Phase memory of the electronic polarization in transient nonlinear optical spectra of gallium arsenide at 2 eV

We present a detailed study of transient nonlinear optical spectra for the model semiconductor gallium arsenide in the canonical pump-test configuration with 2-eV incident light pulses of 70-fs duration. Starting from first principles we show that the shape of the omnipresent ``spike'' around zero delay time is closely connected with a transient phase memory of the driven interband transitions. The characteristic time dependence of all nonlinear pump-test spectra reflects the influence of the dominant momentum- and energy-relaxation processes on the single-particle distributions which are coupled by the pump and test pulses. The concepts discussed are of general validity for all optically excited direct-band-gap semiconductors.