Energy Spectrum of a Degenerate Fermi Gas at the BEC-BCS Crossover

A theoretical study of the BCS-BEC crossover is presented. Starting from a two-channel Boson-Fermion resonance model, the BCS-Bogoiubov mean-field method and the Green's function method are adopted. The result shows that we can end up with a BCS-type theory but with a composite order parameter. Calculation shows that the Bose condensate of BCS Cooper pairs is proportional to the molecular BEC of Bose molecules. The resonance superfluid phase is indicated by the energy spectrum with an obvious interpretation of the transition mechanism.