  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.
