Creation and Detection of Skyrmions in a Bose-Einstein Condensate

We present the first experimental realization and characterization of two-dimensional Skyrmions and half-Skyrmions in a spin-2 Bose-Einstein condensate. The continuous rotation of the local spin of the Skyrmion through an angle of $\pi$ (and half-Skyrmion through an angle of $\pi /2$) across the cloud is confirmed by the spatial distribution of the three spin states as parametrized by the bending angle of the $l$ vector. The winding number $w=(0,1,2)$ of the internal spin states comprising the Skyrmions is confirmed through matter-wave interference.

Figure 1

The absorption image (a) of a 2D Skyrmion created in spin-2 ${}^{87}\mathrm{Rb}$. The winding number $w$ for each spin state is indicated. The contrast of the image has been increased to make the $|-2⟩$ state more visible. The relative populations of the $|2⟩$, $|0⟩$, and $|-2⟩$ states are: 51%, 30%, 19%. (b) Azimuthally averaged lineouts (points) for each spin state agree well with the plots of (1) (solid lines) for the ${\beta }_1(\overline{r})$ determined by a nonlinear least-squares regression. (c) 3D plot of the solid lines in (b), where the colors red, green, and blue correspond to the $|2⟩$, $|0⟩$, and $|-2⟩$ states, respectively. The winding number of the spin state is indicated by the number of arrowheads. (d) The polarization of the Skyrmion. The points represent $|{\varphi }_2(\overline{r}){|}^2-|{\varphi }_{-2}(\overline{r}){|}^2$ from (b), and closely match the solid line: $l_z(\overline{r})=n(\overline{r})\cos {\beta }_1(\overline{r})$. (e) The vector plot of the Skyrmion $l$ vector clearly shows the rotation of the local spin through an angle of $\pi$ across the cloud. The same ${\beta }_1$ was used for all theory plots, and the goodness of fit for (b),(d) is $R_1^2=0.977$, $R_1^2=0.982$, respectively.

Figure 2

Absorption image (a) of a half-Skyrmion created in spin-2 ${}^{87}\mathrm{Rb}$. The lineouts (b), reconstruction (c), polarization (d), and $l$ vector (e) have been fit, processed, and presented as in Fig. 1. The relative populations of the $|2⟩$, $|0⟩$, and $|-2⟩$ states are: 54%, 31%, 15%, and the goodness of fit for (b),(d) is $R_2^2=0.996$, $R_2^2=0.999$, respectively.

Figure 3

Matter-wave interference of (0, 1, 2) and (0, $-1$, $-2$) coreless vortices alongside numerical predictions. The contrast of the data and corresponding theory has been increased for the $|0⟩$, $|-2⟩$ states to make the structure more visible. The relative populations of the $|2⟩$, $|0⟩$, $|-2⟩$ states for (a) and (b) are 49%, 30%, 21% and 50%, 30%, 20%.