Anisotropic superfluidity in the two-species polar Fermi gas

We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic $s$-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter $\alpha$ defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluids, suggesting a possible pairing symmetry transition by tuning the $s$-wave or dipolar interaction strength.

Figure 1

Deformation parameter $\alpha$ as a function of $s$-wave coupling strength $1/k_{F}a$ at $C_{\mathit{dd}}=1$ for the singlet superfluid.

Figure 2

(a) Momentum-integrated angular number distribution. (b) Angle-averaged momentum number distribution $n_k(k)=\int n(\mathbf{k})d\Omega /4\pi$ at $1/k_{F}a=-1$ and $C_{\mathit{dd}}=1$ for the singlet superfluid.

Figure 3

Radial number distribution in momentum space at $1/k_{F}a=-1$ and $C_{\mathit{dd}}=1$ and different polar angles for the singlet superfluid.

Figure 4

Radial gap parameter profile in momentum space at $1/k_{F}a=-1$ and $C_{\mathit{dd}}=1$ and different polar angles for the singlet superfluid.

Figure 5

(a) Critical temperature as a function of dipole-dipole interaction strength $C_{\mathit{dd}}$ for singlet superfluid at $1/k_{F}a=-1$ and for triplet superfluid. (b) Critical temperature as a function of $1/k_{F}a$ at $C_{\mathit{dd}}=1$ for singlet superfluid.