We apply the stochastic master equations (quantum filter) derived by Gough et al. (Proc. 50th IEEE Conference on Decision and Control, 2011) to a system consisting of a cavity driven by a multimode single photon field. In particular, we analyse the c
onditional dynamics for the problem of cross phase modulation in a doubly resonant cavity. Through the exact integration of the stochastic equations, our results reveal features of the problem unavailable from previous models.
