I've always wondered if it's possible to bind two photons, in particular by gravitational interaction. Photons don't have a rest mass, but do nevertheless have a gravitational mass, by which they can attract each other. However, I can't imagine a bound state. My intuition of special relativity goes against it. Is it possible at all? Can photons at least bend each other's trajectories?
Interactions of other kinds (non gravitational) are also an acceptable answer, but I'm not interested in (if they exist) effective interactions in matter.