  We discuss using a table-top ion interferometer to search for deviations from
Coulomb's inverse-square law. Such deviations would result from non-classical
effects such at a non-zero photon rest mass. We discuss the theory behind the
proposed measurement, explain which fundamental, experimentally controllable
parameters are the relevant figures of merit, and calculate the expected
performance of such a device in terms of these parameters. The sensitivity to
deviations in the exponent of the inverse-square law is predicted to be a few
times $10^{-22}$, an improvement by five orders of magnitude over current
experiments. It could measure a non-zero photon rest mass smaller than
$9\times10^{-50}$ grams, nearly 100 times smaller than current laboratory
experiments.
