Superfluidity of a pure spin current in ultracold Bose gases

We study the superfluidity of a pure spin current, which is a spin current without a mass current. We examine two types of pure spin currents, planar and circular, in a spin-1 Bose gas. For the planar current, it is usually unstable but can be stabilized by the quadratic Zeeman effect. The circular current can be generated with spin-orbit coupling. When the spin-orbit coupling strength is weak, we find that the circular pure spin current is the ground state of the system and thus a superflow. We discuss the experimental schemes to realize and detect a pure spin current.

Figure 1

Amplitudes (a1, b1, c1) and phase angles (a2, b2, c2) of the three-component wave function $\psi ={({\psi }_1,{\psi }_0,{\psi }_{-1})}^T$ in the ground state of Hamiltonian (5) for a BEC of ${}^{23}\mathrm{Na}$ confined in a pancake trap. The particle number is ${10}^5$, the radial frequency of the trap is $2\pi \times 55$ Hz, and the dimensionless spin-orbit coupling strength is $\kappa =0.04$. The confinement in the $z$ direction is very tight, with ${\omega }_z=2\pi \times 4200$ Hz, so the system is effectively two-dimensional. Units of the $X$ and $Y$ axes are $a_h$.

Figure 2

Distribution of the spin current densities ${\mathbf{J}}_x^s$ (blue arrow), ${\mathbf{J}}_y^s$ (red arrow), and ${\mathbf{J}}_z^s$ (black arrow) of the ground state shown in Fig. 1. The length of the arrows represents the strength of the spin current. The arrow length of different colors is not to scale. $\kappa =0.04$. Units of the $X$ and $Y$ axes are $a_h$.