Stefan at Backreaction has a great post up about measuring the quantum state of a bouncing neutron. If you drop a basketball, it falls freely along a geodesic in the curved spacetime around the Earth, until it comes in contact with the floor; at that point it bounces back up and falls freely again. The cycle repeats, although basketballs come with dissipation (otherwise you wouldn’t hear them bounce), so the bounces gradually lose altitude, unless you impart some force to the ball by dribbling.
Well, the same goes for neutrons, except that there isn’t any appreciable dissipation, so the neutrons just keep bouncing. And neutrons are subatomic particles, so we can imagine observing not just their classical position, but their quantum wavefunction! And that’s what people like Valery Nesvizhevsky have been able to do, using interferometry. I won’t explain the details, since Stefan has already done it better than I could, and you should read it there.
So there’s both “quantum” and “gravity” involved here, although not “quantum gravity.” The neutron is quantized, but the effects are just those of a classical background gravitational field. (Quantum gravity would become involved if you measured the gravitational field caused by the neutron, and that’s a bit harder.) But still, you’re observing the effects of spacetime curvature on the wavefunction of a subatomic particle, which is pretty neat. And it’s plausible that someday measurements could improve enough that you’re measuring Newton’s inverse-square law for gravity at very small scales, which is relevant for constraining all sorts of theoretical models. And I’m guessing that you could even test the Equivalence Principle, if you could do the same exact experiment with some other kind of neutral particle (a hydrogen atom, maybe?). But really, it’s just cool, and that’s its own reward.
Also from Backreaction I learned that the current mood of the internet is:
It’s good to be updated on these things.