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Hanbury Brown―Twiss effect

to a surprising number of people the idea that the arrival of photons at two separated detectors can ever be correlated was not only heretical but patently absurd, and they told us so in no uncertain terms, in person, by letter, in print, and by publishing the results of laboratory experiments, which claimed to show that we were wrong.

—R. Hanbury Brown, Boffin: A Personal Story of the Early Days of Radar, Radio Astronomy and Quantum Optics.

As far as we know, this fundamental effect has never been directly observed with light, and indeed its very existence has been questioned.

—Correlation between Photons in two Coherent Beams of Light. R. Hanbury Brown and R. Q. Twiss in Nature 177:27 (1956).

the Brown—Twiss effect, far from requiring a revision of quantum mechanics, is an instructive illustration of its elementary principles.

—The Question of Correlation between Photons in Coherent Light Rays. E. M. Purcell in Nature 178:1449 (1956).

The Hanbury Brown―Twiss effect is one of the most beautiful results of modern Physics: the 20th century Eratosthenes experiment (the one with the shadow).

It arises from the fact that when waves interfere—a well-known and understood process—they develop correlations. This surprisingly escaped notice until a young engineer working for British intelligence (Hanbury Brown) got a grip on the effect to create a new type of stellar interferometer out of it.

As a result, in a modern (quantum-mechanical) picture, bosons have a tendency to be detected together ("bunching"). This occurs on scales that span from stars ($10^{12}$cm, for which the first underlying technique was initially developed) to nuclear matter ($10^{-12}$cm).

In Optics, this relates to photons from thermal sources (so, natural ones: lightbulbs, stars, etc.) arriving together on the photodetector. This is surprising because you would expect them to be uncorrelated.

It is a subtle and counter-intuitive effect of interferences, which needed all the insights, wit and persistence of a young engineer to be discovered in the form of an intensity interference, centuries after wave (or field) interferences (by Huygens, Fresnel and others). This was quickly understood (by Purcell) to be a particular case of quanta correlations and became the seed for the field of quantum optics.

It is also a capital story in the History of Science, with drama, coup de théâtres, and a beautiful moral.

Historical background

Hanbury Brown was an engineer working for British intelligence when he got the idea of intensity correlations by noticing similarities of the wiggles made by the radar signal on oscilloscopes. After the war, he got to bring this idea to build a radio-wave interferometer and indeed could implement the technique at Jodrell bank. He sought assistance from a pure Mathematician, Richard Quintin Twiss, of whom very little is known in comparison. Together they developed the theory, interestingly, despite initial negative results from Twiss who calculated this would not work out (Hanbury convinced him otherwise!)

They then turned to the optical field, which was quite a natural continuation, but this exerted very much opposition from physicists (remember, Hanbury was an engineer and Twiss a mathematician), even though they managed to demonstrate the effect experimentally, with five-foot diameter searchlights left over from the Second World War.

The controversy was put to rest by Purcell who argued that the effect ought to be expected from the symmetry of the wavefunction, and also predicted that the opposite anticorrelations would thus result for fermionic (anti-symmetrized) wavefunctions.

The technique was subsequently applied to astronomy in the visible spectrum, with the measurement of the angular size of Sirius (α Canus Majoris A).

It also became pivotal in high-energy and nuclear physics. The first apparition of the effect was in bubble chambers experiments in pion production from antiprotons by Goldhaber et al. (known as the GGLP [Goldhaber-Goldhaber-Lee-Pais], one of the most cited papers in nuclear physics), which allowed them to measure the radius of the particle-interaction region, the first time that a radius of interactions was measured. This triggered a whole new field of intensity interferometry which is relevant for many phenomena.

Literature

Hanbury Brown's main papers on this topic with Twiss are (note that the opening one is not with Twiss):

1. Apparent Angular Sizes of Discrete Radio Sources: Observations at Jodrell Bank, Manchester. R. Hanbury Brown, R. C. Jennison and M. K. Das Gupta in Nature 170:1061 (1952).
2. A new type of interferometer for use in radio astronomy. R. Hanbury Brown and R.Q. Twiss in Phil. Mag. 45:663 (1954).
3. A Test of a New Type of Stellar Interferometer on Sirius. R. Hanbury Brown and R. Q. Twiss in Nature 178:1046 (1956).
4. Correlation between Photons in two Coherent Beams of Light. R. Hanbury Brown and R. Q. Twiss in Nature 177:27 (1956).
5. The Question of Correlation between Photons in Coherent Light Rays. R. Hanbury Brown and R. Q. Twiss in Nature 178:1447 (1956).

He also has a four-part series with Twiss, which I have not studied yet:

1. Interferometry of the intensity fluctuations in light. I. Basic theory of the correlation between photons in coherent beams of radiation. R. Hanbury Brown and R. Twiss in Proc. Roy. Soc A 242:300 (1957).
2. Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light. R. Hanbury Brown and R. Twiss in Proc. R. Soc. Lond. A 243:291 (1958).
3. Interferometry of the intensity fluctuations in light. III. Applications to Astronomy. R. Hanbury Brown and R. Twiss in Proc. Roy. Soc [ 248:199] (1958).
4. Interferometry of the intensity fluctuations in light IV. A test of an intensity interferometer on Sirius A. R. Hanbury Brown and R. Twiss in Proc. R. Soc. Lond. A 248:222 (1958).