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Particle Density Distributions in Fermi Gas Superfluids: Molecular Boson Effects

We show how to describe the $T \neq 0$ behavior associated with the usual BCS- Bose Einstein condensation (BEC) crossover ground state. We confine our attention here to the BEC and near-BEC regime where analytical calculations are possible. At finite $T$, non-condensed fermion pairs must be included, although they have been generally ignored in the literature. Within this BEC regime we compute the equations of state for the one and two channel models; these two cases correspond to whether Feshbach resonance effects are omitted or included. Differences between these two cases can be traced to differences between the nature of a Cooper pair and bosonic condensate. Our results are also compared with the Gross Pitaevskii equations of state for true bosons. Differences found here are associated with the underlying fermionic character of the system. Finally, the particle density distribution functions for a trap containing superfluid fermionic atoms are computed using a Thomas-Fermi approach. The one and two channel behavior is found to be very different; we find a narrowing of the density profile as a result of Feshbach resonance effects. Importantly, we infer that the ratio between bosonic and fermionic scattering lengths depends on the magnetic detuning and is generally smaller than 2. Future experiments will be required to determine to what extent this ratio varies with magnetic fields.