Absolute determination of the single-photon optomechanical coupling rate via a Hopf bifurcation

We establish a method for the determination of the single-photon optomechanical coupling rate, which characterizes the radiation pressure interaction in an optomechanical system. The estimation of the rate with which a mechanical oscillator, initially in a thermal state, undergoes a Hopf bifurcation, and reaches a limit cycle, allows us to determine the single-photon optomechanical coupling rate in a simple and consistent way. Most importantly, and in contrast to other methods, our method does not rely on knowledge of the system's bath temperature and on a calibration of the signal. We provide the theoretical framework, and experimentally validate this method, providing a procedure for the full characterization of an optomechanical system, which could be extended outside cavity optomechanics, whenever a resonator is driven into a limit cycle by the appropriate interaction with another degree of freedom.