Quantum mechanics is a realm of weirdness: electrons being linked to each other even though the vastness of the universe might separate them, things being in two places at once, and, of course, knowledge precluding knowledge. This last is the standard bearer of quantum oddity: measuring the momentum of an object precludes precise knowledge of where that object is. But I think I have found something that is stranger than them all.

Researchers have suggested that it might be possible to make measurements that trick a photon into thinking it is, in fact, a crowd of photons.

Let's imagine that we want to introduce a phase shift to one single photon through a control photon. A phase shift is basically a time delay. In traditional optics this delay is applied through high-intensity light beams: a high intensity pulse can modify the refractive index of the medium through which it propagates. Our signal photon traveling through that medium will see that different refractive index and either be delayed or sped up.

The problem is that we want to do this all with single photons, and just one photon does not fit the definition of high intensity.

It seems a bit hopeless, right? However, in quantum mechanics, things are not all that they seem. One type of measurement in particular—called a weak measurement—can give very strange results. For instance, if you measure the spin of an electron using a weak measurement, you can be reasonably certain that you haven't disturbed the spin state of the electron, but, you might get a strange value. Electrons only take on spin values of +1/2 or -1/2, but a weak measurement could return something like 100. So, under the right circumstances, that single electron can behave as if it had the spin effect of 200 electrons.

In our case, we're using two photons. A single control photon goes through a beam splitter where it gets the choice of going through the medium with a signal photon—the one we want to phase shift—or go through a separate channel. These paths are then recombined at another beam splitter, but this beam splitter isn't quite balanced. In a perfectly balanced splitter, the control photon will always exit the beam splitter in the same direction, called the bright port. In an unbalanced beam splitter, it's possible for a photon to sometimes head off in a different direction, called the dark port.

When you calculate the possible ways that a photon could hit a detector looking at the dark port, one of them is that there are simply more photons traveling through the medium with the signal photon than on the path outside the medium. Even better, the closer to balanced the detector is, the rarer the clicks on the detector for the dark port are. So, to get a click, you need a much larger number of photons in the medium with the signal photon. Even if you know you only send in one photon at a time.

In other words, we are measuring the number of photons, but getting an answer that is wrong by several orders of magnitude. The truly weird thing: nature believes us rather than reality.

If we make a weak measurement on the number of photons in the control photon beam, then a single photon is misreported as several hundred. And, if everything is set up correctly—which, in this case, means that we only look for phase shifts on the signal photon when the dark port detector clicks—that lone control photon will have a much larger effect on the refractive index of the medium. The end result is that the phase of the signal photon is shifted by lot more than would normally be expected.

The catch is that this is a work of theory. And the phase shifts, even with this amplification factor, may be really small. Even so, I can imagine that if you chose your medium correctly (say an alkali metal gas), and your wavelengths correctly (right on the edge of an absorption feature of the gas), then it might well be possible to observe the amplification of the phase shift.

Like the Bell inequalities and entanglement, we will have to wait before this can be tested. But, unlike some quantum phenomena, it won't be decades from theory to experiment.

Physical Review Letters, 2011, DOI: 10.1103/PhysRevLett.107.133603