Testing quantum gravity using pulsed optomechanical systems

An interesting idea, dating back to Feynman Report from Chapel Hill Conference, edited by C. M. DeWitt and D. Rickles (1957), argues that quantum mechanics may break down for large masses if one entertains the possibility that gravity can be ``classical,'' thereby leading to predictions different from conventional low-energy quantum gravity. Despite the technical difficulty in testing such deviations, a large number of experimental proposals have been put forward due to the high level of fundamental interest. Here, we consider the Schr\"odinger-Newton (SN) theory and the correlated worldline (CWL) theory, and show that they can be distinguished from conventional quantum mechanics, as well as each other, by performing pulsed optomechanics experiments. For CWL specifically we develop a framework resembling the commonly used ``Heisenberg-picture'' treatment of coupled oscillators, allowing one to perform simple calculations for such systems without delving into the deeper path-integral formalism. We find that discriminating between the theories will be very difficult until experimental control over low frequency quantum optomechanical systems is pushed much further. However, the predicted departures of SN and CWL from quantum mechanics occur at the same scale, so both alternative models could in principle be probed by a single experiment.