Quantum-kinetic study of femtosecond pump-and-probe spectra of bulk GaAs

We present quantum-kinetic calculations for pump-and-probe signals of bulk semiconductors based on the second Born approximation for electron--LO-phonon interaction. The relaxation process of laser-excited electron-hole pairs is studied along the whole frequency domain including the exciton resonance. This allows a description of carrier cooling due to LO phonons at arbitrary long time delays, from initial hole burning at the pump frequency until exciton bleaching after accumulation near the band extrema. At low temperature, a bottleneck effect is predicted for small pump intensities. At room temperature, signatures of upward scattering become visible. The numerical results for GaAs are in good qualitative agreement with recent measurements [A. Leitenstorfer et al., Phys. Rev. Lett. 76, 1545 (1996); C. F\"urst et al., Phys. Rev. Lett. 78, 3733 (1997)].