Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect

TL;DR

This study uses Fabry-Perot interferometry to detect and confirm Abelian and non-Abelian anyonic braiding statistics in fractional quantum Hall systems, providing experimental evidence for non-Abelian anyons and their potential for quantum computing.

Contribution

It introduces a new interferometry-based method to detect anyonic braiding and confirms the existence of non-Abelian anyons in the $ u=5/2$ FQH state.

Findings

Confirmed Abelian anyonic phase of 2π/3 in $ u=7/3$ state

Observed phase slips consistent with Majorana non-Abelian anyons in $ u=5/2$ state

Provided experimental support for non-Abelian anyons as qubits

Abstract

In this paper, we report on the study of Abelian and non-Abelian statistics through Fabry-Perot interferometry of fractional quantum Hall (FQH) systems. Our detection of phase slips in quantum interference experiments demonstrates a powerful, new way of detecting braiding of anyons. We confirm the Abelian anyonic braiding statistics in the $\nu = 7/3$ FQH state through detection of the predicted statistical phase angle of $2\pi/3$, consistent with a change of the anyonic particle number by one. The $\nu = 5/2$ FQH state is theoretically believed to harbor non-Abelian anyons which are Majorana, meaning that each pair of quasiparticles contain a neutral fermion orbital which can be occupied or unoccupied and hence can act as a qubit. In this case our observed statistical phase slips agree with a theoretical model where the Majoranas are strongly coupled to each other, and strongly coupled to the edge modes of the interferometer. In particular, an observed phase slip of approximately $\pi$ is interpreted as a sudden flip of a qubit, or entry of a neutral fermion into the interferometer. Our results provide compelling support for the existence of non-Abelian anyons.