BCS-BEC Crossover of a Quasi-two-dimensional Fermi Gas: the Significance of Dressed Molecules

TL;DR

This paper investigates the BCS-BEC crossover in a quasi-two-dimensional Fermi gas, emphasizing the crucial role of dressed molecules in accurately modeling the system's behavior across the resonance.

Contribution

It compares two mean-field models and demonstrates that including dressed molecules is essential for realistic descriptions of the crossover in quasi-2D Fermi gases.

Findings

Model with dressed molecules shows decreasing cloud size from BCS to BEC

Model without dressed molecules predicts constant cloud size

Including dressed molecules aligns theory with expected physical behavior

Abstract

We study the crossover of a quasi-two-dimensional Fermi gas trapped in the radial plane from the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime by crossing a wide Feshbach resonance. We consider two effective two-dimensional Hamiltonians within the mean-field level, and calculate the zero-temperature cloud size and number density distribution. For a model 1 Hamiltonian with renormalized atom-atom interaction, we observe a constant cloud size for arbitrary detunings. For a model 2 Hamiltonian with renormalized interactions between atoms and dressed molecules, the cloud size deceases from the BCS to BEC side, which is consistent with the picture of BCS-BEC crossover. This qualitative discrepancy between the two models indicates that the inclusion of dressed molecules is essential for a mean-field description of quasi-two-dimensional Fermi systems, especially on the BEC side of the Feshbach resonance.