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arXiv:cond-mat/0210397 · Physical Review A

Skyrmion excitation in a two-dimensional spinor Bose-Einstein condensate

Hui Zhai, Wei-Qiang Chen, Zhan Wei Xu, Lee Chang

Published Oct 3, 2003• 32 citations
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Abstract

We study the properties of coreless vortices (skyrmions) in spinor Bose-Einstein condensates. We find that this excitation is always energetically unstable, it always decays to an uniform spin texture. We obtain the skyrmion energy as a function of its size and position, a key quantity in understanding the decay process. We also point out that the decay rate of a skyrmion with high winding number will be slower. The interaction between skyrmions and other excitation modes are also discussed.

DOI
10.1103/physreva.68.043602

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We study the properties of coreless vortices (skyrmions) in spinor Bose-Einstein condensates. We find that this excitation is always energetically unstable, it always decays to an uniform spin texture. We obtain the skyrmion energy as a function of its size and position, a key quantity in understanding the decay process. We also point out that the decay rate of a skyrmion with high winding number will be slower. The interaction between skyrmions and other excitation modes are also discussed.
We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.
Dynamics of skyrmionic spin texture in the spin-1 Bose-Einstein condensate is examined by analytical and numerical means. We show the skyrmion (coreless vortex) to be inherently unstable in the sense that the state initially prepared purely within the antiferromagnetic (ferromagnetic) order parameter manifold inevitably evolves into a mixture of both. The vorticity-dependent drift in the presence of the trapping potential also contributes to the disintegration of the initial spin texture manifold. We argue that the notion of a skyrmion as a topologically protected entity becomes ill defined during the dynamical evolution process.
The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum tunneling, Rabi oscillations, the coupling between spin gradients and superfluid flow, squeezed spin states, vortices and other topological excitations. Theoretically, there have been already some studies of the ground-state properties of these systems and their line-like vortex excitations. In analogy with nuclear physics or the quantum Hall effect, we explore here the possibility of observing point-like topological excitations or skyrmions. These are nontrivial spin textures that in principle can exist in a spinor Bose-Einstein condensate. In particular, we investigate the stability of skyrmions in a fictitious spin-1/2 condensate of Rb87 atoms. We find that skyrmions can exist in this case only as a metastable state, but with a lifetime of the order of, or even longer than, the typical lifetime of the condensate itself. In addition to determining the size and the lifetime of the skyrmion, we also present its spin texture and finally briefly consider its dynamical properties.
We investigate an experimental method for imprinting Skyrmion spin textures in a spinor Bose–Einstein condensate by rapidly moving the zero-field center of a three-dimensional (3D) quadrupole magnetic field through the condensate. Various excitations such as 2D Skyrmions and coreless vortices were created in spin-1 sodium condensates, initially prepared in a uniform polar or ferromagnetic phase. The spin textures were characterized with the spatial distribution of the spin tilt angle, which is found to be in good quantitative agreement with the local description of single spins under the field rotation. We demonstrate the creation of a highly charged Skyrmion in a trapped condensate by applying the imprinting process multiple times.