An optical trinary digit with three-photon down-conversion

It is shown that the onset of signal oscillations in the parametric nonlinear process of three-photon down-conversion is analogous with a first-order phase transition. Such an oscillator exhibits phase tristability, such that by reaching above the oscillation threshold it can take three different states with uniform phase contrasts. An analytically solvable second-order oscillator model is derived and the stability of the trinary phase states is proven through a Lyapunov function. The phase tristability of a three-photon down-conversion oscillator intrinsically emulates a classical trinary digit (trit). Such a trinary digit can be utilized for applications in unconventional computing.