Switching noise as a probe of statistics in the fractional quantum Hall effect

We propose an experiment to probe the unconventional quantum statistics of quasi-particles in fractional quantum Hall states by measuring current noise. The geometry we consider is that of a Hall bar where two quantum point contacts introduce two interfering amplitudes for back-scattering. Thermal fluctuations of the number of quasi-particles enclosed between the two point contacts produce current noise, reflecting the statistics of the quasi-particles. We analyze abelian ν = 1 /q states and the non-abelian ν = 5 / 2 state. Probing the statistics is challenging in both the abelian and the non-abelian cases, necessitating experiments sensitive to the non-local statistical interaction between quasi-particles. Our findings indicate that charge fluctuations on the island result in a unique type of noise specific to the fractional quantum Hall effect. For the non-abelian case, we identify an even-odd effect in the noise spectrum originating from the non-abelian properties of quasi-particles, suggesting that the noise spectrum of back-scattered current may serve as a probe for the distinctive properties of abelian FQHE states and the non-abelian ν = 5 / 2 state.