We demonstrate that certain vortices in spinor Bose-Einstein condensates are non-Abelian anyons and may be useful for topological quantum computation. We perform numerical experiments of controllable braiding and fusion of such vortices, implementing the actions required for manipulating topological qubits. Our results suggest that a new platform for topological quantum information processing could potentially be developed by harnessing non-Abelian vortex anyons in spinor Bose-Einstein condensates. arXiv:1805.10009v2 [cond-mat.quant-gas]

We have studied computationally the collision dynamics of spin-2 Bose-Einstein condensates initially confined in a triple-well trap. Depending on the intra-and inter-component relative phases of the initial state spinor wave function, the collision of the three condensate segments produces one of many possible vortex-antivortex lattices after which the system transitions to quantum turbulence. We find that the emerging vortex lattice structures can be described in terms of multi-wave interference. We show that the three-segment collisions can be used to systematically produce staggered vortex-antivortex honeycomb lattices of fractional-charge vortices, whose collision dynamics are known to be non-Abelian. Such condensate collider experiments could potentially be used as a controllable pathway to generating non-Abelian superfluid turbulence with networks of vortex rungs.arXiv:1412.6186v1 [cond-mat.quant-gas]

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We study computationally the collision dynamics of vortices in a two-dimensional spin-2 BoseEinstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation-an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.

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