Time Resolved Phase Space Tomography of an Optomechanical Cavity

TL;DR

This paper experimentally investigates the phase space distribution of a dual-cavity optomechanical system, demonstrating state transitions and comparing results with theoretical models, with implications for quantum superposition states.

Contribution

It introduces a phase space tomography method for a dual-cavity optomechanical system and studies the dynamics of state transitions near the oscillation threshold.

Findings

Measured PSD during state transitions induced by microwave detuning

Observed real-time evolution from cooled to self-oscillating states

Results agree with Fokker-Planck theoretical predictions

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.