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arXiv:1111.6338 · Physical Review A

Crystallized half-skyrmions and inverted half-skyrmions in the condensation of spin-1 Bose gases with spin-orbit coupling

Shih-Wei Su, I-Kang Liu, Y.-C. Tsai, Weijian Liu, Shih-Chuan Gou

Published Aug 2, 2012• 73 citations
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Abstract

The nonequilibrium dynamics of a rapidly quenched spin-1 Bose gas with spin-orbit coupling is studied. By solving the stochastic projected Gross-Pitaevskii equation, we show that crystallization of half-skyrmions (merons), can occur in a spinor condensate of ${}^{87}$Rb. The stability of such a crystal structure is analyzed. Likewise, inverted half-skyrmions can be created in a spin-polarized spinor condensate of ${}^{23}$Na. Our studies provide a chance to explore the fundamental properties of skyrmionlike matter.

DOI
10.1103/physreva.86.023601

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The nonequilibrium dynamics of a rapidly quenched spin-1 Bose gas with spin-orbit coupling is studied. By solving the stochastic projected Gross-Pitaevskii equation, we show that crystallization of half-skyrmions (merons), can occur in a spinor condensate of 87{}^{87}87Rb. The stability of such a crystal structure is analyzed. Likewise, inverted half-skyrmions can be created in a spin-polarized spinor condensate of 23{}^{23}23Na. Our studies provide a chance to explore the fundamental properties of skyrmionlike matter.
We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on spin-1 Bose-Einstein condensates (BECs). By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respectively, which can be imaged by using the polarization-dependent phase-contrast method.
We investigate the spontaneous generation of crystallized topological defects via the combining effects of fast rotation and rapid thermal quench on spin-1 Bose-Einstein condensates (BECs). By solving the stochastic projected Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a hexagonal lattice of skyrmions and a square lattice of half-quantized vortices can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respectively, which can be imaged by using the polarization-dependent phase-contrast method.
We investigate the half-skyrmion excitations induced by spin-orbit coupling in the rotating and rapidly quenched spin-1 Bose-Einstein condensates. We give three expressions of the corresponding spin vectors to describe the half-skyrmion. Our results show that the half-skyrmion excitation depends on the combination of spin-orbit coupling and rotation, and it originates from a dipole structure of spin which is always embedded in three vortices constructed by each condensate component respectively. When both the strength of spin-orbit coupling and the rotation frequency are larger than some critical values, the half-skyrmions encircle the center with one or several circles to form a radial lattice, which occurs even in the strong ferromagnetic/antiferromagnetic condensates. We can use both the spin-orbit coupling and the rotation to adjust the radial lattice. The realization and the detection of the half-skyrmions are compatible with current experimental technology.
We present an overview of our recent theoretical studies on the quantum phenomena of the spin-1 Bose-Einstein condensates, including the phase diagram, soliton solutions and the formation of the topological spin textures. A brief exploration of the effects of spin-orbit coupling on the ground-state properties is given. We put forward proposals by using the transmission spectra of an optical cavity to probe the quantum ground states: the ferromagnetic and polar phases. Quasi-one-dimension solitons and ring dark solitons are studied. It is predicted that characteristics of the magnetic solitons in optical lattice can be tuned by controlling the long-range light-induced and static magnetic dipoledipole interactions; solutions of single-component magnetic and single-, two-, three-components polar solitons are found; ring dark solitons in spin-1 condensates are predicted to live longer lifetimes than that in their scalar counterparts. In the formation of spin textures, we have considered the theoretical model of a rapidly quenched and fast rotating trapped spin-1 Bose-Einstein condensate, whose dynamics can be studied by solving the stochastic projected Gross-Pitaevskii equations. Spontaneous generation of nontrivial topological defects, such as the hexagonal lattice skyrmions and square lattice of half-quantized vortices was predicted. In particular, crystallization of merons (half skyrmions) can be generated in the presence of spin-orbit coupling.
By exploring the spin-orbit-coupled rotating pseudo-spin-1/2 Bose-Einstein condensates with the stochastic projected Gross-Pitaevskii equations, we prove the existence of the circular-hyperbolic skyrmion, which possesses two extreme values of Sz{S}_{z}Sz​. The nonequal intraspecies interactions and interspecies interactions cause the two components to be wholly disproportionate when the system reaches the equilibrium state. The circular-hyperbolic skyrmion results from the vortex-dipole structure. For the miscible condensates, the increase of spin-orbit coupling enhances the creation of the circular-hyperbolic skyrmion, and makes them link one after another locally. In particular, the circular-hyperbolic skyrmion even can form a chain when the spin-orbit coupling is only in one direction. For the immiscible condensates, the hyperbolic skyrmion occurs at the center, while the circular-hyperbolic skyrmion occurs at the outskirts of the condensates. The increase of the spin-orbit coupling restricts the creation of the hyperbolic skyrmion and enhances the creation of the circular-hyperbolic skyrmion.
Motivated by the recent experiment of Choi et al. [Phys. Rev. Lett. 108, 035301 (2012)], we simulate, within the Gross-Pitaevskii equation, the process of creating a skyrmion in an antiferromagnetic spin-1 Bose-Einstein condensate via the magnetic-field rotation method. Complex skymion structures are found and the factors influencing them are discussed. The dynamics of the system is mainly quasiperiodic. When the center of the skyrmion is displaced from the trap center, half vortices can be found at an intermediate stage of the dynamical evolution, but they do not necessarily lead to the destruction of the skyrmions.