Braiding and Fusion of Non-Abelian Vortex Anyons

Abstract

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]

Controlled creation and decay of singly-quantized vortices in a polar magnetic phase

“…Our experimental and theoretical analysis of the decay process in three dimensions suggests the emergence of HQVs. Similar techniques may be used to generate pairs of filled-core vortices in the magnetic phases of spin-2 condensates, where vortex collisions are predicted to possess a non-Abelian character 13,14,16,19 and for which the topological interfaces may lead to exotic phenomena such as vortices with triangular cores 14 .…”

“…ortices in superfluids with internal degrees of freedom, such as those existing within spinor Bose-Einstein condensates (BECs) 1,2 and superfluid liquid He-3 3,4 , exhibit a much richer phenomenology than do simple line vortices in scalar superfluids. Notable examples abound, including vortices with fractional charges [5][6][7][8][9][10][11] , vortices with like charges that sum to zero 12 , vortices with charges that do not commute [13][14][15][16][17][18][19] , and nonsingular textures with angular momentum [20][21][22][23][24][25] . These features, among others, hint at their highly counter-intuitive dynamics.…”

Geometric phases of a vortex in a superfluid

“…These results also generalise to Fermi superfluids and spinor Bose-Einstein condensates. In the former case [18,42] Cooper-like pairing results in the effective vortex charge being κ/2 in contrast to the quantum of circulation κ for the bosonic scalar superfluid, while in the latter case the fractional vortices are anyons that in general acquire a non-abelian exchange Berry phase upon braiding [13,43].…”

Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron $^3P_2$ superfluids

“…Due to the nontrivial first homotopy group π 1 Z × h T * (× h is a product defined in Ref. [12] and T * is the universal covering group of T ), 1/3 quantized non-Abelian vortices are allowed [13][14][15]. Two vortices belonging to non-commutative elements of π 1 do not reconnect in collisions, instead creating a rung vortex connecting them [14].…”