  Recently it was proposed to use cavity-optomechanical systems to test for
quantum gravity corrections to quantum canonical commutation relations [Nat.
Phys. 8, 393-397 (2012)]. Improving the achievable precision of such devices
represents a major challenge that we address with our present work. More
specifically, we develop sophisticated paths in phase-space of such
optomechanical system to obtain significantly improved accuracy and precision
under contributions from higher-order corrections to the optomechanical
Hamiltonian. An accurate estimate of the required number of experimental runs
is presented based on a rigorous error analysis that accounts for mean photon
number uncertainty, which can arise from classical fluctuations or from quantum
shot noise in measurement. Furthermore, we propose a method to increase
precision by using squeezed states of light. Finally, we demonstrate the
robustness of our scheme to experimental imperfection, thereby improving the
prospects of carrying out tests of quantum gravity with near-future
optomechanical technology.
