Quantum Monte Carlo studies of superfluid Fermi gases

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the $s$-wave scattering length and the Fermi wave vector, $a{k}_F$. We report results for the ground-state energy, the pairing gap $\Delta$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_F<-1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\Delta$ is much smaller than the Fermi gas energy $E_{\mathrm{FG}}$. When $a>0$, the interaction is strong enough to form bound molecules with energy $E_{\mathrm{mol}}$. For $1∕a{k}_F\gtrsim 0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\Delta$ and gas energy per particle approaching $\mid E_{\mathrm{mol}}\mid ∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $-0.5<1∕a{k}_F<0.5$, is discussed.