Early-stage relaxation of hot electrons by LO phonon emission

Ultrafast spectroscopy gives insight into the relaxation and dephasing of e lectrons during the first femtoseconds after an optical excitation. A theor etical description of this early-time regime requires a proper treatment of retardation effects for the different scattering processes. The scattering of electrons by optical phonons is investigated within the S-matrix formal ism. This perturbative scheme, equivalent to the non-equilibrium Green's fu nction technique of Kadanoff and Baym [Quantum Statistical Mechanics (Benja min, New York, 1962)], reproduces the phonon oscillations observed in four- wave mixing experiments on GaAs. The differential transmission spectrum, ho wever, shows a sharper phonon replica than in experiments where additional dephasing mechanisms such as electron correlation effects may further broad en the replica.