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 quasi-Boson, which can give rise to an additional pair-ing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy (2ν) 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 BCS-BEC crossover of theNozì eres 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 (LDA). 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 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 c. We also discuss the " phase diagram " above T c as a function of the tunable threshold energy 2ν. We introduce a characteristic temperature T * (2ν) describing the effective 1 crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.