  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.
