Measurement of Neutron Whispering Gallery States Using a Pulsed Neutron Beam

A neutron whispering gallery state is a quantum state localized on a material surface bound by the centrifugal force and the material potential. Precise measurements of such quantum states enable tests of quantum mechanics in non-inertial frames, characterization of the surface potential, and searches for hypothetical short-range interactions at the nanometer scale. We observed a neutron whispering gallery state on a ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$ concave mirror using a pulsed cold neutron beam. The measured results agree with theoretical calculations within $1.9\mathrm{\%}$ for the centrifugal acceleration $a\approx 7\times {10}^7\mathrm{m}\mathrm{/}{\mathrm{s}}^2$, which is due to unmodeled deviations of the shape of the concave mirror edge from an ideal one. We found that the sensitivity itself was $1\times {10}^{-4}$, which is two orders of magnitude better than the above agreement.