Four-Body Problem and BEC-BCS Crossover in a Quasi-One-Dimensional Cold Fermion Gas

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 $a_{\mathrm{aa}}$ displays a confinement-induced resonance. We compute the dimer-dimer scattering length $a_{\mathrm{dd}}$ and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

Figure 1

Scattering length $a_{\mathrm{dd}}$ as a function of ${\Omega }_B$. Dashed curves give exact limiting results, and the solid curve interpolates by adding these. Inset: Same but neglecting all closed-channel excitations. Here the solid curve gives the exact result.

Figure 2

Squared ratio of breathing and dipole mode frequency as a function of $-a_{\perp }/a$. Here we have chosen $N{\omega }_z/{\omega }_{\perp }=1/3$.