  We theoretically investigate the effect of broken inversion symmetry on the
generation and control of ultrafast currents in a transparent dielectric (SiO2)
by strong femto-second optical laser pulses. Ab-initio simulations based on
time-dependent density functional theory predict ultrafast DC currents that can
be viewed as a non-linear photogalvanic effect. Most surprisingly, the
direction of the current undergoes a sudden reversal above a critical threshold
value of laser intensity I_c ~ 3.8*10^13 W/cm2. We trace this switching to the
transition from non-linear polarization currents to the tunneling excitation
regime. We demonstrate control of the ultrafast currents by the time delay
between two laser pulses. We find the ultrafast current control by the
non-linear photogalvanic effect to be remarkably robust and insensitive to
laser-pulse shape and carrier-envelope phase.
