Feasibility Analysis of a Proposed Test of Quantum Gravity via Novel Optical Magnetometry in Xenon

Quantum gravity (QG) theory aims to unite quantum mechanics and general relativity. Some formulations of QG lead to a Generalized Uncertainty Principle model, where the canonical uncertainty relations are modified by a leading-order correction term that is linear in momentum, which translates into a momentum-dependent Larmor frequency of spins precessing in a magnetic field. We propose a novel experiment, based on high-precision optical magnetometry using two-photon spectroscopy in spin-polarized xenon-129 atoms immersed in a magnetic field to detect the momentum-dependent correction of the atoms' Larmor frequency, from which the QG correction of the uncertainty relations can be determined or restricted by a much tighter bound than obtained to date. In the proposed experiment, an ultraviolet laser is tuned across the Doppler-broadened profile of the atomic ensemble to facilitate momentum-dependent excitation, where the emitted fluorescence oscillates at the Larmor frequency. We show that existing bounds on the leading-order QG correction can be improved with existing laser technology by a factor of $10^7$, with near-future technology expected to deliver an improvement of $10^9$.