  A microscopic approach that is based on the multisubband semiconductor Bloch
equations formulated in the basis of a 14-band ${\mathbf k} \cdot {\mathbf p}$
model is employed to compute the temporal dynamics of photocurrents in GaAs
quantum wells following the excitation with femtosecond laser pulses. This
approach provides a transparent description of the interband, intersubband, and
intraband excitations, fully includes all resonant as well as off-resonant
excitations, and treats the light-matter interaction non-perturbatively. For
linearly polarized excitations the photocurrents contain contributions from
shift and rectification currents. We numerically compute and analyze these
currents generated by the excitation with femtosecond laser pulses for [110]-
and [111]-oriented GaAs quantum wells. It is shown that the often employed
perturbative $\chi^{(2)}$-approach breaks down for peak fields larger than
about 10~kV/cm and that non-perturbative effects lead to a reduction of the
peak values of the shift and rectification currents and to temporal
oscillations which originate from Rabi flopping. In particular, we find a
complex oscillatory photon energy dependence of the magnitudes of the shift and
rectification currents. Our simulations demonstrate that this dependence is the
result of mixing between the heavy- and light-hole valence bands. This is a
surprising finding since the bandmixing has an even larger influence on the
strength of the photocurrents than the absorption coefficient. For
[110]-oriented GaAs quantum wells the calculated photon energy dependence is
compared to experimental results and a good agreement is obtained which
validates our theoretical approach.
