  We experimentally study the phase space distribution (PSD) of a mechanical
resonator that is simultaneously coupled to two electromagnetic cavities. The
first one, operating in the microwave band, is employed for inducing either
cooling or self-excited oscillation, whereas the second one, operating in the
optical band, is used for displacement detection. A tomography technique is
employed for extracting the PSD from the signal reflected by the optical
cavity. Measurements of PSD are performed in steady state near the threshold of
self-excited oscillation while sweeping the microwave cavity detuning. In
addition, we monitor the time evolution of the transitions from an
optomechanically cooled state to a state of self excited oscillation. This
transition is induced by abruptly switching the microwave driving frequency
from the red-detuned region to the blue-detuned one. The experimental results
are compared with theoretical predictions that are obtained by solving the
Fokker-Planck equation. The feasibility of generating quantum superposition
states in the system under study is briefly discussed.
