Figure 1

(a) Schematic diagram of the system. The weakly coupled spin-one BECs are trapped in a double-well potential, which gives strong (weak) confinement in the $y-z$ plane ($x$ direction). A uniform magnetic field $B\widehat{z}$ is applied along the $z$ direction. (b),(c) Shown are spin vector patterns corresponding to (b) an SJV centered on the blue cross and (c) a FDW. The parameters are $\kappa ={\kappa }_c/2$ for the SJV and $\kappa =2{\kappa }_c$ for the FDW. Other parameters are $q=0$ and $\alpha =\pi /2$. See the text for more details of the parameters and spin patterns.Reuse & Permissions

Figure 2

(a),(b) $|{\psi }_1^l(x){|}^2$ for a FDW and an SJV, respectively, using the same parameters as in Fig. 1. The dashed (dotted) curves are calculated with (without) the constant atom density approximation, and the solid curves show numerical solutions found by evolving the GPEs in imaginary time. (c) Phase diagram of the topological excitations. The SJV is dynamically stable in region I (yellow). The FDW is unstable in both regions I and II. In region III, the system exhibits a polar ground state phase (see the text). The red circle (blue triangle) marks system parameters in region I (II), which are discussed in the text.Reuse & Permissions

Figure 3

(a) Schematic diagram showing phase imprinting of the coupled spinor BECs by a focused laser beam (red region). The phase-imprinting laser is switched on at $t=0$ and only affects atoms in the region $-r_b<x<r_b$ spanned by the beam (upper panel). The laser beam is switched off at time $\tau =\pi /(\beta I_0)$ and coherently flips all atomic spins in the region $-r_b<x<r_b$ (lower panel). (b),(c) Color maps showing how the spin vectors ${\overrightarrow{\mathbf{F}}}^l$ and ${\overrightarrow{\mathbf{F}}}^r$, respectively, evolve after the phase imprint when $\kappa =2{\kappa }_c$. The orientation (${\varphi }^j$) and magnitude ($|{\overrightarrow{\mathbf{F}}}^j|$) of the local spin vector in the $x\mathrm{\text{−}}y$ plane are represented, respectively, by the color and brightness of the images (see scale). The two black stripes (where $|{\overrightarrow{\mathbf{F}}}^j|=0$) visible for $|\gamma |t<5$ at $x/r_b=\pm 1$ show the initial formation of two FDWs. At later times, the stripes vanish, indicating the decay of the FDWs. (d),(e) Same as (c) and (d), respectively, except that $\kappa ={\kappa }_c/2$. Again, two black stripes centered at $x/r_b=\pm 1$ indicate the initial formation of two FDWs for $|\gamma |t<5$. In this case, though, the FDW evolves toward a new quasistatic spin texture [green and red stripes in (d) and (e)]. At $|\gamma |t=50$, this spin texture corresponds to the local spin vectors shown in (f). Comparing the region of (f) within the dashed blue box to Fig. 1b, we see that an SJV with $\alpha =\pi /2$ (see the text) has formed, centered at $x/r_b\approx -1$ (blue cross). An anti-SJV with opposite spin vector rotation has formed within the dashed red box centered at $x/r_b\approx 1$ (red cross). In our simulations, $r_x=1250$ and $r_b=100$ (see the text).Reuse & Permissions