  Microwave optomechanical circuits have been demonstrated in the past years to
be extremely powerfool tools for both, exploring fundamental physics of
macroscopic mechanical oscillators as well as being promising candidates for
novel on-chip quantum limited microwave devices. In most experiments so far,
the mechanical oscillator is either used as a passive device element and its
displacement is detected using the superconducting cavity or manipulated by
intracavity fields. Here, we explore the possibility to directly and
parametrically manipulate the mechanical nanobeam resonator of a cavity
electromechanical system, which provides additional functionality to the
toolbox of microwave optomechanical devices. In addition to using the cavity as
an interferometer to detect parametrically modulated mechanical displacement
and squeezed thermomechanical motion, we demonstrate that parametric modulation
of the nanobeam resonance frequency can realize a phase-sensitive parametric
amplifier for intracavity microwave photons. In contrast to many other
microwave amplification schemes using electromechanical circuits, the presented
technique allows for simultaneous cooling of the mechanical element, which
potentially enables this type of optomechanical microwave amplifier to be
quantum-limited.
