# Correlations, Dynamics, and Interferometry of Anyons in the Lowest Landau Level

## TL;DR

This paper systematically studies the quantum statistics and dynamics of anyons in the lowest Landau level, exploring their behavior in traps, interferometers, and connections to quantum optics and black hole physics.

## Contribution

It develops a formalism for two-anyon systems in the LLL, including fractional angular momentum, coherent states, and interferometry, linking quantum Hall physics with quantum optics.

## Key findings

- Analysis of anyon exchange phase factors
- Description of non-equilibrium dynamics with saddle potentials
- Proposal of interferometry schemes for anyons

## Abstract

In this article, we present a systematic study of quantum statistics and dynamics of a pair of anyons in the lowerst Landau level (LLL), of direct relevance to quasiparticle excitations in the quantum Hall bulk. We develop the formalism for such a two-dimensional setting of two charged particles subject to a transverse field, including fractional angular momentum states and the related algebra stemming from the anyonic boundary condition, coherent state descriptions of localized anyons, and bunching features associated with such anyons. We analyze the dynamic motion of the anyons in a harmonic trap, emphasizing phase factors emerging from exchange statistics. We then describe non-equilibrium dynamics upon the application of a saddle potential, elaborating on its role as a squeezing operator acting on LLL coherent states, and its action as a beam splitter for anyons. Employing these potential landscapes as building blocks, we analyze anyon dynamics in a quantum Hall bulk interferometer. We discuss parallels between the presented LLL setting and other realms, extensively in the context of quantum optics, whose formalism we heavily borrow from, and briefly in that of black hole phenomena.