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

TL;DR

This paper proposes a method using cold atoms in an optical lattice to experimentally detect the non-Abelian statistics of anyonic excitations in the Kitaev honeycomb model through vortex braiding and ancilla-assisted measurement.

Contribution

It introduces a scheme to generate and manipulate non-Abelian anyons in cold atom systems, enabling experimental probing of their unique braiding statistics.

Findings

Demonstrates how vortex braiding affects ground state degeneracy

Shows control of anyonic states via atomic rotations

Proposes ancilla atom measurement for state discrimination

Abstract

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