The GRANIT project is the follow-up of the pioneering experiments that first observed the quantum states of neutrons trapped in the earths 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.
