Anyonic braiding in optical lattices

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...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2007-11, Vol.104 (47), p.18415-18420
Main Authors: Zhang, Chuanwei, Scarola, V.W, Tewari, Sumanta, Das Sarma, S
Format: Article
Language:English
Subjects:
Atoms
Braiding
Computational topology
Ground state
Lasers
Lattice theory
Mathematical lattices
Microwaves
Optics
Physical Sciences
Quantum computers
Quantum statistics
Quantum theory
Statistics
Topology
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Summary: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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0709075104