Unvortex Lattice and Topological Defects in Rigidly Rotating Multicomponent Superfluids

Abstract

By examining rotating ferromagnetic spinor condensates through the perspective of large spin, we identify a novel type of topological point defects in the magnetization texture. These defects are not predicted by conventional homotopy analysis but rather by the Riemann-Hurwitz formula. The magnetization texture in the system is described by an equal-area mapping from the plane to the sphere of magnetization, forming a lattice of uniformly charged Skyrmions. This lattice contains doubly-quantized (winding number = 2) point defects arranged on the sphere in a tetrahedral configuration. The fluid found to be rotating rigidly, except at the point defects, where the vorticity vanishes. This vorticity structure describes an unconventional "unvortex" lattice, which contrasts with the well-known vortex lattice in scalar rotating superfluids, where vorticity is concentrated exclusively within defect points. Numerical results are presented, confirming these predictions and demonstrating their persistence in smaller-spin condensates.

Figures (4)

• Figure 1: The “ unvortex” lattice, obtained numerically for (a): $F=100$, (b): $F=8$, (c): $F=1$. A triangular lattice of cores forms around each point defect, which are predicted by the Riemann-Hurwitz formula. For large $F$, the condensate rotates rigidly between the cores.
• Figure 2: An illustration of the magnetic texture \ref{['eq:texture=000020exmpl']} for $k=2$. Each magnetization vector is the image of two different points, except for the magnetization of the defect itself at the origin.
• Figure 3: The magnetization texture mapping $\hat{\mathbf{n}}\left(\mathbf{r}\right)$ is obtained by dividing the plane into triangles and mapping them to spherical triangles indicated by matching colors (the orange triangle is in the back of the sphere). $k=2$ defects (red points) are located at the vertices of the triangles, with $N=4$ of them per unit cell. The images of the defects are arranged in the shape of a tetrahedron on the sphere. Each unit cell covers the sphere $Q=2$ times, as the two triangles outlined in dashed black lines each close up to form one tetrahedron.
• Figure 4: Blue curve: vorticity around a $k=2$ defect, calculated from Eq. \ref{['eq:=000020vor']} using the numerical solution of \ref{['eq:key2']}. Points: numerical gradient descent simulation results for the angle-averaged vorticity around a $k=2$ defect for various values of $F$.