Measuring fractional charge and statistics in fractional quantum Hall fluids through noise experiments

TL;DR

This paper proposes a three-terminal T-junction experiment to directly measure fractional charge and statistics of quasiparticles in fractional quantum Hall states through noise analysis, providing a new way to confirm their topological properties.

Contribution

It introduces a novel experimental setup and theoretical analysis for independently detecting fractional charge and statistics in FQH states via noise measurements.

Findings

Noise signatures reveal fractional charge and statistics.

Vortices in Laughlin states show bunching behavior.

Higher Jain states exhibit anti-bunching effects.

Abstract

A central long standing prediction of the theory of fractional quantum Hall (FQH) states that it is a topological fluid whose elementary excitations are vortices with fractional charge and fractional statistics. Yet, the unambiguous experimental detection of this fundamental property, that the vortices have fractional statistics, has remained an open challenge. Here we propose a three-terminal ``T-junction'' as an experimental setup for the direct and independent measurement of the fractional charge and statistics of fractional quantum Hall quasiparticles via cross current noise measurements. We present a non-equilibrium calculation of the quantum noise in the T-junction setup for FQH Jain states. We show that the cross current correlation (noise) can be written in a simple form, a sum of two terms, which reflects the braiding properties of the quasiparticles: the statistics dependence captured in a factor of $\cos\theta$ in one of two contributions. Through analyzing these two contributions for different parameter ranges that are experimentally relevant, we demonstrate that the noise at finite temperature reveals signatures of generalized exclusion principles, fractional exchange statistics and fractional charge. We also predict that the vortices of Laughlin states exhibit a ``bunching'' effect, while higher states in the Jain sequences exhibit an ``anti-bunching'' effect.