The whispering gallery effect in neutron scattering

GENERAL SCIENTIFIC SUMMARY Introduction and background. Neutron localization in 'centrifugal states' near a curved mirror surface is a quantum analog of the so-called whispering gallery wave. Here, the boundary effective well is formed by the centrifugal effective potential and the neutron-matter optical potential. Such scattering could also be understood in terms of so-called 'quantum bouncer'. The experiment consists of the scattering of cold neutrons at the surface of a well polished cylindrical mirror made of single-crystal silicon. The probability of neutron scattering was measured as a function of the neutron wavelength and the deviation angle.

Main results. We present the first experimental evidence for neutron localization in the quasistationary quantum states, in the whispering gallery wave modes, near a cylindrical mirror surface. Also we present a formalism that describes quantitatively the neutron scattering at a cylindrical mirror surface and compare the experimental results to this model.

Wider implications. Deeply bound centrifugal quantum states may present a kind of precision clock with long lifetime; highly excited states are very sensitive to the precise wall potential shape. Therefore they are a promising tool for studying fundamental neutron-matter interaction, quantum neutron optics and surface physics effects. Measurement of the gravitationally bound and centrifugal quantum states of neutrons could be considered as a first direct confirmation of the weak equivalence principle for a massive particle in a quantum state.

Figure. The neutron count rate is shown as a function of the neutron wavelength (y-axis) and the deviation angle (x-axis). Experimental data.