Oscillation and Generation of Nonclassical States in Three-Photon Down-Conversion

The process of three-photon down-conversion 3 $\omega \to \omega +\omega +\omega$ in an optical cavity is analyzed theoretically. A classical feature of this system is a first-order transition of the fundamental mode above a threshold $3\omega$ pump power. We calculate the properties of the intra- and extracavity states using analytical calculations and quantum trajectory simulations. A positive, non-Gaussian Wigner function exhibiting a threefold symmetry is found. Above threshold the Wigner function displays separate peaks among which tunneling occurs.