Quantum Interpretation
The above discussion makes it clear that the Hanbury Brown and Twiss (or photon bunching) effect can be entirely described by classical optics. The quantum description of the effect is less intuitive: if one supposes that a thermal or chaotic light source such as a star randomly emits photons, then it is not obvious how the photons "know" that they should arrive at a detector in a correlated (bunched) way. A simple argument suggested by Ugo Fano captures the essence of the quantum explanation. Consider two points and in a source which emit photons detected by two detectors and as in the diagram. A joint detection takes place when the photon emitted by is detected by and the photon emitted by is detected by (red arrows) or when 's photon is detected by and 's by (green arrows). The quantum mechanical probability amplitudes for these two possibilities are denoted by and respectively. If the photons are indistinguishable, the two amplitudes interfere constructively to give a joint detection probability greater than that for two independent events. The sum over all possible pairs, in the source washes out the interference unless the distance is sufficiently small.
Fano's explanation nicely illustrates the necessity of considering two particle amplitudes, which are not as intuitive as the more familiar single particle amplitudes used to interpret most interference effects. This may help to explain why some physicists in the 1950s had difficulty accepting the Hanbury Brown Twiss result. But the quantum approach is more than just a fancy way to reproduce the classical result: if the photons are replaced by identical fermions such as electrons, the antisymmetry of wave functions under exchange of particles renders the interference destructive, leading to zero joint detection probability for small detector separations. This effect is referred to as antibunching of fermions . The above treatment also explains photon antibunching : if the source consists of a single atom which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible. Antibunching, whether of bosons or of fermions, has no classical wave analog.
From the point of view of the field of quantum optics, the HBT effect was important to lead physicists (among them Roy J. Glauber and Leonard Mandel) to apply quantum electrodynamics to new situations, many of which had never been experimentally studied, and in which classical and quantum predictions differ.
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