  We derived a general and exact expression of current for quantum parametric
charge pumps in the non-adiabatic regime at finite pumping frequency and finite
driving amplitude. The non-perturbative theory predicts a remarkable plateau
structure in the pumped current due to multi-photon assisted processes in a
double-barrier quantum well pump involving only a {\it single} pumping
potential. It also predicts a current reversal as the resonant level of the
pump crosses the Fermi energy of the leads.
