  The fully nonlinear response of a many-level tunneling system to a strong
alternating field of high frequency $\omega$ is studied in terms of the
Schwinger-Keldysh nonequilibrium Green functions. The nonlinear time dependent
tunneling current $I(t)$ is calculated exactly and its resonance structure is
elucidated. In particular, it is shown that under certain reasonable conditions
on the physical parameters, the Fourier component $I_{n}$ is sharply peaked at
$n=\frac {\Delta E} {\hbar \omega}$, where $\Delta E$ is the spacing between
two levels. This frequency multiplication results from the highly nonlinear
process of $n$ photon absorption (or emission) by the tunneling system. It is
also conjectured that this effect (which so far is studied mainly in the
context of nonlinear optics) might be experimentally feasible.
