for the interchannel matrix elements, numerical methods for the solution of the nonlinear eigenvalue problem, and a renormalization procedure to remove ultraviolet divergences are presented. From the structure of the two-body solutions we identify the relevant degrees of freedom which describe the resonance behavior in the lowest Bloch band. These degrees of freedom, which we call dressed molecules, form an effective closed channel in a many-body model of the resonance, the Fermi resonance Hamiltonian (FRH). It is shown how the properties of the FRH can be determined numerically by solving a projected lattice two-channel model at the two-particle level. As opposed to single-channel lattice models such as the Hubbard model, the FRH is valid for general s-wave scattering length and resonance width. Hence, the FRH provides an accurate description of the BEC-BCS crossover for ultracold fermions on an optical lattice.