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A thought experiment is proposed to demonstrate the existence of agravitational, vector Aharonov-Bohm effect. A connection is made between thegravitational, vector Aharonov-Bohm effect and the principle of local gaugeinvariance for nonrelativistic quantum matter interacting with weakgravitational fields. The compensating vector fields that are necessitated bythis local gauge principle are shown to be incorporated by the DeWitt minimalcoupling rule. The nonrelativistic Hamiltonian for weak, time-independentfields interacting with quantum matter is then extended to time-dependentfields, and applied to problem of the interaction of radiation withmacroscopically coherent quantum systems, including the problem ofgravitational radiation interacting with superconductors. But first we examinethe interaction of EM radiation with superconductors in a parametric oscillatorconsisting of a superconducting wire placed at the center of a high Qsuperconducting cavity driven by pump microwaves. We find that the thresholdfor parametric oscillation for EM microwave generation is much lower for theseparated configuration than the unseparated one, which then leads to anobservable dynamical Casimir effect. We speculate that a separated parametricoscillator for generating coherent GR microwaves could also be built.

A Gravitational Aharonov-Bohm Effect, and its Connection to Parametric Oscillators and Gravitational Radiation