  The GRANIT project is the follow-up of the pioneering experiments that first
observed the quantum states of neutrons trapped in the earth's gravitational
field at the Institute Laue Langevin (ILL). Due to the weakness of the
gravitational force, these quantum states exhibit most unusual properties: peV
energies and spatial extensions of order 10 $\mu$m. Whereas the first series of
observations aimed at measuring the properties of the wave functions, the
GRANIT experiment will induce resonant transitions between states thus
accessing to spectroscopic measurements. After a brief reminder of achieved
results, the principle and the status of the experiment, presently under
commissioning at the ILL, will be given. In the second part, we will discuss
the potential of GRANIT to search for new physics, in particular to a modified
Newton law in the micrometer range.

Nuclear Experiment;High Energy Physics - Phenomenology