Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets

TL;DR

This paper demonstrates how spectroscopic experiments on small quantum Hall droplets can reveal Haldane fractional exclusion statistics through characteristic signatures in the excitation spectrum, supported by numerical simulations.

Contribution

It introduces a method to detect fractional exclusion statistics in quantum Hall droplets via spectroscopy, linking transition rules to quasihole states.

Findings

Spectroscopic signatures of fractional exclusion statistics identified.

A 'many-body selection rule' relates transitions to quasihole states.

Numerical simulations confirm theoretical predictions.

Abstract

We show how spectroscopic experiments on a small Laughlin droplet of rotating bosons can directly demonstrate Haldane fractional exclusion statistics of quasihole excitations. The characteristic signatures appear in the single-particle excitation spectrum. We show that the transitions are governed by a "many-body selection rule" which allows one to relate the number of allowed transitions to the number of quasihole states on a finite geometry. We illustrate the theory with numerically exact simulations of small numbers of particles.