We discuss a theory of the ultrafast non-linear optical response of excitons in the Quantum Hall system. Our theory focusses on the role of the low energy collective electronic excitations of the cold, strongly correlated, two-dimensional electron gas (2DEG) present in the ground state. It takes into account ground state electron correlations and Pauli exchange and interaction effects between the photoexcited excitons and the collective excitations. Our formulation addresses both the initial coherent regime, where the dynamics is determined by exciton and 2DEG polarizations, and the subsequent incoherent regime, dominated by population dynamics.We describe non-Markovian memory, dephasing, and correlation effects and a non-linear exciton hybridization due to the non-instantaneous interactions. We identify the signature of the coherent inter-Landau level magnetoplasmon (MP) in the temporal profile of the three-pulse time-integrated four-wave-mixing signal in the initial coherent regime.Comment: 36 pages, 6 figures, to appear in Chemical Physics; There are some differences between this version and the version published in Chemical Physic

Using three-pulse four-wave-mixing optical spectroscopy, we study the ultrafast dynamics of the quantum Hall system. We observe striking differences as compared to an undoped system, where the 2D electron gas is absent. In particular, we observe a large off-resonant signal with strong oscillations. Using a microscopic theory, we show that these are due to many-particle coherences created by interactions between photoexcited carriers and collective excitations of the 2D electron gas. We extract quantitative information about the dephasing and interference of these coherences.

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