Observation of Wall-Vortex Composite Defects in a Spinor Bose-Einstein Condensate

Seji Kang, Sang Won Seo, Hiromitsu Takeuchi, and Y. Shin

Phys. Rev. Lett. 122, 095301 – Published 8 March 2019

Abstract

We report the observation of spin domain walls bounded by half-quantum vortices (HQVs) in a spin-1 Bose-Einstein condensate with antiferromagnetic interactions. A spinor condensate is initially prepared in the easy-plane polar phase, and then, suddenly quenched into the easy-axis polar phase. Domain walls are created via the spontaneous $Z_{2}$ symmetry breaking in the phase transition and the walls dynamically split into composite defects due to snake instability. The end points of the defects are identified as HQVs for the polar order parameter and the mass supercurrent in their proximity is demonstrated using Bragg scattering. In a strong quench regime, we observe that singly charged quantum vortices are formed with the relaxation of free wall-vortex composite defects. Our results demonstrate a nucleation mechanism for composite defects via phase transition dynamics.

Received 20 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.095301

Physics Subject Headings (PhySH)

Quantum phase transitions Quantum quench Topological defects

Spinor Bose-Einstein condensates

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Seji Kang^1,2, Sang Won Seo¹, Hiromitsu Takeuchi³, and Y. Shin^1,2,*

¹Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea
²Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea
³Department of Physics and Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Osaka 558-8585, Japan

^*yishin@snu.ac.kr

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Vol. 122, Iss. 9 — 8 March 2019

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Images

Figure 1
Schematic illustration of the wall-vortex composite defect in the EAP phase of an antiferromagnetic spinor BEC. The order parameter of the polar phase has a discrete symmetry under the operation of $(ϕ, \hat{d}) \to (ϕ + π, - \hat{d})$ . The double-head arrow denotes the spin director $\hat{d}$ and the color of each arrow head indicates the superfluid phase $ϕ$ . (a) Domain wall at the interface of two domains with opposite spin directions. $\hat{d}$ flips to the opposite direction across the wall. The density distributions $n_{0, \pm 1}$ of the three $m_{z} = 0, \pm 1$ spin components are displayed. (b) Domain wall bounded by a HQV. As the two domains are continuously connected to each other with changing $ϕ$ by $π$ , the domain wall spatially terminates and a HQV is formed at the wall end point.
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Figure 2
Creation of wall-vortex composite defects in a BEC via quantum quench into the EAP phase. Time-of-flight absorption images of the three spin components of the BEC at various hold times $t$ after the quench for $q_{f} / h = 1.0 Hz$ . Density-depleted lines in the $m_{z} = 0$ component represent the position of domain walls, which are filled by the $m_{z} = \pm 1$ components.
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Figure 3
Detection of superflow near the defect end points by using Bragg scattering [11]. (a), (b) Absorption images of the $m_{z} = 0$ component at $t = 600 ms$ after quench for $q_{f} / h = 2.6 Hz$ and (c), (d) the corresponding images of the Bragg signal $S_{B}$ [21], where the color indicates the direction of the superflow along the Bragg scattering axis ( $x^{'}$ ). The filled circle (cross) mark denotes the counterclockwise (clockwise) circulation directions of the HQVs at the wall end points. The dashed lines indicate the boundary of the whole condensate. (e), (f) Schematic description of the composite defect configurations corresponding to (a) and (b), respectively. The domain wall region is denoted by a grey area with a white center line and the superflow direction is indicated by a red arrow.
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Figure 4
Temporal evolution of wall-vortex composite defects in the quenched BEC for $q_{f} / h = 10.6 Hz$ . (a) Absorption images of the $m_{z} = 0$ component taken at various hold times $t$ after the quench. A complex network of domain walls is nucleated and the walls dynamically split into many composite defects. (b) Free defect number $N_{d}$ as a function of $t$ . $N_{rd}$ denotes the number of round defects, whose shape aspect ratio is $< 1.2$ , and $N_{nrd} = N_{d} - N_{rd}$ . Each data point was obtained from five measurements of the same experiment and its error bar denotes their standard deviation. (c), (d) Schematic description of free composite defects with different HQV configurations. The superfluid phase winding around the free defect is (c) $2 π$ or (d) 0. (e) In situ images of the axial magnetization $M_{z}$ in the quenched BEC at $t = 900 ms$ (left) and 2 s (right), showing long-lived magnetized defects.
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