When a neutron beam passes through a slit its transverse motion is quantized, just like a particle in a box. Indeed, for the experimental set-up used by Rauch and co-workers, there are 360 bound states in the potential created by the slit. Levy-Leblond and Greenberger predicted that this quantization in the transverse direction would lead to a phase shift in the longitudinal direction that could be detected with a neutron interferometer. This is what the Vienna-Grenoble team has done.

Rauch and co-workers actually used a silicon multi-slit system consisting of 186 slits - each 22.1 microns wide - to increase the intensity in their experiment. A thermal beam of neutrons from the ILL reactor was converted into a beam with a well-defined neutron energy and this beam was then split into two components. One component passed through the slit system, while the other did not. The two beams were then recombined and the neutron signal was measured as a function of the path difference between the two beams. The measured value of the shift was 2.8 degrees, which was in good agreement with the theoretical prediction of 2.5 degrees.

The phase shift arises mostly from neutrons whose classical trajectories do not touch the walls of the slits, and is therefore another example of the non-local nature of quantum mechanics. Earlier this year another team at the ILL observed quantum motion in a neutron beam in the gravitational potential of the Earth - the first time that quantum motion had been observed in a gravitational potential.