"Exact Solution for an 1D Boson-Fermion Model and application to ultra-cold atoms"

Abstract

The progress in ultra-cold atoms experiments allowing to tune fermionic systems through a Feshbach resonance where itinerant fermionic atoms may form tightly bound pairs ("bosonic" molecules) [1,2] has led to a renewed theoretical interest in boson-fermion models. We study a 1D boson fermion resonance model describing itinerant spin-1/2 fermions and itinerant scalar bosons coupled through a local interaction of strength g, which describes the binding of a pair of opposite spin fermions to form a scalar boson and the reverse process. The model also includes a detuning term characterized by a detuning parameter ν. It is found that the model has an exact solution by Bethe Ansatz.