The minimal-coupling Hamiltonian that describes the quantum-mechanical interaction of charged matter and electromagnetic fields, implies the existence of an optical analog of the Aharonov-Bohm effect that may be observable as a resistivity change in mesoscopic conductor loops. In superconducting quantum interference devices (SQUIDs) the ponderomotive potential adds to the chemical potential, altering the Josephson oscillation frequency. These interactions do not involve the absorption or random scattering of quanta, but merely the mutual nonlinear phase shift of matter and electromagnetic waves, and thus (in principle) support back-action-evading measurement schemes. The well-known electrostatic Aharonov-Bohm effect can be used to detect potentials produced by optical rectification, another back-action evading process. Only the SQUID implementation seems likely to produce back-action-evading readouts of quantum amplitude fluctuations larger than Johnson noise. © 1990 The American Physical Society.