Probing Non-Abelian Statistics with Quasiparticle Interferometry

We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, expressing outcomes in terms of the modular $S$-matrix. In particular, this result applies to fractional quantum Hall interferometry, and we give a detailed treatment of the Read-Rezayi states, providing explicit predictions for the recently observed $\nu =12/5$ plateau.

Figure 1

A two point-contact interferometer for measuring braiding statistics. The hatched region contains a FQH liquid. The front gates (F) are used to bring the opposite edge currents (indicated by arrows) close to each other to form two tunneling junctions. Applying voltage to the central gate creates an antidot in the middle and controls the number $n$ of quasiholes contained there. A side gate (S) can be used to change the shape and path length in the interferometer.