Controlled localization of anyons in a graphene quantum Hall interferometer

TL;DR

This study demonstrates gate-controlled manipulation of anyons in a graphene quantum Hall interferometer, enabling precise control over their populations and phases, which is crucial for topological quantum computing.

Contribution

It introduces a method to tune and observe both abelian and non-abelian anyons in a graphene FQH interferometer using a central gate-controlled dot/anti-dot.

Findings

Controlled phase slips observed for both abelian and non-abelian states.

Phase slips for abelian anyons match theoretical predictions.

Evidence of localized non-abelian anyons at half filling.

Abstract

Exchange statistics are a fundamental principle of quantum mechanics, dictating the symmetry of identical particle wavefunctions and thereby enabling emergent phenomena of many-body quantum states. The exchange-induced unitary transformation of both abelian and non-abelian anyonic wavefunctions can be probed using electronic fractional quantum Hall (FQH) interferometers, where quasiparticles propagating along the interfering FQH edge braid with those localized within the interferometer. Here, we add a gate-controlled dot/anti-dot in the center of a bilayer graphene FQH interferometer cavity to tune the number of enclosed anyons. We observe hundreds of controlled phase slips in the diagonal conductance across the interferometer for both abelian and non-abelian states, consistent with discrete changes in the localized quasiparticle population. For abelian anyons, the observed phase slips agree with the theoretically expected value. At half filling, our results suggest the interfering edge carries charge $|e^*/e| = 1/2$ abelian excitations, whereas charge $|e^*/e| = 1/4$ putative non-abelian anyons remain localized in the interferometer cavity. Controlling the population of localized $e/4$ anyons in an interferometer marks a significant milestone towards observing their non-local exchange statistics and building a fault tolerant topological qubit based on non-abelian anyon manipulation.