An exactly solvable model of the BCS-BEC crossover

TL;DR

This paper presents an exactly solvable one-dimensional model that describes the continuous transition from BCS superfluidity to Bose-Einstein condensation, connecting fermionic and bosonic systems through an integrable framework.

Contribution

It introduces a new integrable model that captures the BCS-BEC crossover in one dimension, bridging two well-known models and enabling exact analysis of the transition.

Findings

Ground state energy analysis across the crossover

Characterization of elementary excitations and correlations

Proposal for experimental realization with cold atoms

Abstract

We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.