Interacting Fibonacci anyons in a Rydberg gas

Abstract

The physics of interacting Fibonacci anyons can be studied with strongly interacting Rydberg atoms in a lattice, when due to the dipole blockade the simultaneous laser excitation of adjacent atoms is forbidden. The Hilbert space maps then directly on the fusion space of Fibonacci anyons. Interactions between anyons are generated and controlled by the intensity and frequency of the excitation laser. Fusion outcomes of neighboring anyons can be determined experimentally via the measurement of three-point correlations among three consecutive atoms. Our work shows that a Rydberg lattice gas constitutes a natural physical platform for the experimental exploration of topological quantum liquids of non-Abelian anyons.