Anyonic Interferometry and Protected Memories in Atomic Spin Lattices

Systems with topological order can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and might be used for naturally error-free quantum computation. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.