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We study photo-assisted transport for the edge states of a two dimensionalelectron gas in the fractional quantum Hall regime, pinched by a single quantumpoint contact. We provide a general expression of the photo-assisted currentusing a Keldysh-Floquet approach, when the AC drive is applied either directlyto the edge states, or when it modulates the tunneling amplitude at the quantumpoint contact. Strikingly, for a simple cosine modulation of the tunnelingamplitude, the phase shift of the second harmonic of the photoassisted currentis directly related to the scaling dimension of the quasiparticle operatorsdescribing the fractional excitations. As the scaling dimension is intimatelyrelated to the statistics, our proposal of a gate modulation of thebackscattered current provides a diagnosis of the statistics of Laughlinquasiparticles using a simple quantum point contact geometry.

Photo-assisted current in the fractional quantum Hall effect as a probe of the quasiparticle operator scaling dimension