Tabletop tests of quantum gravity

Abstract

Models of quantum gravity imply a fundamental revision of our description of position and momentum. This revision manifests in modifications of the canonical commutation relations. Experimental tests of such modifications remain an outstanding challenge. In recent years, tabletop experiments to test for quantum gravity have been proposed. This thesis address two main challenges to such experiments.

The first contribution is related to the recent proposal to use cavity-optomechanical systems to test for these deformations [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 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 uncertainty in mean photon number, which can arise from classical fluctuations or from quantum shot noise in measurements. 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.

The second contribution is based on the fact that the deformations in the canonical commutator scale with the mass of test particles, which motivates experiments using macroscopic composite particles. Here we consider a challenge to such tests, namely that quantum gravity corrections of canonical commutation relations are expected to be suppressed with increasing number of constituent particles. Since the precise scaling of this suppression is unknown, it needs to be bounded experimentally and explicitly incorporated into rigorous analyses of quantum gravity tests. We analyse this scaling based on concrete experiments involving macroscopic pendula and provide tight bounds that exceed those of current experiments based on quantum mechanical oscillators. Furthermore, we discuss possible experiments that promise even stronger bounds.

Thus, the work in this thesis brings rigorous and well-controlled tests of quantum gravity closer to reality.