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arXiv:1302.5504 · Chinese Physics B

Skyrmion crystals in pseudo-spin-1/2 Bose—Einstein condensates

Cong Zhang, Wenan Guo, Shiping Feng, Shi-Jie Yang

Published Nov 1, 2013• 3 citations
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Abstract

Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates which are described by the coupled nonlinear Gross-Pitaevskii equations where the intraspecies and interspecies coupling constants are assumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. These stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, the crystal of skyrmion-antiskyrmion pairs is formed in the soliton limit.

DOI
10.1088/1674-1056/22/11/110308

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Exact two-dimensional solutions are constructed for the pseudo-spin-1/2 Bose-Einstein condensates which are described by the coupled nonlinear Gross-Pitaevskii equations where the intraspecies and interspecies coupling constants are assumed to be equal. The equations are decoupled by means of re-combinations of the nonlinear terms of the hyperfine states according to the spatial dimensions. These stationary solutions form various spin textures which are identified as skyrmion crystals. In a special case, the crystal of skyrmion-antiskyrmion pairs is formed in the soliton limit.
We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a ``skyrmion'' and a ``meron-pair,'' respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.
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.
We present several exact solutions to the coupled nonlinear Gross–Pitaevskii equations which describe the motion of the one-dimensional spin-2 Bose–Einstein condensates. The nonlinear density–density interactions are decoupled by making use of the properties of Jacobian elliptical functions. The distinct time factors in each hyperfine state implies a "Lamor" procession in these solutions. Furthermore, exact time-evolving solutions to the time-dependent Gross–Pitaevskii equations are constructed through the spin-rotational symmetry of the Hamiltonian. The spin-polarizations and density distributions in the spin-space are analyzed.