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 noninertial 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>SiO</a:mi><a:mn>2</a:mn></a:msub></a:math> concave mirror using a pulsed cold neutron beam. The measured results agree with theoretical calculations within 1.9% for the centrifugal acceleration <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>a</c:mi><c:mo>≈</c:mo><c:mn>7</c:mn><c:mo>×</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mn>7</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi mathvariant="normal">m</c:mi><c:mo>/</c:mo><c:msup><c:mrow><c:mi mathvariant="normal">s</c:mi></c:mrow><c:mrow><c:mn>2</c:mn></c:mrow></c:msup></c:mrow></c:math>, 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>1</g:mn><g:mo>×</g:mo><g:msup><g:mn>10</g:mn><g:mrow><g:mo>−</g:mo><g:mn>4</g:mn></g:mrow></g:msup></g:math>, which is two orders of magnitude better than the above agreement.