  We investigate the nonlinear response of an anharmonic monostable quantum
mechanical resonator to strong external periodic driving. The driving thereby
induces an effective bistability in which resonant tunneling can be identified.
Within the framework of a Floquet analysis, an effective Floquet-Born-Markovian
master equation with time-independent coefficients can be established which can
be solved straightforwardly. Various effects including resonant tunneling and
multi-photon transitions will be described. Our model finds applications in
nano-electromechanical devices such as vibrating suspended nano-wires as well
as in non-destructive read-out procedures for superconducting quantum bits
involving the nonlinear response of the read-out SQUID.
