Boson-Fermion Resonance Model in One Dimension

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.