In nondegenerate parametric amplification of light, one pump photon is destroyed and two photons are simultaneously created, one in each of two modes with different frequencies (the signal and idler). If m signal photons are counted in time t, what is the state of the idler conditioned on this result? The projection postulate cannot be used to answer this question as photon-counting measurements are not ‘‘first-kind’’ measurements. We use a theory of continual quantum-counting measurements to show that in general the idler field is left in a classical mixture of number states with at least m quanta. In an appropriate limit this mixture reduces to an exact number state with m quanta.

• Received 27 June 1988

DOI:https://doi.org/10.1103/PhysRevA.39.2493