Quantum behavior of a four-wave mixer operated in a nonlinear regime

A four-wave mixer model is presented for which exact analytic results can be obtained in a regime where the usual perturbation procedures no longer apply. It is shown that under suitable conditions the output of such a four-wave mixer consists of a superposition of macroscopically distinguishable states. Such states can be identified with a homodyne detector which is able to observe the interference between the macroscopically distinguishable components. Further, it is shown that the device can act as an even-odd filter which will switch incoming pump light between two output ports depending on whether there is an even or odd number of pump photons.