Fermi excitations in a trapped atomic Fermi gas with a molecular Bose condensate

We discuss the effect of a molecular Bose condensate on the energy of Fermi excitations in a trapped two-component atomic Fermi gas. The single-particle Green's functions can be approximated by the well-known BCS form, in both the BCS (Cooper pairs) and BEC (Feshbach resonance molecules) domains. The composite Bose order parameter ${\tilde Δ}$ describing bound states of two atoms and the Fermi chemical potential $μ$ are calculated self-consistently. In the BEC regime characterized by $μ<0$, the Fermi quasiparticle energy gap is given by $\sqrt{μ^2+{\tilde Δ}^2}$, instead of $|{\tilde Δ}|$ in the BCS region, where $μ>0$. This shows up in the characteristic energy of atoms from dissociated molecules.

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