Hong–Ou–Mandel effect

The Hong–Ou–Mandel effect is a two-photon interference effect in quantum optics which was demonstrated in 1987 by three physicists from the University of Rochester: Chung Ki Hong, Zhe Yu Ou and Leonard Mandel. The effect occurs when two identical single-photon waves enter a 50:50 beam splitter, one in each input port. When the photons are identical they will extinguish each other. If they become more distinguishable, the probability of detection will increase. In this way the interferometer can accurately measure bandwidth, path lengths and timing.

When a photon enters a beam splitter, there are two possibilities: it will either be reflected or transmitted. The relative probabilities of transmission and reflection are determined by the reflectivity of the beam splitter. Here, we assume a 50:50 beam splitter, in which a photon has equal probability of being reflected and transmitted.

Next, consider two photons, one in each input mode of a 50:50 beam splitter (see figure 1). There are four possibilities for the photons to behave: 1) The photon coming in from above is reflected and the photon coming in from below is transmitted; 2) Both photons are transmitted; 3) Both photons are reflected; 4) The photon coming in from above is transmitted and the photon coming in from below is reflected. We assume now that the two photons are identical in their physical properties (i.e., polarization, spatio-temporal mode structure, and frequency).

Since the state of the beam splitter does not "record" which of the four possibilities actually happens, Feynman rules dictates that we have to add all four possibilities at the amplitude level. In addition, reflection off the bottom side of the beam splitter introduces a relative phase shift of −1 in the associated term in the superposition. This is required by the reversibility (or unitarity) of the quantum evolution of the beam splitter. Since the two photons are identical, we cannot distinguish between the output states of possibilities 2 and 3 in figure 1, and their relative minus sign ensures that these two terms cancel. This can be interpreted as destructive interference.

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