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arXiv:cond-mat/0306112 · Physical Review Letters

Energetically Stable Particlelike Skyrmions in a Trapped Bose-Einstein Condensate

Craig M. Savage, Janne Ruostekoski

Published Jul 1, 2003• 127 citations
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Abstract

We numerically show that a topologically nontrivial 3D Skyrmion can be energetically stable in a trapped two-component atomic Bose-Einstein condensate, for the parameters of 87Rb condensate experiments. The separate conservation of the two atomic species can stabilize the Skyrmion against shrinking to zero size, while drift of the Skyrmion due to the trap-induced density gradient can be prevented by rotation or by a laser potential.

DOI
10.1103/physrevlett.91.010403

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We numerically show that a topologically nontrivial 3D Skyrmion can be energetically stable in a trapped two-component atomic Bose-Einstein condensate, for the parameters of 87Rb condensate experiments. The separate conservation of the two atomic species can stabilize the Skyrmion against shrinking to zero size, while drift of the Skyrmion due to the trap-induced density gradient can be prevented by rotation or by a laser potential.
We show that the stability of three-dimensional skyrmions in trapped Bose-Einstein condensates depends critically on scattering lengths, atom numbers, trap rotation, and trap anisotropy. In particular, for the $^{87}\mathrm{Rb}\ensuremath{\mid}F=1,{m}_{f}=\ensuremath{-}1⟩$, $\ensuremath{\mid}F=2,{m}_{f}=1⟩$ hyperfine states stability is sensitive to the scattering lengths at the 2% level, where the differences between them are crucial. In a cigar shaped trap, we find stable skyrmions with slightly more than $2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ atoms, a number which scales with the inverse square root of the trap frequency. These can be stabilized against drift out of the trap by laser pinning.
Searching for novel topological objects is always an intriguing task for scientists in various fields. We study a three-dimensional (3D) topological structure called a 3D dimeron in trapped two-component Bose-Einstein condensates. The 3D dimeron differs from the conventional 3D skyrmion for the condensates hosting two interlocked vortex rings. We demonstrate that the vortex rings are connected by a singular string and the complexity constitutes a vortex molecule. The stability of the 3D dimeron is examined in two different models using the imaginary time evolution method. We find that the stable 3D dimeron can be naturally generated from a vortex-free Gaussian wave packet incorporating a synthetic non-Abelian gauge potential into the condensates.
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.