Early-stage relaxation of hot electrons by LO phonon emission

Ultrafast spectroscopy gives insight into the relaxation and dephasing of electrons during the first femtoseconds after an optical excitation. A theoretical 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 formalism. This perturbative scheme, equivalent to the non-equilibrium Green’s function technique of Kadanoff and Baym @Quantum Statistical Mechanics ~Benjamin, New York, 1962!#, reproduces the phonon oscillations observed in four-wave mixing experiments on GaAs. The differential transmission spectrum, however, shows a sharper phonon replica than in experiments where additional dephasing mechanisms such as electron correlation effects may further broaden the replica.