A ug 2 00 5 Theory of ultrafast exciton dynamics in the Quantum Hall system

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 nonlinear 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.