In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensities received by two detectors from a beam of particles. HBT effects can generally be attributed to the wave–particle duality of the beam, and the results of a given experiment depend on whether the beam is composed of fermions or bosons. Devices which use the effect are commonly called intensity interferometers and were originally used in astronomy, although they are also heavily used in the field of quantum optics.
History In 1954, Robert Hanbury Brown and Richard Q. Twiss introduced the intensity interferometer concept to radio astronomy for measuring the tiny angular size of stars, suggesting that it might work with visible light as well. Soon after they successfully tested that suggestion: in 1956 they published an in-lab experimental mockup using blue light from a mercury-vapor lamp, and later in the same year, they applied this technique to measuring the size of Sirius. In the latter experiment, two photomultiplier tubes, separated by a few meters, were aimed at the star using crude telescopes, and a correlation was observed between the two fluctuating intensities. Just as in the radio studies, the correlation dropped away as they increased the separation (though over meters, instead of kilometers), and they used this information to determine the apparent angular size of Sirius.
This result was met with much skepticism in the physics community. The radio astronomy result was justified by Maxwell's equations, but there were concerns that the effect should break down at optical wavelengths, since the light would be quantised into a relatively small number of photons that induce discrete photoelectrons in the detectors. Many physicists worried that the correlation was inconsistent with the laws of thermodynamics. Some even claimed that the effect violated the uncertainty principle. Hanbury Brown and Twiss resolved the dispute in a neat series of articles (see References below) that demonstrated, first, that wave transmission in quantum optics had exactly the same mathematical form as Maxwell's equations, albeit with an additional noise term due to quantisation at the detector, and second, that according to Maxwell's equations, intensity interferometry should work. Others, such as Edward Mills Purcell immediately supported the technique, pointing out that the clumping of bosons was simply a manifestation of an effect already known in statistical mechanics. After a number of experiments, the whole physics community agreed that the observed effect was real. The original experiment used the fact that two bosons tend to arrive at two separate detectors at the same time. Morgan and Mandel used a thermal photon source to create a dim beam of photons and observed the tendency of the photons to arrive at the same time on a single detector. Both of these effects used the wave nature of light to create a correlation in arrival time – if a single photon beam is split into two beams, then the particle nature of light requires that each photon is only observed at a single detector, and so an anti-correlation was observed in 1977 by H. Jeff Kimble. Finally, bosons have a tendency to clump together, giving rise to Bose–Einstein correlations, while fermions due to the Pauli exclusion principle, tend to spread apart, leading to Fermi–Dirac (anti)correlations. Bose–Einstein correlations have been observed between pions, kaons and photons, and Fermi–Dirac (anti)correlations between protons, neutrons and electrons. For a general introduction in this field, see the textbook on Bose–Einstein correlations by Richard M. Weiner. A difference in repulsion of Bose–Einstein condensate in the "trap-and-free fall" analogy of the HBT effect affects comparison. Also, in the field of particle physics, Gerson Goldhaber et al. performed an experiment in 1959 in Berkeley and found an unexpected angular correlation among identical pions, discovering the ρ0 resonance, by means of ρ 0 → π − π + {\displaystyle \rho ^{0}\to \pi ^{-}\pi ^{+}} decay. From then on, the HBT technique started to be used by the heavy-ion community to determine the space–time dimensions of the particle emission source for heavy-ion collisions. For developments in this field up to 2005, see for example this review article.
Wave mechanics
The HBT effect can, in fact, be predicted solely by treating the incident electromagnetic radiation as a classical wave. Suppose we have a monochromatic wave with frequency ω {\displaystyle \omega } on two detectors, with an amplitude E ( t ) {\displaystyle E(t)} that varies on timescales slower than the wave period 2 π / ω {\displaystyle 2\pi /\omega } . (Such a wave might be produced from a very distant point source with a fluctuating intensity.) Since the detectors are separated, say the second detector gets the signal delayed by a time τ {\displaystyle \tau } , or equivalently, a phase ϕ = ω τ {\displaystyle \phi =\omega \tau } ; that is,
E 1 ( t ) = E ( t ) sin ( ω t ) , {\displaystyle E_{1}(t)=E(t)\sin(\omega t),}
E 2 ( t ) = E ( t − τ ) sin ( ω t − ϕ ) . {\displaystyle E_{2}(t)=E(t-\tau )\sin(\omega t-\phi ).}
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