Abstract
Optical nonlinear processes in whispering gallery mode resonators require the phase matching that is profoundly different from that in bulk crystals or waveguides. We analyze the phase matching conditions for frequency doubling and parametric down conversion in the resonators, and find the configurations allowing for simultaneous occurrence of these two processes. Such double phase matching gives us access to a variety of interesting quantum nonlinear optical phenomena. For example, it can lead to antibunched emission of photon pairs through the quantum Zeno photonic blockade.
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