Welcome to PF;
Nobody knows how fundamental particles interact gravitationally - such a model would be a theory of quantum gravity. Gravity is usually treated as a perturbation or neglected entirely - since our best models so far have the effect as so much smaller than pretty much everything else on that scale.
However - as you surmise, it is a field of active research at a range of scales.
i.e. See:
Greenberger, D. M.; Overhauser, A. W.
The role of gravity in quantum theory; Scientific American, vol. 242, May 1980, p. 66-76.
Experiments with a neutron interferometer demonstrating the effects of gravitational fields on the quantum mechanical wave properties of subatomic particle are discussed. The principles of the neutron interferometer, which is usually composed of a single crystal of silicon, are presented, and an experiment carried out to measure the effects of Earth's gravity on the phase of the neutron is presented. Results indicating that a weak gravitational field shifts the phase of a neutron wave by the amount predicted by the Schroedinger equation are noted, and the implications of these results for the interpretation of the equivalence principle in quantum mechanics are considered. Other neutron interferometer experiments revealing the effects of Earth and particle rotation on the phase and sign of the neutron wave function, respectively, are presented, and the significance of the experimental results to grand unification theories is assessed.
Abelea, H. Jenkea, T. et al;
QuBounce: the dynamics of ultra-cold neutrons falling in the gravity potential of the Earth; Nuclear Physics A, Volume 827, Issues 1–4, 15 August 2009, Pages 593c–595c; http://dx.doi.org/10.1016/j.nuclphysa.2009.05.131
The dynamics of a quantum mechanical wave packet bouncing off a hard surface in the gravitational field of the Earth combines quantum theory with aspects of Newtonian mechanics at short distances. We realize such a quantum bouncing ball with ultracold neutrons. By quantum interference, this experiment is sensitive to gravity-like forces at a length scale below 10 μm and can test speculations on large extra dimensions of submillimeter size of space-time or the origin of the cosmological constant in the universe.
Also found this thing
Rioux F.
Evidence for Quantized Gravitational States of the Neutron Department of Chemistry
St. John's University/College of St. Benedict (self published)
http://www.users.csbsju.edu/~frioux/neutron/neutron.htm
... no idea how good it is - appears to relate to the previous cited.
Includes additional references at the bottom.
That should be enough to refine your search.