  Parametrically modulated optomechanical systems have been recently proposed
as a simple and efficient setting for the quantum control of a micromechanical
oscillator: relevant possibilities include the generation of squeezing in the
oscillator position (or momentum) and the enhancement of entanglement between
mechanical and radiation modes. In this paper we further investigate this new
modulation regime, considering an optomechanical system with one or more
parameters being modulated over time. We first apply a sinusoidal modulation of
the mechanical frequency and characterize the optimal regime in which the
visibility of purely quantum effects is maximal. We then introduce a second
modulation on the input laser intensity and analyze the interplay between the
two. We find that an interference pattern shows up, so that different choices
of the relative phase between the two modulations can either enhance or cancel
the desired quantum effects.
