Pairing and superfluid properties of dilute fermion gases at unitarity

We study the system of a dilute gas of fermions in three dimensions, with attractive interactions tuned to the unitarity point, using the nonperturbative restricted path-integral Monte Carlo method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state quantum Monte Carlo calculations. We identify the temperature $T^{*}\approx 0.70{ϵ}_F$, below which pairing correlations develop, and estimate the critical temperature for the superfluid transition $T_c\approx 0.245{ϵ}_F$ from a finite size scaling analysis of the superfluid density.

Figure 1

(Color online) The upper panel shows the energy per particle for $N=10,20$ in units of ${ϵ}_{FG}=(3∕5){ϵ}_F$ for different choices of the imaginary time step $\tau$. These results obtained for a temperature $T=0.0543{ϵ}_F$ indicate that the time step $\tau =0.00957{ϵ}_F^{-1}$ optimizes the competing requirements of small time step error and efficient computation. The lower panel shows the energy as a function of the parameter $\alpha$ in the pairing function at a temperature of $T=0.0543{ϵ}_F$ and time step $\tau =0.00957{ϵ}_F^{-1}$. The energy has a broad minimum at $\alpha =10–18$, leading to our choice of $\alpha =10$.

Figure 2

(Color online) The energy per particle as a function of $T$ for $N=10$ and 20 (dashed line; error bars not shown but comparable to $N=10$.) The upper inset magnifies the energy at low temperature, obtained using the BCS-like nodes. The lower inset shows the energy for $N=10$ in the temperature region where the lowest energy is obtained by changing from free-fermion nodes (“Free”) to the BCS-like nodes (“BCS”).

Figure 3

(Color online) The pair correlation function of the two species of fermions at different values $T$. Note the sharp increase in pair correlation from $0.67T_F$ to $0.54T_F$.

Figure 4

(Color online) The superfluid fraction ${\rho }_s∕\rho$ as a function of $T$ for $N=20$.

Figure 5

(Color online) The scaled, linearized, superfluid density $N^{1∕3}{\rho }_s∕\rho$ as a function of $T$ for $N=10$, 20, 30, and 40. The intersection of the four lines gives the superfluid transition temperature as $T_c\approx 0.255T_F$.