Exotic Vortex States with Discrete Rotational Symmetry in Atomic Fermi Gases with Spin-Orbital–Angular-Momentum Coupling

We investigate the superfluidity of a two-component Fermi gas with spin-orbital-angular-momentum coupling (SOAMC). Because of the intricate interplay of SOAMC, two-photon detuning and atom-atom interaction, a family of vortex ground states emerges in a broad parameter regime of the phase diagram, in contrast to the usual case where an external rotation or magnetic field is generally required. More strikingly, an unprecedented vortex state, which breaks the continuous rotational symmetry to a discrete one spontaneously, is predicted to occur. The underlying physics are elucidated and verified by numerical simulations. The unique density distributions of the predicted vortex states enable a direct observation in experiment.

Figure 1

Schematic of the setup (a) and energy levels (b). A pair of LG Raman laser beams with opposite orbital angular momenta $\pm \ell \hslash$ copropagates and generates SOAMC along the $z$ axis in the two-dimensional Fermi gas. $\delta$ is the two-photon detuning.

Figure 2

(a) The ground-state phase diagram of the BdG simulations (solid lines) and the effective model (dash-dotted lines) in the $E_b\text{−}\delta$ plane for a superfluid Fermi gas with SOAMC. Vortex-$Q$ ($Q=1$, 2) denotes a single-vortex state with velocity $Q$. (b) The spatial amplitude $|\mathrm{\Delta }(x,y)|$ (left column) and phase $\varphi (x,y)$ (middle column) of the order parameter for the vortex phases in (a), and the right column gives the corresponding atomic radial density $n_{\sigma }(r)$ for each vortex. Here we have taken $N_{\mathrm{atom}}=50$, $\chi /E_F=0.7$ and $\mathrm{\Omega }/E_F=0.21$.

Figure 3

The amplitude (a1)–(a4) and phase (b1)–(b4) distributions of the order parameter $\mathrm{\Delta }(r)$ in the $x\text{−}y$ plane for different two-photon detuning $\delta /E_F=0$, 0.1, 0.3, and 0.4. (c1)–(c4) The corresponding momentum distributions $|\mathrm{\Delta }(k_x,k_y)|$. (d) The radial distributions $|C_m(r)|$ of the $m$ component for order parameters in (a1)–(a4), respectively. Other parameters are $\chi /E_F=0.7$, $E_b/E_F=0.3$, $\mathrm{\Omega }/E_F=0.14$, and the unit of momentum $k_{\mathrm{osc}}=\sqrt{2{\omega }_r}$.

Figure 4

The normalized density distributions of $n(\mathbf{r})$ for different vortex states in Fig. 3: (a) a single vortex state with rotational symmetry for $\delta /E_F=0.1$, (b) an exotic vortex with ${\mathcal{C}}_3$ symmetry for $\delta /E_F=0.3$, and (c) an exotic vortex with ${\mathcal{C}}_5$ symmetry for $\delta /E_F=0.4$.