Correlated two-Leviton states in the fractional quantum Hall regime

TL;DR

This paper investigates how strong correlations in the fractional quantum Hall regime influence the interaction between two Levitons, revealing that their backscattered charge depends on system parameters and can be tuned via pulse separation.

Contribution

It demonstrates that strong correlations induce an effective interaction between Levitons, affecting backscattered charge and enabling controllable tuning through system parameters.

Findings

Backscattered charge for two Levitons differs from twice that of a single Leviton.

Effective interaction between Levitons is induced by the strongly-correlated background.

Backscattered charge depends on pulse separation, temperature, and filling factor.

Abstract

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.