Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics

TL;DR

This paper proposes a time-of-flight experiment to detect anyonic statistics in ultracold atom quantum Hall states by measuring the mean square radius of expanding clouds, validated through Monte Carlo simulations.

Contribution

It introduces a novel, experimentally feasible method to observe anyonic statistics in fractional quantum Hall states of ultracold atoms.

Findings

Method successfully distinguishes anyonic phases in simulations.

Validated for $ u=1/2$ and $1/3$ fractional quantum Hall states.

Discusses extensions to light-based quantum Hall systems and non-Abelian anyons.

Abstract

We propose a standard time-of-flight experiment as a method for observing the anyonic statistics of quasiholes in a fractional quantum Hall state of ultracold atoms. The quasihole states can be stably prepared by pinning the quasiholes with localized potentials and a measurement of the mean square radius of the freely expanding cloud, which is related to the average total angular momentum of the initial state, offers direct signatures of the statistical phase. Our proposed method is validated by Monte Carlo calculations for $\nu=1/2$ and $1/3$ fractional quantum Hall liquids containing a realistic number of particles. Extensions to quantum Hall liquids of light and to non-Abelian anyons are briefly discussed.