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

TL;DR

This paper studies how a Feshbach resonance influences the superfluid transition in trapped Fermi gases, revealing a BCS-BEC crossover that affects density profiles and introduces a characteristic temperature T* for the normal phase crossover.

Contribution

It extends previous uniform gas models to include harmonic traps using LDA, analyzing the impact of Feshbach resonance on superfluid transition and density profiles.

Findings

Density profile shape changes across the BCS-BEC crossover.

Composite Bosons appear above Tc in the BEC regime.

The phase diagram includes a characteristic temperature T* for the normal phase crossover.

Abstract

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 pairing interaction between the Fermi atoms. This attractive interaction becomes stronger as the threshold energy 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 the Nozi`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 Tc, 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 Tc. We also discuss the "phase diagram" above Tc as a function of the tunable threshold energy. We introduce a characteristic temperature T* describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.