Feasibility analysis of a proposed test of quantum gravity via optical magnetometry in xenon

We present an analysis of the sensitivity limits of a proposed experimental search for quantum gravity, using an approach based on optical magnetometry in the noble gas isotope ${}_{129}\mathrm{Xe}$. The analysis relies on a general uncertainty principle model that is consistent with most formulations of quantum gravity theory, where the canonical uncertainty relations are modified by a leading-order correction term that is linear in momentum. In turn, this correction modifies the magnetic moment of the spin-polarized ${}_{129}\mathrm{Xe}$ atoms that are immersed in a magnetic field in the proposed experiment, which results in a velocity-dependent variation of their Larmor frequency, that is detected via two-photon laser spectroscopy. The thermal distribution of atomic velocities, in conjunction with the Doppler effect, is used to scan the interrogating laser over different atomic velocities and search for a corresponding variation in their Larmor frequencies. We show that the existing bounds on the leading-order quantum gravity correction can be improved by ${10}^7$ with existing technology, where another factor of ${10}^2$ is possible with near-future technical capabilities.