Multi-state fermionic Hamiltonian approach to the study of the BEC-BCS crossover in ultracold fermionic atom gases.

We study the crossover between the BEC and BCS regimes in an ultracold fermionic atom gas, in the framework of a multi-state fermionic Hamiltonian using a finite-range interaction. We compare the predictions for the ground-state properties of a 2- state (one-channel) model, with the ground-state properties of a 3-state ($^{40}$K-like), and a 4-state ($^{6}$Li-like) model, respectively. We discuss signatures of the onset of superfluidity as predicted by the $s$-wave mean-field approximation of the zero-temperature Hamiltonian.