Continuous state reduction of correlated photon fields in photodetection processes

A general theory is developed that describes continuous state reduction of two quantum-mechanically correlated photon fields by continuous photodetection of one of the fields. The effects of measurement back action and quantum correlation on the state reduction of the other field are highlighted from the viewpoint of continuous photodetection. Nonunitary time evolutions of the density operators and photon statistics are exactly described for both fields. The obtained formulas are applied to parametrically generated photon twins, i.e., signal and idler fields. The continuous state reduction of the signal field by photodetection of the idler field is examined. It is shown that the Manley-Rowe relation can be generalized to the intermediate state under the photodetection process; that is, the initial quantum correlation remains intact throughout the ``destructive'' photodetection process if we retain the information about the idler readout. The obtained results are compared to the case in which the idler readout is discarded. In this case, the Manley-Rowe relation can no longer hold. This fact demonstrates that retaining the readout information is essential for preserving the established quantum correlation.