<title>Spatio-temporal dynamics of optical nonlinearities in semiconductor quantum wells</title>

Abstract

We present results of the optically excited dynamics in semiconductor quantum wells on short length and time scales. Nonlinear optical experiments are performed with high temporal and high spatial resolution. To interpret the experimental findings calculations are performed on different approximation levels. Two different time regimes are investigated: in the incoherent time regime we study the dynamics of heating, cooling, and the formation of excitons by measuring the temporal behavior of the lateral expansion rate of locally created electron-hole pairs or excitons. A monomolecular exciton formation process is found. The experimental results in this regime are well reproduced by the Boltzmann equation for incoherent exciton densities with phenomenological scattering rates. In addition we have performed a microscopic density matrix analysis for the heating scenario where we have modeled explicitly the initial transformation of coherent excitations into incoherent exciton densities. It is found that the heating due to scattering with acoustic phonons gives reasonable agreement with the observed rates. In the coherent time regime a spatio-temporal beating is observed. This unexpected non-monotonic modulation of the spatial width arises from excitonic wave-packets which modulate the detected lateral profile of the optical nonlinearity in a characteristic way. It is explained by the superposition of various signal components which are detected simultaneously due to the collinearity of our experiment. This effect is illustrated by calculations using a simplified model on the Hartree-Fock level.