FRACTIONAL WINDINGS OF THE SPINOR CONDENSATES ON A RING

We study the uniform solutions to the one-dimensional (1D) spinor Bose–Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the spin-gauge symmetry. All fractional windings can be denoted as nk/(m+n), with nk<m+n<2F, for arbitrary spin-F Bose–Einstein condensation (BEC). Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional (2D) spinor condensates.