Fermion Superfluids of Nonzero Orbital Angular Momentum near Resonance

We study the pairing of Fermi gases near the scattering resonance of the $\ell \ne 0$ partial wave. Using a model potential which reproduces the actual two-body low energy scattering amplitude, we have obtained an analytic solution of the gap equation. We show that the ground state of $\ell =1$ and $\ell =3$ superfluids are orbital ferromagnets with pairing wave functions $Y_{11}$ and $Y_{32}$, respectively. For $\ell =2$, there is a degeneracy between $Y_{22}$ and a “cyclic state.” Dipole energy will orient the angular momentum axis. The gap function can be determined by the angular dependence of the momentum distribution of the fermions.

Figure 1

Chemical potential ($\mu$) for $\ell =1$ resonance as a function of $-1/k_F{a}_1$. We have taken $r_1=-3b$, $k_0$ given by Eq. (13), and $k_F{r}_1=-0.09$. The linear portion agrees exactly with Eqs. (25, 26). The switching to $\mu ={\mathcal{E}}_F$ at the atomic side is very sudden. It corresponds to crossover to weak coupled $p$-wave superfluid and is controlled by the smallness of $k_F{r}_1$. It takes place around $E_b/2\sim {\mathcal{E}}_F$ or $(k_F{a}_1{)}^{-1}\sim k_F{r}_1$.