Tristable Phase of Parametric Three-Photon Down-Conversion

The cubic nonlinear process of three-photon down-conversion is investigated. It is shown that the onset of parametric oscillations of the subharmonic signal is accompanied by phase tristability. An analytically solvable second-order oscillator model is derived for the signal. The stability of the ternary phase states is proven through a Lyapunov function and the influence of noise is investigated. The presence of phase tristability can be utilized for all-optical implementation of the Potts model for unconventional computing applications.