Time-resolved phase-space tomography of an optomechanical cavity

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 (SEO), 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 SEO 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.