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

We present a theoretical formulation of the coherent ultrafast nonlinear optical response of a strongly correlated system and discuss an example where the Coulomb correlations dominate. We separate out the correlated contributions to the third-order nonlinear polarization, and identify non-Markovian dephasing effects coming from the noninstantaneous interactions and propagation in time of the collective excitations of the many-body system. We discuss the signatures, in the time and frequency dependence of the four-wave-mixing (FWM) spectrum, of the inter-Landau level magnetoplasmon excitations of the two-dimensional electron gas in a perpendicular magnetic field. We predict a resonant enhancement of the lowest Landau-level (LL) FWM signal, a strong non-Markovian dephasing of the next LL magnetoexciton (X), a symmetric FWM temporal profile, and strong oscillations as a function of time delay, of quantum kinetic origin. We show that the correlation effects can be controlled experimentally by tuning the central frequency of the optical excitation between the two lowest LL's.