Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas

TL;DR

This paper analytically solves the four-body problem in a quasi-one-dimensional Fermi gas, revealing how the dimer-dimer scattering length governs the BEC-BCS crossover in this confined geometry.

Contribution

It provides an exact analytical solution for the four-body problem and links the dimer-dimer scattering length to the many-body crossover behavior.

Findings

Computed the dimer-dimer scattering length $a_{dd}$

Demonstrated $a_{dd}$ determines the BEC-BCS crossover

Analyzed effects of confinement-induced resonance

Abstract

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length $a_{aa}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{dd}$, and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.