Fabry-Perot interferometer and non-Abelian quantum Hall states

This chapter reviews proposed transport experiments in the quantum Hall regime in a system designed to form the solid state analog of the Fabry-Perot interferometer. We review studies of that system for a series of quantum Hall states in the second Landau Level called the Read-Rezayi states. We focus here on two types of experiments. The first is a lowest order interference experiment of the fundamental quasi-holes of the system. The second is a Coulomb blockade based measurement which probes features in the flow of electrons through a closed part of the system. Both experiments were suggested as ways to answer a single question: do these quantum Hall states support excitation obeying non-Abelian statistics? After introducing the concept of non-Abelian statistics, reviewing these proposed experiments and the predictions made for their results, we also comment on some of the assumptions made during the analysis and the outcome of their violation.