Pair condensation in the BCS-BEC crossover of ultracold atoms loaded onto a 2D square lattice

TL;DR

This paper explores the continuous transition from weakly-bound Cooper pairs to tightly-bound molecules in a 2D optical lattice, analyzing key properties across interaction strengths using mean-field theory.

Contribution

It provides an analytical and numerical study of the BCS-BEC crossover in a 2D lattice, focusing on pair binding energy, energy gap, and condensate fraction.

Findings

Pair binding energy varies with interaction strength.

Energy gap shows a smooth crossover behavior.

Condensate fraction increases with stronger interactions.

Abstract

We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-bound Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal-long-range-order for fermions we calculate analytically and numerically the pair binding energy, the energy gap and the condensate fraction of Cooper pairs as a function of interaction strength and filling fractor of atoms in the lattice at zero temperature.