The search for experimental tests of quantum gravity is on. A few years ago Valery Nesvizhevsky and colleagues found the first hints of quantum gravity involving quantized bound states of neutrons. The potential well used to trap the neutrons was created using the earth's gravitational field, and the researchers reported that as neutrons fell into the well toward the center of the earth, they did not move continuously but rather jumped from one height to another in discrete intervals.
The original paper can be found here:
While string theory and loop quantum gravity get all the attention, there are other approaches being studied. One of these (which I confess I don't know much about) is called non-commutative geometry. I found this interesting paper which builds upon the neutron work, claiming to study non-commutative geometry using this type of experiment: