Theory of photon-pair correlations in parametric downconversion in a microcavity

A theory of spontaneous parametric downconversion in a nonlinear crystal that is placed inside a microcavity in the degenerate, collinear, type I arrangement is given. Both atom and field variables are fully quantized. The photon-correlation function for the entangled photon pairs produced has a much longer correlation time (~0.4 ns) than that without the cavity (of the order of subpicoseconds) and can be measured directly with fast photodetectors. We also calculate the resonant suppression and enhancement in the photon-pair count rate as a function of cavity length. The results are in qualitative agreement with recent downconversion experiments [Phys. Rev. Lett. 85, 2556 (1999)] in a 4.5-mm cavity.