Anyonic Braiding in Optical Lattices*

Topological quantum computation proposes to use braiding of collective excitations implanted in topologically protected coherent quantum states of many particles, as opposed to a single particle, to aid in or even perform quantum computation. Here we explicitly work out a realistic experimental scheme to create, braid and detect topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. A key feature of topological excitations is their braiding statistics, how they behave when one excitation is taken around another. An observation of the non-trivial braiding statistics described in this Report would directly establish the existence of anyons, quantum particles which are neither fermions nor bosons. Demonstrating anyonic braiding statistics is tantamount to observing a new form of matter, topological matter. Once created, excitations in quantum topological matter, as opposed to delicate single particle quantum states, can provide a robust way to encode and manipulate quantum information.