  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, a corresponding theoretical formalism of cavity quantum
optomechanics that captures the nonlinearities of both the radiation-pressure
interaction and the cavity response is needed to unlock these capabilities.
Here, we develop such a nonlinear cavity quantum optomechanical framework,
which we then utilize to propose how position measurement can be performed
beyond the breakdown of the linearized approximation. 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.
