The Colored Hanbury Brown–Twiss Effect

The Colored Hanbury Brown–Twiss Effect

Article: published in Scientific Reports by E. del Valle and Fabrice P. Laussy, IFIMAC researchers.

Hanbury Brown was a young British engineer working on the secret development of the radar as part of the British war effort. When he noticed that radar signals detected by different antennas produced wiggles on the oscilloscopes that were clearly correlated in shape, he got the idea to use this fact for a new type of “intensity” interferometry. This would allow to use very long baselines (distance between the detectors) which is directly related to the interferometer’s precision. As such his idea would go much beyond the precision of the standard amplitude interferometers. This wonderful insight was correct and the idea was used in radio-astronomy.

Hanbury Brown then proposed to use this effect in the optical domain. While completely correct on logical grounds, it was however (correctly) perceived as photon-interferences, which were then deemed impossible (one famous preconception was Dirac’s textbook statement: “each photon interferes only with itself. Interference between different photons never occurs.”) This caused a lot of opposition from famous scientists of the time, until more careful analysis and the persistence of Hanbury Brown (joined by Twiss to formalize the underlying maths) led to recognition of the Hanbury Brown–Twiss (HBT) effect: two photons coming from different sources, possibly different stars from different galaxies, tend to arrive together on the detector, in a peculiar and counter-intuitive fashion known as “bunching”. This occurs for indistinguishable photons, i.e., with the same characteristics (frequency, polarization, etc.), from thermal sources. These results were in fact the basis for Glauber to formalize the theory of quantum optics, for which he was awarded the Nobel prize in 2005, and served as the foundation for the classification of different types of light: those that occur naturally around us (the thermal sources already mentioned) but also the laser, that cancel the bunching effect to provide uncorrelated photons, and a hot topic of contemporary physics: quantum sources, that produce photons behaving like electrons, that is, avoiding each other. This finding has been one of the revolution of sciences, although it tends to be overlooked as being ultimately subtle and still counter-intuitive. In particular, it gave a whole new meaning to the important concept of “coherence”.

Recently, in Scientific Reports, we have observed the HBT effect for photons that were also tagged in frequency, that is, instead of recording only the arrival time, we also kept track of their energy (linked to the frequency through the Planck constant). We then analyzed the HBT correlations between all possible combination of frequencies, thereby turning the HBT number into a landscape, the so-called two-photon spectrum. There we observed that the photon correlations have built-in the structure that they can exhibit as a whole, namely, photons of the same frequency are positively correlated (bunched) while photon of opposite frequency as compared to the mean are negatively correlated (antibunched). This is a generic property for all types of light, and we have called it for this reason the “boson form factor”. It subtends the correlations upon detection for any optical field. For instance, while photons from a thermal source tend to be detected together, those that are detected with mismatched frequency because of some fluctuations, are less so bunched than the average. Those of the same frequency are more bunched. For photons from a single-photon source, the anticorrelation is also more pronounced for distinct frequencies and less so for identical frequencies, going against the general trend of avoiding each others.

The most striking manifestation of the boson form factor is for coherent light, i.e., that from a laser, where photons have no correlations at all. But keeping their frequency, on the other hand, reveals bunching of same-frequency photons, like thermal sources, and antibunching of opposite-frequency-photons, like quantum sources. We have used a polariton condensate, that emits coherent light, to observe this effect in its most striking manifestation. It is shown in the figure (the diagonal shows identical frequencies while the antidiagonal those that are different, with color code red for bunching, blue for antibunching and white for uncorrelated). The effect can also be described theoretically, by following the standard procedure but retaining the frequency throughout. We have provided both a classical and quantum description, as the effect can be explained from these two points of view.

In conclusion, it is both beautiful and elegant that the HBT correlations are modulated in this way through an internal structure that can be revealed by frequency-resolving. This is an intrinsic correlation of detected photons that subtends all types of dynamics, including more complicated systems, that can sculpt correlations of a much more intricate character through a variety of nonlinear processes. In all cases, still, the HBT effect is there, bringing photons closer together when having the same frequency or pushing them apart when having opposite frequencies. We have termed this extension of one of the most important experiments of contemporary optics: the colored Hanbury Brown–Twiss effect. [Full article]