Has there been any experiments, or are there any references, demonstrating gravity between atoms? If so, what are the key experiments/papers? Or if not, what is the smallest thing that has actually experimentally been shown to be affected by gravity?

I don't know of specific papers demonstrating gravity between larger objects, but I can vaguely remember learning about them in my classical physics class as an undergraduate. However, I have never heard of experiments demonstrating gravity at atomic or subatomic levels.

I don't have a physics background so it's not obvious to me, so just looking to see the actual research/evidence behind it, so I can start to try to imagine how gravity works at a quantum level.

Groups in Seattle, Colorado, and perhaps others managed to measure and verify Newton's inverse-square law at submillimeter distances comparable to 0.1 millimeters, see e.g.


  Sub-millimeter tests of the gravitational inverse-square law: A
  search for "large" extra dimensions
  
  Motivated by higher-dimensional theories that predict new effects, we
  tested the gravitational $\frac{1}{r^{2}}$ law at separations ranging down to 218
  micrometers using a 10-fold symmetric torsion pendulum and a rotating
  10-fold symmetric attractor. We improved previous short-range
  constraints by up to a factor of 1000 and find no deviations from
  Newtonian physics.


This is a 14 years old paper (with 600+ citations) and I think that these experiments were very hot at that time because the warped- and large-dimensions models in particle physics that may predict violations of Newton's law had been proposed in the preceding two years. 

But I believe that there's been some extra progress in the field. At that time, the very fine measurement up to 200 microns etc. allowed them to deduce something about the law of gravity up to 10 microns. These are extremely clever, fine mechanical experiments with torsion pendulums, rotating attractors, and resonances. The force they are able to see is really tiny.

To see the gravitational force of a single atom is obviously too much to ask (so far?) – the objects whose gravity is seen in the existing experiments contain billions or trillions of atoms. Note that the (attractive) gravitational force between two electrons is about $10^{45}$ times weaker than the (repulsive) electrostatic one!

Most of the research in quantum gravity has nothing whatever to do with proposals to modify Newton's laws at these distance scales. Indeed, gravity is the weakest force and it's so weak that for all routinely observable phenomena involving atoms, it can be safely neglected. The research in quantum gravity is dealing with much more extreme phenomena – like the evaporation of tiny black holes – that can't be seen in the lab.

Plots and links to new papers available over here (thanks, alemi)
