Figure 1

Planar spin textures. Spins aligned with two-dimensional (a) quadrupole and (b) hexapole magnetic fields produce textures with winding numbers $-1$ and $-2$, respectively. Counterclockwise traversal of the dashed contours in (a) and (b) leads to clockwise (negative) spin rotation, with the winding number defined as the integer number of revolutions made by the spin vector while circumnavigating the singularity at the origin [20].Reuse & Permissions

Figure 2

Coreless vortex formation in a spinor Bose-Einstein condensate. Coreless vortices were imprinted by ramping $B_z\to 0$ and diagnosed by suddenly switching (a)–(d) $B_z\ll 0$ and (e)–(h) $B_z\gg 0$. Axial absorption images display the optical density of condensates after 20 ms of ballistic expansion (a),(e) without and (b),(f) with a magnetic field gradient applied to separate the different spin states. (c),(g) Azimuthally averaged optical density vs radial position for spin components shown in (b) and (f), respectively. The radial separation of the spin states resulted from their relative phase windings and is a clear signature of the skyrmion/meron wave function [Eq. (4)]. (d),(h) Axial magnetization per particle, $M/N=({\mu }_B/2)\times ({\tilde{n}}_{m_F=+1}-{\tilde{n}}_{m_F=-1})/{\tilde{n}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$, vs radial position. The absorption imaging light was resonant with the $F=2\to F^{\prime }=3$ transition. The atoms were optically pumped into the $F=2$ hyperfine level with a pulse resonant with the $F=1\to F^{\prime }=2$ transition. This provided equal imaging sensitivity to each spin state. The field of view in (a), (b), (e), and (f) is $1.0\mathrm{m}\mathrm{m}\times 3.0\mathrm{m}\mathrm{m}$.Reuse & Permissions