  In the previous paper [M. Tsang, Phys. Rev. A 81, 063837 (2010), e-print
arXiv:1003.0116], I proposed a quantum model of a cavity electro-optic
modulator, which can coherently couple an optical cavity mode to a microwave
resonator mode and enable novel quantum operations on the two modes, including
laser cooling of the microwave mode, electro-optic entanglement, and
backaction-evading optical measurement of a microwave quadrature. In this
sequel, I focus on the quantum input-output relations between traveling optical
and microwave fields coupled to a cavity electro-optic modulator. With
red-sideband optical pumping, the relations are shown to resemble those of a
beam splitter for the traveling fields, so that in the ideal case of zero
parasitic loss and critical coupling, microwave photons can be coherently
up-converted to "flying" optical photons with unit efficiency, and vice versa.
With blue-sideband pumping, the modulator acts as a nondegenerate parametric
amplifier, which can generate two-mode squeezing and hybrid entangled photon
pairs at optical and microwave frequencies. These fundamental operations
provide a potential bridge between circuit quantum electrodynamics and quantum
optics.
