Hartree-Fock-Bogoliubov theory of dipolar Fermi gases

We apply the Hartree-Fock-Bogoliubov theory to a system of uniform dipolar fermionic polar molecules, which recently has attracted much attention due to rapid experimental progress in achieving such systems. By calculating the anisotropic superfluid-order parameter and the critical temperature $T_c$, we show that high-$T_c$ superfluid can be achieved with a quite modest value of interaction strength for polar molecules. In addition, we also show that the presence of the Fock-exchange interaction enhances superfluid pairing.

Figure 1

Contour of the momentum distribution function $n(\mathbf{k})$ for $C_{\mathit{dd}}=1$ at temperatures (a) $T=0$ and (b) $T=0.3\hspace{0.5em}{T}_F$. In (a), we draw the Fermi surface. The solid line is the Fermi surface obtained from the self-consistent calculation of this work, the dotted line is the one obtained from the variational approach developed in Refs. [10, 11]. In (b), the lines from outside to inside correspond to $n(\mathbf{k})=0.1$, 0.3, 0.5, 0.7, and 0.9, respectively. Here, and in other plots, $\mathbf{k}$ is in units of the Fermi wave number of the noninteracting system $k_F=(6{\pi }^{2}n){}^{1/3}$.

Figure 2

(a) Gap parameter $\Delta (\mathbf{k})$ [in units of $E_F=\hslash {}^2{k}_F^2/(2m)$] at $T=0$ for $C_{\mathit{dd}}=1$. (b) The corresponding contour plot of the momentum distribution function $n(\mathbf{k})$. The lines from outside to inside correspond to $n(\mathbf{k})=0.1$, 0.3, 0.5, 0.7, and 0.9, respectively.

Figure 3

${\Delta }_l(k)$ for $C_{\mathit{dd}}=1$ at zero temperature.

Figure 4

(a) Chemical potential $\mu$ as a function of temperature for a superfluid state (dashed line) and a normal state (solid line). Energy and temperature are in units of $E_F$ and $T_F$, respectively. Here, $C_{\mathit{dd}}=1$. The arrow indicates the location of $T_c$. A superfluid state exists for $0<T<T_c$. (b) $T_c$ as a function of $C_{\mathit{dd}}$. Here, the dots are numerical data, and the smooth curve is a fit according to Eq. (10).