Position measurement and the nonlinear regime of cavity quantum optomechanics

Position measurement is central to cavity quantum optomechanics and underpins a wide array of sensing technologies and tests of fundamental physics. Excitingly, several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved, however, an approach for mechanical position measurement and a corresponding theoretical formalism are needed to unlock these capabilities. Here, we develop a framework of cavity quantum optomechanics that captures the nonlinearities of both the radiation-pressure interaction and the cavity response and propose how position measurement can be performed in this regime. Our proposal utilizes optical general-dyne detection, ranging from single to dual homodyne, to obtain mechanical position information imprinted onto both the optical amplitude and phase quadratures and enables both pulsed and continuous modes of operation. These cavity optomechanical nonlinearities are now being confronted in a growing number of experiments, and our framework will allow a range of advances to be made in e.g. quantum metrology, explorations of the standard quantum limit, and quantum measurement and control.