Correlations in photon-numbers and integrated intensities in parametric processes involving three optical fields

Two strongly-pumped parametric interactions are simultaneously realized in a single nonlinear
crystal in order to generate three strongly correlated optical fields. By combining together the outputs of
two of the three detectors measuring intensities of the generated fields, we obtain the joint photocount
statistics between the single field and the sum of the other two. We apply a microscopic quantum theory
developed earlier to determine the joint photon-number distribution and the joint quasi-distributions of
integrated intensities and prove nonclassical nature of the three-mode state. Finally, by performing a
conditional measurement on the single field, we obtain a state endowed with a sub-Poissonian statistics, as
testified by the analysis of the conditional Fano factor. The role of quantum detection efficiencies in this
conditional state-preparation method is discussed in detail.