Interaction of ultrashort light pulses with semiconductors: Effective Bloch equations with relaxation and memory effects

Abstract

Within the framework of the Keldysh formalism, a simple prescription for the derivation of quantum kinetic equations is given, which makes use of a real-time, multiband generalization of the Kadanoff-Baym ansatz. Such equations are given explicitly for the case of a two-band semiconductor interacting with classic optical pulses of very short duration, while the carriers can also interact with phonons and/or with one another via the screened or unscreened Coulomb potential. They take on the form of optical Bloch equations for interband polarization and intraband carrier distributions, with relaxation terms containing memory effects. In the initial coherent regime the influence of scattering events involving nondiagonal components of the two-band density matrix is shown to be of the same order as that of the more traditional diagonal scattering. Memory effects in collision integrals, which account for the time-energy uncertainty principle in scattering events, also change drastically the energy dependence of the scattering rates in this regime. Therefore, these two effects must be taken into account to achieve a correct description of femtosecond thermalization of optically excited semiconductor plasmas.