Practical considerations and fundamental limitations of quantum gravity detection using rare-earth ions

Sammanfattning

To probe the unsolved intersection between quantum mechanics and general relativity, this thesis theoretically investigates and attempts to further develop an experiment designed to detect quantum gravity signatures via a rare-earth-ion doped microresonator. Leading theories on quantum gravity predict deformations to the Heisenberg uncertainty principle, which would affect the dynamics of the resonator via the Heisenberg equation. The investigated experiment aims to measure this deformation via the accumulated phase of a probe laser that dispersively couples to the doped ions in the resonator. The thesis examines the deformed dynamics for the purpose of investigating different measurement schemes, and concludes that the previously proposed scheme of two interactions between the laser and the resonator needs to be modified to either include additional interactions or measure how the resonator frequency scales with its mass and amplitude. To facilitate the necessary dispersive coupling, we successfully simulate a spectral-hole burning scheme under an applied magnetic gradient, which revealed that the gradient must be operated at an offset and that magnetic fields cause unwanted broadening of the holes. Finally, to achieve the strict noise suppression required to resolve the subtle deformations, we designed and simulated phononic crystal structures, proving their ability to isolate the resonator from thermal noise through acoustic bandgaps.The novel experimental framework investigated in this work offers a potential solution to the fundamental problem of empiric detection of quantum gravity. This thesis constitutes a meaningful step towards the successful realization of the experiment.