Correlated two-Leviton states in the fractional quantum Hall regime

We consider a two-dimensional electron system in the Laughlin sequence of the fractional quantum Hall regime to investigate the effect of strong correlations on the mutual interaction between two Levitons, single-electron excitations generated by trains of quantized Lorentzian pulses. We focus on two-Leviton states injected in a single period with a time separation $\Delta t$. In the presence of a quantum point contact operating in the weak-backscattering regime, we compute the backscattered charge by means of the Keldysh technique. In the limit of an infinite period and zero temperature, we show that the backscattered charge for a two-Leviton state is not equal to twice the backscattered charge for a single Leviton. We present an interpretation for this result in terms of the wave-packet formalism for Levitons, thus proposing that an effective interaction between the two Levitons is induced by the strongly-correlated background. Finally, we perform numerical calculations in the periodic case by using the Floquet formalism for photo-assisted transport. By varying the system parameters such as pulse width, filling factor and temperature we show that the value of the backscattered charge for two-Leviton states is strongly dependent on the pulse separation, thus opening scenarios where the effective interaction between Levitons can be controllably tuned.