Hanbury Brown and Twiss Interference for Bosons and Fermions
In 1956, British astronomers Robert Hanbury Brown and Richard Q. Twiss measured the stellar radius of Sirius by making use of a new type of interferometer [1, 2]. This was based not on the usual amplitude interference but rather on radiation intensity, exploiting the fact that photons emitted by the star are governed by Bose–Einstein statistics. In contrast to fermions, such as electrons or neutrons, which tend to avoid one another (the basis of the Pauli exclusion principle), bosons, such as photons or pions, prefer to "bunch" together.[more]
This Demonstration describes a simplified Hanbury Brown and Twiss apparatus that detects the coincidence counts of two detectors, both receiving incoherent radiation from two sources with a controllable delay, emitting either bosons or fermions. It is observed that boson coincidence counts reach a maximum when the delay time is reduced to zero. By contrast, fermion counts are reduced as the delay time is decreased. These are shown in the graphic as simulated oscilloscope traces, showing signal versus time. You can control the efficiency of the apparatus. For lower efficiencies, the response curve becomes flatter as the maximum or minimum is suppressed.[less]
The amplitudes of the four pictured boson or fermion trajectories are designated: . The total amplitude of the process in which two particles are incident on each of the two detectors is given by , where the plus sign applies to bosons and the minus sign to fermions. The corresponding intensity is then equal to
We assume simple approximations to the amplitudes:
where is the time delay in the crossed paths. The radiation frequency and the time delay depend on the types of particles and the specifics of the experiment. Their magnitudes are left unspecified, so that our results are completely general.
Using the preceding amplitudes, the two-detector correlation intensities work out to
for bosons and fermions, respectively.
 R. Hanbury Brown and R. Q. Twiss, "Correlation between Photons in Two Coherent Beams of Light," Nature, 177(4497), 1956 pp. 27–29. doi:10.1038/177027a0.
 R. Hanbury Brown and R. Q. Twiss, "A Test of a New Type of Stellar Interferometer on Sirius," Nature, 178(4541), 1956 pp. 1046–1048. doi:10.1038/1781046a0.
 Wikipedia. "Hanbury Brown and Twiss Effect." (Aug 22, 2019) en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect.
 U. Fano, "Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources," American Journal of Physics, 29(8), 1961 pp. 539–545. doi:10.1119/1.1937827.