Testing non-classical theories of electromagnetism with ion interferometry

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.