We propose to test the law of gravitation at small distances by quantum interference deep into the theoretically interesting regime of 1000 times gravity. The idea is to explore a unique system consisting of a particle, the neutron, and a macroscopic object, the mirror, and its precise measurement of quantum de Broglie phases. This will be done for the first time by an application of Ramsey’s method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. Such measurements with ultra-cold neutrons will offer a sensitivity to Newton’s law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism. Our approach explores therefore a region of parameter space that is complementary to the supermicron reach of upcoming microcantilever and torsion balance experiments.
