Unified view of the second-order and the fourth-order interferences in a single interferometer

Two-photon interferences are very important in quantum optics and other coherence phenomena of quantum mechanics. Here we show that two kinds of interferences, the second- and the fourth-order interferences, can arise in either separate or combined forms in different regions by tuning the time delay in a single interferometer continuously. Particularly, in the combined form we can observe the fourth-order interference in the envelope and the second-order in the fringe. It is also demonstrated that two individual photons behave differently from time-energy entangled photons in this interferometer. This example elucidates clearly that bi-photon phenomena are different from the phenomena with two photons.