Photon correlations and interference in type-I optical parametric down-conversion

In this work we develop a quantum theory for fourth-order interference effects of non-degenerate (ND) and degenerate (D) photons produced in type I spontaneous parametric down-conversion. In the first part of this work we include the effect of crystal dispersion whereby we obtain distinct amplitudes for ND and D photons. In the second part, the effects produced by changes in crystal length and beam-waist radius on photon-pair correlations and fourth-order interference were examined. The effect of such changes on ND and D photons was found to be different and therefore we conclude that ND and D photons are inherently distinguishable quantum states of the photon field.