Correlations and beam splitters for quantum Hall anyons

TL;DR

This paper investigates two localized anyons in the lowest Landau level, revealing how their correlations interpolate between fermionic and bosonic behaviors, and proposes using a saddle potential as a beam splitter to measure these signatures.

Contribution

It introduces a method to analyze anyonic correlations using a saddle potential as a beam splitter, bridging quantum optics and quantum Hall physics.

Findings

Anyonic signatures interpolate between fermionic and bosonic tendencies.

Saddle potential acts as a beam splitter for anyons.

Proposed measurement scheme for anyonic correlations.

Abstract

We study the system of two localized anyons in the lowest Landau level and show how anyonic signatures extrapolating between anti-bunching tendencies of fermions and bunching tendencies of bosons become manifest in the two-particle correlations. Towards probing these correlations, we discuss the influence of a saddle potential on these anyons; we exploit analogies from quantum optics to analyze the time-evolution of such a system. We show that the saddle potential can act as a beam splitter akin to those in bosonic and fermionic systems and can provide a means of measuring the derived anyonic signatures.