  We consider an electromechanical system where a microwave cavity is coupled
to a mechanical resonator, with a mechanical frequency twice the microwave
frequency. In this regime, the effective photon-phonon interaction is
equivalent to that of a degenerate parametric amplifier, instead of the typical
radiation pressure interaction. If the mechanical resonator is strongly driven,
it undergoes a phase transition to a state where the energy pumped into the
mechanical mode is entirely converted to the photonic mode. Quantum
fluctuations smear this phase transition. We describe these effects with a
steady-state Fokker-Planck equation in the complex P-representation, and
compute the photonic field intensity and quadrature variances, as well as the
mechanical amplitude. This Fokker-Planck method performs better than the
standard linearization results, when compared to numerical simulations.
