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 conditional 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
