Spin-1/2 fermions with attractive interaction in an optical lattice

TL;DR

This paper investigates how attractive spin-1/2 fermions in an optical lattice form molecules and how their densities vary in a trap, revealing a counterintuitive density reduction at strong interactions.

Contribution

It introduces a numerical approach to analyze inhomogeneous densities of fermions and molecules in an optical lattice with attractive interactions.

Findings

Strong interactions cause a decrease in fermion density at the trap center.

Fermions can form bosonic molecules in the lattice.

Numerical solutions reveal competition between unbound fermions and molecules.

Abstract

We study attractive fermions in an optical lattice superimposed by a trapping potential, such that fermions may form bosonic molecules. We map the model onto nonlinear field equations depending on the Nambu-Gor'kov propagator. The resulting field equations where solved numerically by a relaxation technique that allowed us to calculate the inhomogeneous densities of fermions and condensed molecules at zero temperature. When the interactions between fermions are strong there is a competition between unbound fermions and bound molecules leading to an unexpected reduction of the non-homogeneous density of fermions at the center of the trap.