Correlated two-leviton states in the fractional quantum Hall regime
Résumé
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 . 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 photoassisted 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.