The process of 3-photon down conversion 3 + + 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 pump power. We calculate the quantum properties of the steady state both using quantum trajectory simulations, and by perturbation expansion of the density operator. A nongaussian Wigner function exhibiting a threefold symmetry is found. Above threshold the Wigner function displays separate peaks among which tunneling occurs.