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

We present an analysis of the sensitivity limits of a proposed experimental search for quantum gravity, using a novel approach based on optical magnetometry in the noble gas isotope $^{129}$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 $^{129}$Xe atoms that are immersed in a magnetic field in the proposed experiment, which results in a velocity-dependent variation of their Larmour 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.