Collision dynamics of skyrmions in a two-component Bose-Einstein condensate

The dynamics of skyrmions in a two-component Bose-Einstein condensate is numerically investigated in the mean-field theory. When two skyrmions collide with each other, they are first united and then scattered into various states. For head-on collisions, skyrmions with unit winding number are scattered. The collision dynamics with an impact parameter are shown to depend on the relative phase. These dynamic processes are characterized by integer winding numbers.

Figure 1

Dynamics of a single skyrmion. (a) Cross-sectional density profiles of component 1 at $z=z_s$ (upper panels) and those of component 2 at $y=0$ (lower panels), where $z_s$ is the $z$ coordinate of the position of the vortex-ring core in component 2. The insets show the phase profiles. The field of view is $128\xi \times 128\xi$. (b) Time evolution of $z_s$ (red solid line) and the winding number $W$ (blue dashed line).

Figure 2

Dynamics of a collision and scattering of two skyrmions. Isodensity surfaces of component 1 at $|{\psi }_1{|}^2=0.5n_0$ are shown; the color represents the phase at the surface. Each skyrmion in (a) has a winding number $W=1$, and the total winding number is $W_{\mathrm{tot}}=2$. The parameters for preparing the initial skyrmions are $R_s=20\xi , r_s=10\xi , {\mathit{r}}_0=(0,0,\pm 20\xi ), n=\pm 1$, and $\ell =\pm 1$. The size of each box is ${\left(128\xi \right)}^3$. See Ref. [43] for a movie of the dynamics.

Figure 3

Isodensity surfaces of component 1; the color represents the phase at the surface. Each skyrmion in (a) has winding number 2 ($n=\pm 2$ and $\ell =\pm 1$), and the total winding number is $W_{\mathrm{tot}}=4$. Other conditions are the same as those in Fig. 2. See Ref. [43] for a movie of the dynamics.

Figure 4

Isodensity surfaces of component 1; the color represents the phase at the surface. The initial states of two skyrmions and the states after their collision are shown. (a) Winding numbers are 3 and 3 ($W_{\mathrm{tot}}=6$). (b) Winding numbers are 1 and 2 ($W_{\mathrm{tot}}=3$). (c) Winding numbers are $-1$ and 2 ($W_{\mathrm{tot}}=1$). Other conditions are the same as those in Fig. 2. All the skyrmions in the right-hand panels have unit winding number. See Ref. [43] for a movie of the dynamics.

Figure 5

Dynamics of off-axis collisions of skyrmions with $W=1$ ($W_{\mathrm{tot}}=2$) and ${\mathit{r}}_0=(\pm 10\xi ,0,\pm 20\xi )$ (the impact parameter is $20\xi$). Isodensity surfaces of component 1 are shown; the color represents the phase at the surface. The initial phase differences between the two donut-shaped components are (a) 0 and (b) $\pi$. Other conditions are the same as those in Fig. 2. See Ref. [43] for a movie of the dynamics.