Searching for Photon Rest Mass with Matterwave Interferometry

We discuss a proposed test of Coulomb's inverse-square law using matterwave interferometry. A deviation from the inverse-square law could be related to a possible non-zero rest mass of the photon, the exchange Boson for the electro-magnetic force. In the experiment, the wavefunction of ions will be split and recombined inside of a conducting shell. From the interferometer phase, it can be determined if fields in the shell change as the voltage applied to the shell is altered. If a changing field is detected, a violation of Coulomb's law is implied. In such an experiment, using reasonable experimental parameters, it could be possible to detect a photon rest mass as small as a several time $10^{-53}$ kg.