Probing Anisotropic Superfluidity in Atomic Fermi Gases with Rashba Spin-Orbit Coupling

Motivated by the prospect of realizing a Fermi gas with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the twofold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet components emerge, leading to an anisotropic superfluid. We calculate the relevant physical quantities, such as the momentum distribution, the single-particle spectral function, and the spin structure factor, that characterize the system.

Figure 1

(a) Rashbons as evidenced by the two-body phase shift of ${\Gamma }^{-1}(\mathbf{0},\omega )$ at three different scattering lengths. The arrows indicate the position of binding energy. (b) Effective mass of rashbons [$\gamma =M_{\perp }/(2m)$] in the strong SO limit. The inset shows the bound state energy as a function of the scattering length.

Figure 2

(a) Mean-field order parameter as a function of the SO coupling for a homogeneous unitary Fermi gas at zero temperature. The inset shows the chemical potential and the half of bound state energy, both in units of ${ϵ}_F$. (b) Momentum distribution and (c) single-particle spectral function for $\theta =\pi /2$ at $\lambda k_F/{ϵ}_F=2$. Here $\theta$ is the angle between $\mathbf{k}$ and the $z$ axis. The width of the curves in (c) represents the weight factor $(1\pm {\gamma }_{\mathbf{k},\pm })/4$ for each of the four Bogoliubov excitations.

Figure 3

Linear contour plot for the triple pairing correlation $|⟨{\psi }_{\mathbf{k}\uparrow }{\psi }_{-\mathbf{k}\uparrow }⟩|$ between like spins (a) and the singlet pairing correlation $|⟨{\psi }_{\mathbf{k}\uparrow }{\psi }_{-\mathbf{k}\downarrow }⟩|$ between unlike spins (b) for a homogeneous unitary Fermi gas at zero temperature with $\lambda k_F/{ϵ}_F=2$. The zero-momentum dynamic and static spin structure factor are shown in (c) and (d), respectively.

Figure 4

Density distributions of a trapped unitary Fermi gas at $T=0$ (a) and $T=0.8T_{c,0}$ (b). $T_{c,0}$ is the critical temperature in the absence of the SO coupling. (c), (d), and (e) display the log-scale contour plot of the momentum distribution for a trapped SO coupled ideal gas at $T=0$, unitary gas at $T=0$, and unitary gas at $T=0.8T_{c,0}$, respectively. Here the Fermi energy is given by $E_F=(3N{)}^{1/3}\hslash {\omega }_0$, Fermi wave number $k_F=(24N{)}^{1/6}{a}_{\mathrm{ho}}^{-1}$, Thomas-Fermi radius $r_{\mathrm{TF}}=(24N{)}^{1/6}{a}_{\mathrm{ho}}$, and the noninteracting peak density $n_{\mathrm{TF}}=(24N{)}^{1/2}/(3{\pi }^2)a_{\mathrm{ho}}^{-3}$, where $a_{\mathrm{ho}}=\sqrt{\hslash /(m\omega )}$ is the characteristic length of the harmonic oscillator.

Figure 5

Log-scale contour plot of the single-particle spectral function for a trapped unitary Fermi gas at $T=0.8T_{c,0}$. The SO coupling strength in (a) and (b) is $\lambda k_F/E_F=1$, and in (c) and (d) is $\lambda k_F/E_F=2$.