  The existence of electronic coherence can fundamentally change the scenario
of nonlinear interaction of light with quantum systems such as atoms and
molecules, which, however, has escaped from observation in the investigations
of strong field nonlinear optics in the past several decades. Here, we report
on the generation of electronic quantum coherence by strong field ionization of
nitrogen molecules in an intense 800 nm laser field. The coherence is
experimentally revealed by observing a resonant four-wave mixing process in
which the two pump pulses centered at 800 nm and 1580 nm wavelengths are
temporally separated from each other. The experimental observation is further
reproduced by calculating the nonlinear polarization response of N_2^+ ions
using a three-level quantum model. Our result suggests that strong field
ionization provides a unique approach to generating a fully coherent molecular
wavepacket encapsulating the rotational, vibrational, and electronic states.
