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Proc Natl Acad Sci U S A. 2007 Nov 20;104(47):18415-20. Epub 2007 Nov 13.

Anyonic braiding in optical lattices.

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  • 1Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, MD 20742, USA.

Erratum in

  • Proc Natl Acad Sci U S A. 2008 Apr 15;105(15):5945.


Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates.

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