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Modern Physics Letters B

HALF-SKYRMION IN SPINOR BOSE–EINSTEIN CONDENSATES

Yong-Kai Liu, Cong Zhang, Shi-Jie Yang

Published Sep 11, 2013• 2 citations
Publisher

Abstract

In this paper, we present exact solutions to the F = 1 spinor Bose–Einstein condensates with only spin-independent energy by adopting a method of separating the variables, which exhibit nontrivial topology. These solutions can form solitonic fractional vortex and solitonic half-skyrmion with a Q = 1/2 topological charge in the two-dimensional system. We further address a three-dimensional prototype solution.

DOI
10.1142/s0217984913501832

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In this paper, we present exact solutions to the F = 1 spinor Bose–Einstein condensates with only spin-independent energy by adopting a method of separating the variables, which exhibit nontrivial topology. These solutions can form solitonic fractional vortex and solitonic half-skyrmion with a Q = 1/2 topological charge in the two-dimensional system. We further address a three-dimensional prototype solution.
Abstract Topological Skyrmion defects with arbitrary topological charges are shown to appear in spinor F = 1 Bose–Einstein condensates, under the presence of external gauge or magnetic fields with cylindrical symmetry. We show that, depending on the magnetic field boundary conditions, the spin texture, at the planes perpendicular to the cylindrical axis, can be forced to show Skyrmions with topological charge zero, half-integer, or any desired arbitrary value between − 1 / 2 and 1/2. Our findings are obtained by numerically solving the corresponding fully coupled Gross–Pitaevskii equations without any symmetry assumptions and by analyzing the Skyrmion topological charge. We study, both, polar 23 Na and ferromagnetic 87 Rb condensates.
Quantum topological defects usually are excited on density. In this study, we extend the topological defect to another dimensionality: the spin. We indicate that the spin singularity, where the spin density |S| vanishes locally, occurs commonly in the two-dimensional spin-1 Bose-Einstein condensates. We assume a coreless half-quantum vortex solution in the spin-1 Bose-Einstein condensates according to the spin singularity. This half-quantum vortex can further induce a half-quantum spin defect, which is similar to the general half-quantum Skyrmion but its centre proposes singularity on the spin density. We use the variational method to obtain a possible stable solution under the combined interaction of the spin-orbit coupling and the external magnetic field. Our calculation shows that the isotropic spin-orbit coupling provides local energy minimum to stabilize the coreless half-quantum vortex and the corresponding singular half-quantum spin texture excitation. The combined restriction of the isotropic spin-orbit coupling and the perpendicular magnetic field is a key factor to obtain this kind of excitation. Our study also provides the stability phase diagram and the most possible size of the half-quantum vortex. Furthermore, our analysis shows that adjusting of the spin interaction hardly affects the stability of the half-quantum vortex.
The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.