A new paper in Science has shown an impressive result of the possibility of causing 3 different photons to be "bound" or entangled with one another after traversing through a cold rubidium atom gas.
In controlled experiments, the researchers found that when they shone a very weak laser beam through a dense cloud of ultracold rubidium atoms, rather than exiting the cloud as single, randomly spaced photons, the photons bound together in pairs or triplets, suggesting some kind of interaction — in this case, attraction — taking place among them.
Now, without going overboard with the superlatives, it must be stressed that this does not occur in vacuum, i.e. 3 photons just don't say hi to one another and decide to hang out together. The presence of the cold rubidium gas is essential for a photon to bound with one of the atoms to form a polariton:
The researchers then developed a hypothesis to explain what might have caused the photons to interact in the first place. Their model, based on physical principles, puts forth the following scenario: As a single photon moves through the cloud of rubidium atoms, it briefly lands on a nearby atom before skipping to another atom, like a bee flitting between flowers, until it reaches the other end.
If another photon is simultaneously traveling through the cloud, it can also spend some time on a rubidium atom, forming a polariton — a hybrid that is part photon, part atom. Then two polaritons can interact with each other via their atomic component. At the edge of the cloud, the atoms remain where they are, while the photons exit, still bound together. The researchers found that this same phenomenon can occur with three photons, forming an even stronger bond than the interactions between two photons.
This has almost the same flavor as the "attraction" between two electrons in a superconductor to form the bound Cooper pairs, which requires a background of lattice ion vibration or virtual phonons to mediate the coupling.
So photons can talk to one another, and in this case, 3 of them can hang out together. They just need a matchmaker as an intermediary, since they are just way too shy to do it on their own.
And with that sugary concoction, I think I need more coffee this morning.
 Q-Y Liang et al., Science v.359, p.783 (2018).