Triplet down conversion, the process of converting one high-energy photon into three low-energy photons, may soon be experimentally feasible due to advances in optical resonator technology. We use quantum phase-space techniques to analyse the process of degenerate intracavity triplet down conversion by solving stochastic differential equations within the truncated positive-P representation. The time evolution of both intracavity mode populations are simulated, and the resulting steady-states are examined as a function of the pump intensity. Quantum effects are most pronounced in the region immediately above the semi-classical pumping threshold, where our numerical results differ significantly from semi-classical predictions. Regimes of measurable squeezing and bipartite entanglement are identified from steady-state spectra of the cavity output fields. We validate the truncated positive-P description against Monte Carlo wave function simulations, finding good agreement for low mode populations.
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