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 predictio s made for their results, we also comment on some of the assumptions made during the analysis and the outcome of their violation.