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The BCS-BEC crossover problem has become recently of special interest, owing to the rapid experimental advances with trapped Fermi atoms.
For these systems, the effective attraction between Fermi atoms leading to superfluidity is provided by an appropriate use of Fano-Feshbach (molecular) resonances, whereby the atomic scattering length aF can be tuned from negative to positive values across the resonance.
It is shown that an effective single-channel Hamiltonian is sufficient to reproduce all relevant features of the scattering problem, at least in the case of the resonance at about 820G in 6Li. In this way, one can accurately identify the many-body Hamiltonian of the interacting atomic system in terms of the experimentally accessible scattering length aF, with which the relevant approximate treatments in the BCS and BEC limits can be constructed. An extension of the Popov theory for a weakly-interacting (dilute) superfluid Fermi gas, as to include the effects of the collective Bogoliubov-Anderson mode in the diagonal fermionic self-energy beyond BCS mean field, will be presented. In the strong-coupling limit of the fermionic attraction, this generalization of the Popov theory is able to describe a dilute system of composite bosons within the Bogoliubov approximation. It is shown that inclusion of the Bogoliubov-Anderson mode beyond mean field is essential for a quantitative comparison with the experimental density profiles for 6Li across the Fano-Feshbach resonance at low temperature, as well for reproducing the zero-temperature results of Quantum Monte Carlo simulations at the unitarity limit where aF diverges. Finally, improvements of this theory both in the strong- and weak-coupling limits will be discussed. |