We study the number of coincidences in a Hong-Ou-Mandel interferometer exit whose arms have been supplemented with the addition of one or two optical cavities. The fourth-order correlation function at the beam-splitter exit is calculated. In the regime where the cavity length are larger than the one-photon coherence length, photon coalescence and anti-coalescence interference is observed. Feynman's path diagrams for the indistinguishable processes that lead to quantum interference are presented. As application for the Hong-Ou-Mandel interferometer with two cavities, it is discussed the construction of an optical XOR gate.
@article{arxiv.quant-ph/0503217,
title = {Hong-Ou-Mandel interferometer with cavities: theory},
author = {C. Olindo and M. A. Sagioro and C. H. Monken and S. Pádua and A. Delgado},
journal= {arXiv preprint arXiv:quant-ph/0503217},
year = {2016}
}