Recently, it was proposed to use cavity-optomechanical systems to test for quantum gravity corrections to quantum canonical commutation relations [I. Pikovski et al., Nat. Phys. 8, 393 (2012)]. Improving the achievable precision of such devices represents a major challenge that we address with this work. More specifically, we develop sophisticated paths in phase space of such optomechanical systems 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.

• Received 18 September 2017

DOI:https://doi.org/10.1103/PhysRevA.97.063855