Cavity quantum electro-optics

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 optomechanical coupling via radiation pressure, so all previously considered optomechanical 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.

Figure 1

A basic cavity electro-optic system. EOM denotes an electro-optic modulator.

Figure 2

Red-detuned optical pumping cools the microwave mode by transferring energy from the microwave to the optical mode at ${\omega }_a$ via parametric up-conversion. Blue-detuned pumping causes nondegenerate parametric down-conversion to the optical mode at ${\omega }_a$ and the microwave mode.

Figure 3

Electro-optic cooling via detuned pumping of the center optical mode. The parasitic down-conversion process can limit the lowest microwave occupation number one can achieve.