  We study the tunneling mechanism of nonlinear optical processes in solids
induced by strong coherent laser fields. The theory is based on an extension of
the Landau-Zener model with nonadiabatic geometric effects. In addition to the
rectification effect known previously, we find two effects, namely perfect
tunneling and counterdiabaticity at fast sweep speed. We apply this theory to
the twisted Schwinger effect, i.e., nonadiabatic pair production of particles
by rotating electric fields, and find a nonperturbative generation mechanism of
the opto-valley polarization and photo-current in Dirac and Weyl fermions.
