Abstract
The transient third-order polarization at the band gap of undoped and p-doped GaAs is investigated by spectrally and temporally resolved four-wave mixing. Excitonic and free-carrier contributions simultaneously excited within the bandwidth of the 100-fs pulses are clearly distinguished by their different spectral envelopes. The excitonic part dominates at carrier densities below ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and shows a time evolution governed by exciton--free-carrier scattering and by many-body effects. At higher density, the free-carrier polarization has a strength similar to the exciton contribution and exhibits a spectrum resonant to the femtosecond pulses with a photon-echo-like temporal behavior. The data are analyzed by a numerical solution of the semiconductor Bloch equations including an ensemble Monte Carlo simulation of the scattering dynamics of the carriers. The theoretical model is in good agreement with the experimental results.
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