Photon-number-state preparation in nondegenerate parametric amplification

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Abstract
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.

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