  A quantum coherent capacitor subject to large amplitude pulse cycles can be
made to emit or reabsorb an electron in each half cycle. Quantized currents
with pulse cycles in the GHz range have been demonstrated experimentally. We
develop a non-linear dynamical scattering theory for arbitrary pulses to
describe the properties of this very fast single electron source. Using our
theory we analyze the accuracy of the current quantization and investigate the
noise of such a source. Our results are important for future scientific and
possible metrological applications of this source.
