BCS-BEC crossover in a quasi-two-dimensional Fermi gas

TL;DR

This paper develops a mean field theory for the BCS-BEC crossover in a quasi-2D Fermi gas, revealing how higher transverse levels influence pairing even at weak interactions, with implications for recent experiments.

Contribution

It introduces a mean field approach that accounts for multiple transverse levels in quasi-2D Fermi gases, extending understanding of the BCS-BEC crossover in confined geometries.

Findings

Higher transverse levels significantly affect fermion pairing.

In the BEC limit, the system behaves like 3D dimers confined to 2D.

Experimental observations already show effects of these higher levels.

Abstract

We consider a two-component gas of fermionic atoms confined to a quasi-two-dimensional (quasi-2D) geometry by a harmonic trapping potential in the transverse direction. We construct a mean field theory of the BCS-BEC crossover at zero temperature that allows us to extrapolate to an infinite number of transverse harmonic oscillator levels. In the extreme BEC limit, where the confinement length exceeds the dimer size, we recover 3D dimers confined to 2D with weak repulsive interactions. However, even when the interactions are weak and the Fermi energy is less than the confinement frequency, we find that the higher transverse levels can substantially modify fermion pairing. We argue that recent experiments on pairing in quasi-2D Fermi gases [Y. Zhang et al., Phys. Rev. Lett. 108, 235302 (2012)] have already observed the effects of higher transverse levels.