In a surprising discovery, researchers in Belgium found instances where photon bunching is substantially strengthened—instead of weakened—by making photons partially distinguishable via a well-chosen polarization pattern in an interferometer (see video).

The work was led by Nicolas J. Cerf, a professor of quantum mechanics and information theory, as well as director of the Centre for Quantum Information and Communication at the Université Libre de Bruxelles, with Benoît Seron, a Ph.D. student, and Leonardo Novo, a postdoc.

“As quantum physicists, we’re always intrigued by the quantum features exhibited by light,” says Cerf. “Quantum physics is known for giving rise to a number of surprising phenomena, which often challenge our classical intuition. One example is the fact that photons have a natural propensity to coalesce, a.k.a. photon bunching, which is particularly interesting.”

### What is photon bunching?

Light may behave either as a stream of photons or as an electromagnetic wave, according to the complementary principle of quantum mechanics. “The photoelectric effect, for example, is a manifestation of the former behavior, while interference phenomena follow from the latter,” says Cerf.

Because it’s caused by interference, photon bunching is a peculiar consequence of the wave-like behavior of light (see Fig. 1). It can be observed when two photons impinge, each on one side of a half-transparent mirror that splits the incoming beam into a reflected beam and a transmitted beam.

“The celebrated Hong-Ou-Mandel effect teaches us that the two photons always exit on the same side of the mirror, as if bound to each other,” Cerf says. “This actually results from a destructive interference between the photons being both reflected and transmitted—and the net result is they simply can’t be observed separated, each on one side of the mirror.”

It’s well established that if the trajectories of the photons in an interferometer are observed, then everything unfolds as if dealing with classical particles—and all interference effects disappear.

“This can, for example, be verified if the two photons in the Hong-Ou-Mandel experiment have different polarizations, so we can distinguish them and trace back which path each one has taken,” says Cerf. “In this case, the two photons don’t bunch anymore. By extension, in a general scenario involving many photons, it’s commonly assumed that the same rule prevails so that bunching must be maximum for fully indistinguishable photons and gradually decline when photons become increasingly distinguishable. We’ve found that against all odds, this assumption is wrong.”

### Surprising discovery

Cerf and his team were extremely surprised to discover that an interferometric setup (see Fig. 2) involving seven photons with a well-chosen polarization pattern can be found that contradicts this rule in quantum photonics.

“The probability that all seven photons bunch into two output modes is higher if they are made partially distinguishable via their polarization, compared to the ideal case where all photons have the same polarization and are then precisely indistinguishable,” Cerf explains. “Bunching excess is about 7%, which isn’t very high but is enough to disprove what seemed to be an obvious rule in quantum photonics.”

At first, the researchers didn’t believe their findings. “But after rethinking our calculations, we became convinced it had to be the logical consequence of a weird property of the permanent of matrices—it was a shocking result,” Cerf says.

Their trick was to exploit a connection between photon bunching, which involves the fact that photons are particles called bosons, and the mathematical theory of permanents. “The permanent of a matrix is akin to its much better known determinant, but unlike the latter, it still has a number of properties that are only assumed today and not actually proven,” Cerf adds.

Amazingly, old assumptions about permanents can sometimes be disproven by mathematicians—and it’s precisely what the researchers exploited. “A recently found counterexample to an assumption dated to 1984 is the key element we used to prove it’s possible to further enhance photon bunching by fine-tuning the polarization of the photons, leading to anomalous photon bunching,” says Cerf.

### Implications for quantum computing

Beyond being valuable for the fundamental physics of photon interference, a better understanding of the subtleties of photon bunching should be helpful for quantum computation.

“Recent experiments aimed at building an optical quantum computer have reached an unprecedented level of control, and a possible application of bunching within this context could be to validate the quantum operation of such a computer and prove its computational advantage over the best supercomputers,” Cerf says.

And one of the next steps for the team will be “to open the way to an experimental demonstration of this anomalous bunching phenomenon,” Cerf says. “Our proposed method seems to be at the edge of photonic technologies, which have shown fast progress during recent years. Experiments are now run in which many photons are created, interfered via complex optical circuits, and counted with photon-number resolving detectors. So we’re firmly hoping an anomalous bunching experiment will be set up, but we’re a team of theorists.”

On the theory side, the researchers are further analyzing the mechanism of anomalous bunching, trying to see how the bunching excess depends on the setup and can be made bigger. “Furthermore, other assumptions about permanents have been disproven, so we’re naturally exploring whether there could be other unexpected ramifications in quantum photonics,” Cerf says.

**FURTHER READING**

B. Seron, L. Novo, and N. J. Cerf, *Nat. Photon.* (2023); https://doi.org/10.1038/s41566-023-01213-0.