Non-Abelian Anyon Collider

TL;DR

This paper proposes a theoretical framework for a collider that can directly observe the braiding statistics of Abelian and non-Abelian anyons, revealing their unique quantum properties through negative cross correlations.

Contribution

It introduces a non-perturbative, conformal field theory-based model predicting how a collider can distinguish different anyon types via braiding-induced correlations.

Findings

Negative cross correlation depends on anyon type.

The collider can differentiate non-Abelian from Abelian anyons.

Braiding, not direct collision, dominates the process.

Abstract

A collider, where particles are injected to a beam splitter from opposite sides, has been used for identifying quantum statistics of identical particles. The collision leads to bunching of the particles for bosons and antibunching for fermions. In recent experiments, a collider was applied to a fractional quantum Hall regime hosting Abelian anyons. The observed negative cross correlation of electrical currents cannot be understood with fermionic antibunching. Here we predict, based on a conformal field theory and non-perturbative treatment of non-equilibrium anyon injection, that the collider provides a tool for direct observation of the braiding statistics of various Abelian and non-Abelian anyons. Its dominant process is not direct collision between injected anyons, contrary to common expectation, but braiding between injected anyons and an anyon excited at the collider. The dependence of the resulting negative cross correlation on the injection currents distinguishes non-Abelian SU(2)$_k$ anyons, Ising anyons, and Abelian Laughlin anyons.