Interacting Fibonacci anyons in a Rydberg gas

TL;DR

This paper demonstrates how a Rydberg atom lattice can simulate interacting Fibonacci anyons, enabling the study of non-Abelian anyonic physics and topological quantum liquids in a controllable experimental setup.

Contribution

It introduces a method to realize and analyze Fibonacci anyons using Rydberg atoms with dipole blockade, linking atomic physics to topological quantum computation.

Findings

Mapping of Rydberg atom Hilbert space to Fibonacci anyon fusion space

Proposal for tuning laser parameters to create a topological liquid of non-Abelian anyons

Discussion of experimental measurement techniques for anyonic observables

Abstract

A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks of non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $\nu=12/5$. Here we show that 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 and a proper tuning of the laser parameters renders the system into an interacting topological liquid of non-Abelian anyons. We discuss the low-energy properties of this system and show how to experimentally measure anyonic observables.