  In a recent article Wang et al. (Class. Quantum Grav. 23 (2006) L59),
demonstrated that the phase of a particle fluctuates due to interactions with
random deviations of a conformal gravitational field. Furthermore they
demonstrated that atom interferometers are sensitive to these fluctuations and
that sensitivity to Planck scale effects could be achieved with a sufficiently
sensitive interferometer. In this paper we demonstrate that a class of
entangled states, the N-atom Greenberger-Horne-Zeilinger (GHZ) states, provide
a better scaling than atom interferometers and that current experiments are
capable of making a significant impact in this field. We outline an experiment
which uses atomic beams of rubidium atoms excited to Rydberg states. The atoms
undergo controlled collisions in high quality factor microwave resonators in a
sequence that makes the resulting state highly sensitive to conformal field
fluctuations. We show that a significant advance in sensitivity is possible.
