Anyonic Braiding in Optical Lattices

Abstract

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo non-trivial 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 which 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.

22 pages, 5 figures, published version

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Cited by in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Anyonic interferometry and protected memories in atomic spin lattices
• Simulations of quantum double models
• Creation and Manipulation of Anyons in the Kitaev Model
• Minimum instances of topological matter in an optical plaquette
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Anyonic statistics with continuous variables
• Implementing topological quantum manipulation with superconducting circuits
• Finite-Temperature Néel Ordering of Fluctuations in a Plaquette Orbital Model
• Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices