Interferometry of non-Abelian Anyons

TL;DR

This paper develops a comprehensive quantum measurement framework for non-Abelian anyons using interferometry, analyzing charge measurement processes, collapse dynamics, and applying results to fractional quantum Hall systems with explicit experimental predictions.

Contribution

It introduces a general quantum measurement theory for non-Abelian anyons via interferometry and applies it to various models, providing detailed analysis and experimental predictions.

Findings

Superpositions of anyonic charges collapse based on monodromy distinguishability.

Estimated probe numbers needed for reliable charge measurement.

Explicit predictions for interferometry experiments in fractional quantum Hall states.

Abstract

We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they are distinguishable via monodromy with the probe anyons, which also determines the rate of collapse. We give estimates on the number of probes needed to obtain a desired confidence level for the measurement outcome distinguishing between charges, and explicitly work out a number of examples for some significant anyon models. We apply the same techniques to describe interferometry measurements in a double point-contact interferometer realized in fractional quantum Hall systems. To lowest order in tunneling, these results essentially match those from the Mach-Zehnder interferometer, but we also provide the corrections due to processes involving multiple tunnelings. Finally, we give explicit predictions describing state measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-Read state at $\nu=5/2$ and Read-Rezayi state at $\nu = 12/5$.