Point-contact tunneling in the fractional quantum Hall effect: An exact determination of the statistical fluctuations

In the weak backscattering limit, point contact tunneling between quantum Hall edges is well described by a Poissonian process where Laughlin quasiparticles tunnel independently, leading to the unambiguous measurement of their fractional charges. In the strong backscattering limit, the tunneling is well described by a Poissonian process again, but this time involving real electrons. In between, interactions create essential correlations, which we untangle exactly here. Our main result is an exact closed form expression for the probability distribution (P) over cap of the charge N(t) that tunnels in the time interval t. Formally, (P) over cap corresponds to a sum of independent Poisson processes carrying charge ve, 2ve, etc., or, after resummation, processes carrying charge e,n 2e, etc. The distribution illustrates how the crossover between Laughlin quasiparticles and electrons takes place. It also gives information on higher moments for this strongly interacting system, which are of current experimental interest. Upon uncovering functional relations between perturbative integrals, we find, as a second result of current interest, agreement between the thermodynamic Bethe ansatz and the rigorous Keldysh approach.