Boson-Fermion Resonance Model in One Dimension

TL;DR

This paper explores the BCS-BEC crossover in one-dimensional spin 1/2 fermions using the Boson-Fermion resonance model, showing its equivalence to an exactly solvable model and discussing experimental realizations.

Contribution

It demonstrates the equivalence of the Boson-Fermion resonance model to the modified Gaudin-Yang model in 1D and discusses potential experimental methods to realize the crossover.

Findings

Model equivalence to Gaudin-Yang in broad resonance limit

Crossover from BCS-like state to molecular Tonks-Girardeau gas

Potential experimental pathways for realization

Abstract

We discuss the BCS-BEC crossover for one-dimensional spin 1/2 fermions at zero temperature using the Boson-Fermion resonance model in one dimension. We show that in the limit of a broad resonance, this model is equivalent to an exactly solvable single channel model, the so-called modified Gaudin-Yang model. We argue that the one-dimensional crossover may be realized either via the combination of a Feshbach resonance and a confinement induced resonance or using direct photo-association in a two-component Fermi gas with effectively one-dimensional dynamics. In both cases, the system may be driven from a BCS-like state through a molecular Tonks-Girardeau gas close to resonance to a weakly interacting Bose gas of dimers.