Non equilibrium optical properties in semiconductors from first--principles: a combined theoretical and experimental study of bulk silicon

The calculation of the equilibrium optical properties of bulk silicon by using the Bethe--Salpeter equation solved in the Kohn--Sham basis represents a cornerstone in the development of an ab--initio approach to the optical and electronic properties of materials. Nevertheless calculations of the {\em transient} optical spectrum using the same efficient and successful scheme are scarce. We report, here, a joint theoretical and experimental study of the transient reflectivity spectrum of bulk silicon. Femtosecond transient reflectivity is compared to a parameter--free calculation based on the non--equilibrium Bethe--Salpeter equation. By providing an accurate description of the experimental results we disclose the different phenomena that determine the transient optical response of a semiconductor. We give a parameter--free interpretation of concepts like bleaching, photo--induced absorption and stimulated emission, beyond the Fermi golden rule. We also introduce the concept of optical gap renormalization, as a generalization of the known mechanism of band gap renormalization. The present scheme successfully describes the case of bulk silicon, showing its universality and accuracy.