Half-Quantum Vortices in an Antiferromagnetic Spinor Bose-Einstein Condensate

We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using in situ magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The dynamics of HQV pair formation is characterized by measuring the temporal evolutions of the pair separation distance and the core magnetization, which reveals the short-range nature of the repulsive interactions between the HQVs. We find that spin fluctuations arising from thermal population of transverse magnon excitations do not significantly affect the HQV pair formation dynamics. Our results demonstrate the instability of a singly charged vortex in the antiferromagnetic spinor condensate.

Figure 1

Schematic illustration of the half-quantum vortices (HQVs) in the antiferromagnetic (AF) spinor condensate. The superfluid phase $\theta$ and the spin orientation $\overrightarrow{d}$ rotate by $\pi$ around vortex cores having nonzero magnetization $M_z$. The order parameter of the condensate is invariant under the operation of $\theta \to \theta +\pi$ and $\overrightarrow{d}\to -\overrightarrow{d}$ and it is continuous over the disclinations indicated by dashed lines.

Figure 2

Dissociation of a singly charged vortex into two HQVs. (a) Singly charged vortices are generated in a condensate in the polar ($P$) phase and then the condensate is transmuted to the AF phase (see the text). (b) Optical density (OD) image of a condensate containing singly charged vortices. (c) Magnetization-sensitive phase-contrast image of the AF condensate at $t_h=1.5\mathrm{s}$. The images were taken after 24-ms expansion by releasing the trapping potential. Schematic descriptions of (d) a singly charged vortex state with $(q_n,q_s)=(1,0)$ and (e) a state having a pair of HQVs with $(q_n,q_s)=(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},-\frac{1}{2})$.

Figure 3

Formation of a HQV pair with opposite core magnetization. (a) In situ magnetization distribution $M_z(x,y)$ of the condensate at $t_h=1.5\mathrm{s}$. Images of the HQV pairs at (b) $t_h=0.7\mathrm{s}$ and (c) 1.1 s, obtained by averaging over ten images cropped from several magnetization images like (a). (d) Magnetization profiles of the HQV pairs along the separation direction at various hold times $t_h$, from averaged images like (b) and (c). Evolutions of (e) the pair separation distance $s$ and (f) the core magnetization difference $\mathrm{\Delta }{M}_z$.

Figure 4

Spin fluctuations in the AF spinor condensate. In situ magnetization images of the condensate, containing no vortices, at (a) $t_h=0$ s, (b) 1.5 s, and (c) 3 s. (d)–(f) Images taken after 24 ms time-of-flight, where spin fluctuations are enhanced due to self-interference during the expansion [39, 40]. (g) Variance of in situ magnetization $⟨\delta M_z^2⟩$ as a function of the hold time $t_h$. The background noise level is subtracted.

Figure 5

Effect of thermal magnons on the pair dissociation. (a) Vortices are generated in the AF condensate after a dwell time $t_v$. Thermal spin fluctuations increase with $t_v$ [Fig. 4]. (b) Pair separation distance $s$ as a function of the hold time $t_h$ after vortex generation. The data in Fig. 3 are displayed together and labeled as $t_v=0\mathrm{s}$. The solid lines are the lines of $s_0(1-e^{-(t_d-t_0)/{\tau }_s})$ with $s_0=17.6\mu \mathrm{m}$, fit to the data: $(t_0,{\tau }_s)=(0.03,0.29)$ s for $t_v=1\mathrm{s}$ (blue) and $(t_0,{\tau }_s)=(0.44,0.35)\mathrm{s}$ for $t_v=0\mathrm{s}$ (red).