Superfluid transition temperature in a trapped gas of Fermi atoms with a Feshbach resonance

We investigate strong-coupling effects on the superfluid phase transition in a gas of Fermi atoms with a Feshbach resonance. The Feshbach resonance describes a composite quasiboson that can give rise to an additional pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy $2\nu$ of the Feshbach resonance two-particle bound state is lowered. In a recent paper, we showed that in the uniform Fermi gas, this tunable pairing interaction naturally leads to a crossover from a BCS state to a Bose-Einstein condensate (BEC) of the Nozières and Schmitt-Rink kind, in which the BCS-type superfluid phase transition continuously changes into the BEC type as the threshold energy is decreased. In this paper, we extend our previous work by including the effect of a harmonic trap potential, treated within the local-density approximation. We also give results for both weak and strong coupling to the Feshbach resonance. We show that the BCS-BEC crossover phenomenon strongly modifies the shape of the atomic density profile at the superfluid phase-transition temperature $T_{\mathrm{c}},$ reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above $T_{\mathrm{c}}.$ We also discuss the “phase diagram” above $T_{\mathrm{c}}$ as a function of the tunable threshold energy $2\nu .$ We introduce a characteristic temperature $T^{*}\left(2\mathrm{}\nu \right)$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.