  Because of their small decay rates, nanomechanical modes enable studying
strongly nonlinear phenomena for a moderately strong resonant driving. Here we
study the response of a driven resonator to an additional probe field. We
experimentally demonstrate resonant amplification and resonant absorption of
the probe field. The corresponding spectral peaks lie on the opposite sides of
the strong-drive frequency. Even though the fluctuation-dissipation theorem
does not apply, we show that the response to the probe field allows us to
characterize the squeezing of fluctuations about the stable states of forced
oscillations. Our two-tone experiment is done in the classical regime, but our
findings should equally apply to quantum fluctuations as well. In quantum
terms, the observed response is due to multiphoton processes. The squeezing
parameter extracted from the spectra of the response is in excellent agreement
with the calculated value with no free parameters.
