Excitation-Induced Coherent Effects

The theoretical description of the coherent interactions in semiconductors is often successfully described by mean-field theories. Here the Coulomb interaction of a single charge carrier with the periodic potential of the solid and with all other carriers (including exchange interaction due to the Pauli principle) is treated in an averaged way. This is typically done in the random-phase approximation (RPA, also named time-dependent Hartree-Fock approximation) where the temporal evolution of polarizations and populations are implemented by the optical Bloch equations (for reviews see Chap.  4 and, e.g., [94H1, 01C1]). The RPA approach explicitly accounts for the correlation between electron and hole (i.e., excitonic effects) while higher-order correlations are averaged out. Problems arise in this description since the mean-field approach has been derived for dilute ensembles of individual two-level systems. But the (optical) excitations in semiconductors, which are already affected by the Coulomb interaction (new quasi-particles are formed like excitons) are not isolated individuals. They are strongly coupled via the Coulomb interaction which leads to additional correlation effects. In particular at low densities coherent spectral oscillation show up at negative delays in two-beam experiments. Unexpected diffracted signal intensities are detected at negative pulse delay and the diffracted signal itself has a delayed real time dynamics. We will describe here some key experiments and summarize the required modifications of the mean-field approach. There are many resulting effects of interactions between the excited two-level systems which modify their coherent temporal evolution and in turn affect the dynamics of the FWM experiment. Most important are excitation-induced dephasing, excitation-induced shifts of resonances or the two-photon transition to the biexciton. Also excitons and trions can be coherently coupled to form a correlated state similar to the biexciton. Such coherent interactions of different resonances can be analyzed in detail by the experimental technique 2D Fourier transform spectroscopy.