Probing non-Abelian anyonic statistics with cold atoms in an optical lattice

Abstract

We propose a scheme to probe the non-Abelian statistics of the collective\nanyonic excitation in Kitaev's honeycomb model with cold atoms in an optical\nlattice. The generation of the anyonic excitation can be realized by simple\nrotating operation acting on an effective spin-1/2 system, which is encoded in\nthe atomic hyperfine energy levels. The non-Abelian nature of the anyonic\nexcitation is manifested by the braiding of four vortices, which leads to\ndifferent operations on the subspace of degenerate ground states, and thus\nresults in different final states. Here, by introducing an ancilla atom, the\neffective control over the lattice atoms can be realized and the final\ndifferent states can also be imprinted on the ancilla and further distinguished\nby measurement.\n