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We present a theoretical formulation of the coherent ultrafast nonlinearoptical response of a strongly correlated system and discuss an example wherethe Coulomb correlations dominate. We separate out the correlated contributionsto the third-order nonlinear polarization, and identify non-Markovian dephasingeffects coming from the non-instantaneous interactions and propagation in timeof the collective excitations of the many-body system. We discuss thesignatures, in the time and frequency dependence of the four-wave-mixing (FWM)spectrum, of the inter-Landau level magnetoplasmon (MP) excitations of thetwo-dimensional electron gas (2DEG) in a perpendicular magnetic field. Wepredict a resonant enhancement of the lowest Landau level (LL) FWM signal, astrong non-Markovian dephasing of the next LL magnetoexciton (X), a symmetricFWM temporal profile, and strong oscillations as function of time delay, ofquantum kinetic origin. We show that the correlation effects can be controlledexperimentally by tuning the central frequency of the optical excitationbetween the two lowest LLs.Comment: 21 pages, 10 figure

Ultrafast nonlinear optical response of strongly correlated systems: Dynamics in the quantum Hall effect regime