Quantum coherence and its dephasing in femtosecond semiconductor spectroscopy

The electrons in crystals are distributed in energy bands rather than in sharp levels as in atoms or molecules. In semiconductors optical transitions across the band gap generate electrons in the conduction band and holes in the valence bands. Because of the rapid scattering of the excited carriers in the bands by carrier-phonon and carrier-carrier scattering, the interband polarization decays within ten to a few hundred femtoseconds. The study of coherent optical phenomena in semiconductors for the intrinsic band-to-band transitions needs femtosecond spectroscopy. In such studies the pulse width is often short or comparable to the periods of characteristic oscillations. Under these conditions the dephasing can no longer be described by semiclassical Boltzmann kinetics with its instantaneous collisions. Instead one has to incorporate that the collisions need some time which is comparable with the time scale of the optical experiments. Therefore, quantum kinetics introduces memory integrals instead of the energy-conserving semiclassical scattering rates. These memory integrals occur because the optically excited electrons behave in spite of the rapid scattering on these short time intervals still as partially coherent quantum mechanical waves. Using a generalization of the atomic Bloch equations in the form of the so called semiconductor Bloch equations together with the quantum kinetic scattering rates one can analyse femtosecond differential transmission (DTS) and four-wave mixing experiments (FWM) which are sensitive to details of the dephasing kinetics particularly if coherent control techniques are used.