Scientific Method / Science & Exploration

Hanbury-Brown, Twiss, and a bit of Helium

The bunching of bosons and fermions is directly compared.

Back in the 1950s a pair of Australian physicists used a pair of world war two spotlight reflectors to confound the rest of the physics community. They were interested in measuring the diameters of stars, but in doing so discovered some very fundamental properties of light.

All stars but one are too far away to measure their diameter directly. It is, however, possible to make measurements based on the wave properties of light. Light is collected by two telescopes that are separated from each other. The light from the two is recombined to form a pattern of stripes, which you can think of as correlations between the amplitude of the two different light waves. The stripe pattern can be used to derive the stellar diameter because the light from one edge of the star must travel a different distance compared to light from the opposite edge. In principle, most stellar diameters can be measured, however, the atmosphere adds a random factor and that limits the number of stars successfully measured using this method to about six.

Enter Hanbury-Brown and Twiss. They recognized the difficulties of interferometry based on amplitude, but had performed calculations that suggested an alternative method. They showed that not just the amplitude of the light was correlated, but also the intensity. The significance of this is that the random factor added by the atmosphere, which severely influences the correlation between amplitudes, has no effect on the correlation of intensity. The fantastic part was that a couple of World War II spotlights, a light detector, and chart recorder was all it took to show they were right. Nobody understood this at the time and Hanbury-Brown and Twiss spent a considerable part of the next few years patiently explaining why they were right. Eventually the statistical nature of the problem was revealed to be an essential component of the bosonic nature of light. Bosons like to aggregate into the same state. This means that if you detect one photon, the probability of detecting a second one in the vicinity is much more than would be expected if they were independent. So the intensity correlations that Hanbury-Brown and Twiss were measuring were actually the correlations of the arrival times between photons.

On the other hand fermions do not like to aggregate in the same state, so if you detect one fermion then there is unlikely to be a second one in the vicinity. The trouble is that fermions and bosons are so different that it is difficult to run comparable experiments which demonstrate those differences. This has all changed with the development of laser cooling and magnetic trapping, which can cool metallic vapors down to a few nanoKelvin and provide very fine control over atomic states. Since atoms are either bosons or fermions, depending on how many protons, neutrons, and electrons they consist of, a direct comparison of their behavior can be made. To do this, researchers trapped and cooled 3He (a fermion) and 4He (a boson) down to a few microKelvin. Once cooled, the atoms were released from the trap and allowed to drop onto a detector. The detector recorded the position and time of each atom as it hit, which the researchers used to measure the correlation between atomic arrival times. The result is a beautiful mirror image plot, where the arrival times of fermions at locations near to each other are anti-correlated and become uncorrelated as the locations separate. Likewise, boson's arrival times are correlated at nearby locations and uncorrelated as the locations separate.

Although these measurements aren't surprising, they are a beautiful demonstration of statistics in quantum mechanics. They also gave me ample opportunity to reminisce about one of my favorite topics. The successor to the Hanbury-Brown and Twiss interferometer is here, where you will see that stellar diameter measurements have come full circle.

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