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Observation of the Spatial Distribution of Gravitationally Bound Quantum States of Ultracold Neutrons and Its Derivation Using the Wigner Function

Go Ichikawa, S. Komamiya, Y. Kamiya, Y. Minami, M.Tani, Peter W. Geltenbort, K.Yamamura, M. Nagano, T. Sanuki, Shinsuke KAWASAKI, M.Hino, M.Kitaguchi

Published Jan 1, 2014• 0 citations
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Observation of the Spatial Distribution of Gravitationally Bound Quantum States of Ultracold Neutrons and Its Derivation Using the Wigner Function

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Observation of the Gravitationally Bound Quantum States of Ultracold Neutrons with Submicron Spatial Resolution

Go Ichikawa, S. Komamiya, Yoshio Kamiya

(Received July 14, 2013)Ultracold neutrons (UCNs) have very low kinetic energy, therefore they can be bound by terrestrialgravity above a reflecting mirror. The wave function of the bound state has a characteristic modu-lation. We developed a novel technique of magnifying the UCN distribution using a cylindrical rodas a convex mirror to overcome the current neutron detector resolution of several microns. The ob-served modulation is in good agreement with the prediction. The detector resolution is estimatedto be 0:7 m. This is the first observation of gravitationally bound states of UCNs with submicronspatial resolution.

Asia Pacific Physics Conference (APPC)•Mar 19, 2014•1 citation
Ultracold neutrons (UCNs) can be bound by the potential of terrestrial gravity and a reflecting mirror. The wave function of the bound state has characteristic modulations. We carried out an experiment to observe the vertical distribution of the UCNs above such a mirror at the Institut Laue-Langevin in 2011. The observed modulation is in good agreement with that prediction by quantum mechanics using the Wigner function. The spatial resolution of the detector system is estimated to be 0.7 μm. This is the first observation of gravitationally bound states of UCNs with submicron spatial resolution.
We present a theoretical analysis of the experimental data reported by Ichikawa et al. on the spatial distribution of ultracold neutrons in the Earth’s gravitational field above a mirror. The data involve a projection onto a pixelated detector via scattering by a cylindrical mirror. Our study includes a calculation of the theoretical spatial distribution of the probability density associated with the quantum gravitational states of ultracold neutrons. Furthermore, we analyze this spatial distribution using the Wigner function framework. Based on our analysis, we cannot confirm that the experimental data reported by Ichikawa et al. correspond to the spatial distribution of quantum gravitational states of ultracold neutrons.
(Received July 14, 2013)Ultracold neutrons (UCNs) have very low kinetic energy, therefore they can be bound by terrestrialgravity above a reflecting mirror. The wave function of the bound state has a characteristic modu-lation. We developed a novel technique of magnifying the UCN distribution using a cylindrical rodas a convex mirror to overcome the current neutron detector resolution of several microns. The ob-served modulation is in good agreement with the prediction. The detector resolution is estimatedto be 0:7 m. This is the first observation of gravitationally bound states of UCNs with submicronspatial resolution.