Time Resolved Phase Space Tomography of an Optomechanical Cavity

Abstract: 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.