Shot noise and the transmission of dilute Laughlin quasiparticles

We analyze theoretically a three-terminal geometry in a fractional quantum Hall system-studied in a recent experiment-which allows a dilute beam of Laughlin quasiparticles to be prepared and subsequently scattered by a point contact. Employing a chiral Luttinger liquid description of the nu(-1) = m integer edge states, we compute the current and noise of the quasiparticle beam after transmission through the point contact at finite temperature and bias voltage. A refermionization procedure at m = 2 allows the current and noise to be computed nonperturbatively for arbitrary transparency of the point contact. Surprisingly, we find that for weak backscattering the zero-temperature limit is subtle and singular even at fixed finite bias voltage. In particular, at T = 0 the incident charge-e/m quasiparticles are either reflected or else Andreev scattered [backscattering a charge-(-1+1/m)e quasihole and transmitting an electron]-Laughlin quasiparticles are not transmitted in this limit. A direct signature of these Andreev processes should be accessible in a particular cross-correlation noise measurement that we propose.