Quantum Interference in Three Photon Down Conversion

We study degenerate three photon down conversion as a potential scheme for generating nonclassical states of light which exhibit clear signatures of phase space interference. The Wigner function representing these states contains an interference pattern manifesting quantum coherence between distinct phase space components, and has substantial areas of negativity. We develop an analytical description of the interference pattern, which demonstrates how the oscillations of the Wigner function are built up by the superposition principle. We analyze the impact of dissipation and pump uctuations on the visibility of the interference pattern; the results suggest that some signatures of quantum coherence can be observed in the presence of moderate amount of noise.