  The quantum dynamics of the coupling between a cavity optical field and a
resonator microwave field via the electro-optic effect is studied. This
coupling has the same form as the opto-mechanical coupling via radiation
pressure, so all previously considered opto-mechanical effects can in principle
be observed in electro-optic systems as well. In particular, I point out the
possibilities of laser cooling of the microwave mode, entanglement between the
optical mode and the microwave mode via electro-optic parametric amplification,
and back-action-evading optical measurements of a microwave quadrature.
