The 1984 electron theory of the optical properties of laser-excited semiconductors revisited. What happened since?

The 1984 review in this journal wrapped up the quasi-equilibrium many-body theory which was used quite successfully to describe the optical properties of bulk semiconductors at that time. The starting point was to express the optical dielectric function in terms of the photon self-energy, also called the polarization bubble, which could be calculated e.g. by thermal equilibrium electron Green functions. By these means one was able to calculate optical spectra of a probe beam as a function of the density of the electronic excitations generated by a preceeding pump beam. The underlying assumption was that the electronic excitations had enough time to relax into a thermal equilibrium, before they would eventually recombine. The ever shorter getting laser pulses and the simultaneous emergence of the coherent time-resolved nonlinear spectroscopy of semiconductors necessitated the use of a true nonequilibrium many-body theory which could either be formulated in terms of time-dependent equations for reduced density matrices or for Keldysh Green functions. With both methods one calculates at the end the reduced single-particle density matrix. The off-diagonal elements in the band index representation yield the optical polarization as a function of time and as a function of the delay time between two applied pulses. The formalism allows to calculate the induced polarization selectively either in the direction of a refracted beam for four-wave mixing (FWM) or in the direction of the test beam for differential transmission spectroscopy (DTS). The kinetics of the excited electron–hole pairs determines the results of the time-resolved two-beam spectroscopy. If the time resolution of corresponding experiments is shorter than characteristic periods of the scattered bosons, e.g., plasmons or phonons, the semiclassical Boltzmann kinetics fails for the description of the relaxation and dephasing of femtosecond-pulse excited electron–hole pairs. In this ultra-short-time regime which is dominated by quantum coherence, quantum kinetics with its memory effects yields an excellent description of corresponding FWM and DTS experiments. The essential features of carrier–phonon scattering and the carrier–carrier scattering via a time-dependently screened Coulomb potential are discussed. Particularly, the time-dependent build-up of screening by the optically excited carriers is itself a highly interesting quantum kinetic problem. As an extension it is shown that quantum kinetics also yields a consistent description of the kinetics of a Bose–Einstein condensation of excitons, because the changes of the single-particle spectrum at the transition from the normal to the condensed phase are included in the scattering kinetics. The review is concluded with the discussion of the kinetics of the recently observed laser action of microcavity exciton polaritons, which is based on a bosonic condensation of the polaritons in their lowest state.