Quantum effects in one-photon and two-photon interference

Although interference is intrinsically a classical wave phenomenon, the superposition principle which underlies all interference is also at the heart of quantum mechanics. Feynman has referred to interference as really ‘‘the only mystery’’ of quantum mechanics. Furthermore, in some interference experiments we encounter the idea of quantum entanglement, which has also been described as really the only quantum mystery. Clearly interference confronts us with some quite basic questions of interpretation. Despite its long history, going back to Thomas Young at the beginning of the 19th century, optical interference still challenges our understanding, and the last word on the subject probably has not yet been written. With the development of experimental techniques for fast and sensitive measurements of light, it has become possible to carry out many of the Gedanken experiments whose interpretation was widely debated in the 1920s and 1930s in the course of the development of quantum mechanics. Although this article focuses entirely on experiments with light, interference has also been observed with many kinds of material particles like electrons, neutrons, and atoms. We particularly draw the reader’s attention to the beautiful experiments with neutron beams by Rauch and co-workers and others (see, for example, Badurek et al., 1988). Quantum optical interference effects are key topics of a recent book (Greenstein and Zajonc, 1997), an extended rather thorough review (Buzek and Knight, 1995) and an article in Physics Today (Greenberger et al., 1993). The essential feature of any optical interference experiment is that the light from several (not necessarily primary) sources like SA and SB (see Fig. 1) is allowed to come together and mix, and the resulting light intensity is measured at various positions. We characterize interference by the dependence of the resulting light intensities on the optical path length or phase shift, but we need to make a distinction between the measurement of a single realization of the optical field and the average over an ensemble of realizations or over a long time. A single realization may exhibit interference, whereas an ensemble average may not. We shall refer to the former as transient interference, because a single realization usually exists only for a short time. Transient interference effects have been observed in several optical experiments in the 1950s and 1960s. (Forrester et al., 1955; Magyar and Mandel, 1963; Pfleegor and Mandel, 1967, 1968).