The Hanbury Brown–Twiss Effect: Why Photons Bunch

Point two light detectors at the same star and record how the brightness flickers in each. The flickers are correlated, and the correlation fades as you move the detectors apart. That simple observation, made by Robert Hanbury Brown and Richard Twiss in the 1950s, measured the sizes of stars, started a controversy about the nature of light, and helped found modern quantum optics Hanbury Brown and Twiss effect, Wikipedia^[1]. It is the effect behind our Twissa & Hanbra HBT tee.

What is the Hanbury Brown–Twiss effect?

It is a correlation between the intensity fluctuations recorded by two detectors looking at the same light Hanbury Brown and Twiss effect, Wikipedia^[1]. The standard measure is the second-order coherence function Degree of coherence, Wikipedia^[2]:

g⁽²⁾(τ) = ⟨I(t) I(t+τ)⟩ / ⟨I⟩²

Here I(t) is the intensity at time t and τ is the delay between the two detectors' readings. If photons arrived completely at random, g⁽²⁾ would equal 1 at every delay. For starlight, a mercury lamp or any other thermal (chaotic) source, it is larger than 1 at short delays: the photons are bunched Degree of coherence, Wikipedia^[2]. For chaotic light the Siegert relation ties it to the ordinary first-order coherence g⁽¹⁾ Degree of coherence, Wikipedia^[2]:

g⁽²⁾(τ) = 1 + |g⁽¹⁾(τ)|²

so at zero delay, where |g⁽¹⁾| = 1, chaotic light has g⁽²⁾(0) = 2, and at long delays g⁽²⁾ returns to 1 Degree of coherence, Wikipedia^[2]. A perfectly coherent laser beam gives g⁽²⁾ = 1 at every delay Degree of coherence, Wikipedia^[2].

How was the effect discovered?

In 1954 Hanbury Brown and Twiss introduced the intensity interferometer to radio astronomy as a way of measuring the tiny angular sizes of sources, and suggested it might work for visible light too Hanbury Brown and Twiss effect, Wikipedia^[1]. In 1956 they tested that idea in the laboratory with blue light from a mercury-vapour lamp Hanbury Brown and Twiss effect, Wikipedia^[1], in a Nature paper titled “Correlation between photons in two coherent beams of light” Hanbury Brown and Twiss 1956a^[3]. Later the same year they applied the technique to the star Sirius Hanbury Brown and Twiss effect, Wikipedia^[1] Hanbury Brown and Twiss 1956b^[4].

The trick is that an intensity interferometer only ever compares intensities, not the phases of the light waves Hanbury Brown and Twiss effect, Wikipedia^[1]. The two telescopes do not need to be held stable to a fraction of a wavelength, which is what makes ordinary optical interferometers so hard to build. As the detectors are moved apart, the correlation drops, and the separation at which it disappears gives the angular size of the source Hanbury Brown and Twiss effect, Wikipedia^[1].

Why was it controversial?

The result was met with much scepticism. There were concerns that the effect should break down at optical wavelengths, where light arrives as a relatively small number of photons; some physicists worried it was inconsistent with thermodynamics, and some even claimed it violated the uncertainty principle Hanbury Brown and Twiss effect, Wikipedia^[1]. Hanbury Brown and Twiss answered in a series of papers, and Edward Purcell supported them at once, pointing out that the clumping of bosons is a known effect in statistical mechanics Hanbury Brown and Twiss effect, Wikipedia^[1]. After further experiments the physics community agreed the effect was real Hanbury Brown and Twiss effect, Wikipedia^[1].

Why did the HBT effect matter for quantum optics?

The full quantum explanation came from Roy Glauber. His 1963 paper on photon correlations Glauber 1963^[5] and the work that followed built a quantum theory of optical coherence that describes HBT bunching, laser light and much more. Glauber received half of the 2005 Nobel Prize in Physics “for his contribution to the quantum theory of optical coherence” Nobel Prize in Physics 2005: summary^[6].

The theory also predicts light that no classical wave could produce. For any classical field, 1 ≤ g⁽²⁾(0) and g⁽²⁾(τ) ≤ g⁽²⁾(0) Degree of coherence, Wikipedia^[2]:

1 ≤ g⁽²⁾(0), g⁽²⁾(τ) ≤ g⁽²⁾(0)

A single atom can only emit one photon at a time, so its light has g⁽²⁾(0) below 1. That photon antibunching was observed by H. Jeff Kimble in 1977, and it is direct evidence that light is quantized Hanbury Brown and Twiss effect, Wikipedia^[1].

Do fermions show the opposite effect?

Yes. Photons are bosons and tend to bunch. Identical fermions, because of the Pauli exclusion principle, tend to stay apart and show antibunching instead Hanbury Brown and Twiss effect, Wikipedia^[1]. In 2007 Tom Jeltes and colleagues compared the two directly in the same apparatus using two isotopes of helium: helium-4 atoms, which are bosons, showed bunching, while helium-3 atoms, which are fermions, showed antibunching Jeltes et al. 2007^[7]. Our posts on fermions versus bosons and the spin–statistics theorem explain where the difference comes from, and the Condensa BEC sticker shows bosons at their most sociable.

In particle physics the same idea runs in reverse. In 1959 Gerson Goldhaber and colleagues at Berkeley found an unexpected angular correlation among identical pions, the start of using HBT correlations to measure the size of the region where particles are produced in collisions Hanbury Brown and Twiss effect, Wikipedia^[1].

How big were the stars it measured?

The Narrabri Stellar Intensity Interferometer in New South Wales, Australia, ran from 1963 to 1974 Narrabri Stellar Intensity Interferometer, Wikipedia^[8]. Its two large light collectors moved on a circular track so their separation could be set anywhere from 10 to 188 m Narrabri Stellar Intensity Interferometer, Wikipedia^[8]. Hanbury Brown described the instrument in Nature in 1968 Hanbury Brown 1968^[9]. With it, Hanbury Brown, John Davis and Lindsay Allen measured the angular diameters of 32 stars Hanbury Brown, Davis and Allen 1974^[10] Narrabri Stellar Intensity Interferometer, Wikipedia^[8]. Our arithmetic gives the scale: at a wavelength of 440 nm and a 188 m baseline, λ/d ≈ 2.3 × 10⁻⁹ rad, about half a milliarcsecond.

Quick FAQ

Why is the effect so hard to see with ordinary light?

The bunching only lasts for about the coherence time of the light. Our arithmetic for a 1 nm wide band at 500 nm gives a bandwidth of about 1.2 × 10¹² Hz, so a coherence time below a picosecond. Detectors that are slower than that average most of the excess away.

Is the HBT effect used today?

Yes. It is heavily used in quantum optics Hanbury Brown and Twiss effect, Wikipedia^[1], and the same correlations are used to size particle sources in collisions Hanbury Brown and Twiss effect, Wikipedia^[1]. Explore more light designs in our Waves & Optics collection.

References

1. Wikipedia, “Hanbury Brown and Twiss effect”. https://en.wikipedia.org/wiki/Hanbury_Brown_and_Twiss_effect
2. Wikipedia, “Degree of coherence”. https://en.wikipedia.org/wiki/Degree_of_coherence
3. R. Hanbury Brown and R. Q. Twiss (1956), “Correlation between Photons in two Coherent Beams of Light,” Nature 177, 27–29 (DOI 10.1038/177027a0; metadata verified via Crossref). https://doi.org/10.1038/177027a0
4. R. Hanbury Brown and R. Q. Twiss (1956), “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (DOI 10.1038/1781046a0; metadata verified via Crossref). https://doi.org/10.1038/1781046a0
5. Roy J. Glauber (1963), “Photon Correlations,” Physical Review Letters 10, 84–86 (DOI 10.1103/PhysRevLett.10.84; metadata verified via Crossref). https://doi.org/10.1103/PhysRevLett.10.84
6. NobelPrize.org, “The Nobel Prize in Physics 2005”, Nobel Prize Outreach. https://www.nobelprize.org/prizes/physics/2005/summary/
7. T. Jeltes et al. (2007), “Comparison of the Hanbury Brown–Twiss effect for bosons and fermions,” Nature 445, 402–405 (DOI 10.1038/nature05513; metadata verified via Crossref). https://doi.org/10.1038/nature05513
8. Wikipedia, “Narrabri Stellar Intensity Interferometer”. https://en.wikipedia.org/wiki/Narrabri_Stellar_Intensity_Interferometer
9. R. Hanbury Brown (1968), “Stellar Interferometer at Narrabri Observatory,” Nature 218, 637–641 (DOI 10.1038/218637a0; metadata verified via Crossref). https://doi.org/10.1038/218637a0
10. R. Hanbury Brown, J. Davis and L. R. Allen (1974), “The Angular Diameters of 32 Stars,” Monthly Notices of the Royal Astronomical Society 167, 121–136 (DOI 10.1093/mnras/167.1.121; metadata verified via Crossref). https://doi.org/10.1093/mnras/167.1.121

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.