For my honours research I investigated triplet down conversion, a quantum optical process in which a single photon is “split” into three lower energy photons. Some people are surprised that processes like this can occur, but they can and do - as long as energy and momentum and so on are conserved, boundary conditions are satisfied, and there is some nonlinearity to allow the interaction to occur. In fact, triplet down-conversion was experimentally realised shortly after I finished this research project.
My research primarily involved simulating the process using stochastic differential equations in optical phase space. These simulations allowed us to examine the time evolution of the states, but we were more interested in quantum properties of the resulting steady states, in particular squeezing and entanglement.
The majority of my research focussed on the (simpler) “degenerate” case, in which the resulting photons are indistinguishable and have the same energy, but this is not a requirement of the process. Near the end of the project I briefly examined the non-degenerate case, where each of the resulting photons have different energies. Unfortunately the SDEs were numerically unstable, so I resorted to a set of semi-classical ODEs to examine this process.