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Asia Pacific Physics Conference (APPC)

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

Go Ichikawa, S. Komamiya, Yoshio Kamiya

Published Mar 19, 2014• 1 citation
Publisher

Abstract

(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.

DOI
10.7566/jpscp.1.013101

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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.

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(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.
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 studied the neutron quantum states in the potential well formed by the Earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ~25%. A spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1-2 mu m was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen "flow-through" method as well as the feasibility to improve further the accuracy in this experiment
We studied the neutron quantum states in the potential well formed by the Earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ≈25 %. The spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1 μm to 2 μm was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen "flow-through" method as well as the feasibility to improve further the accuracy in this experiment.
In summer 1999 an experiment at ILL, Grenoble was conducted. So-called ultra-cold neutrons (UCN) were trapped in the vertical direction between the Fermi-potential of a smooth mirror below and the gravitational potential of the earth above [Ne00, Ru00]. If quantum mechanics turns out to be a sufficiently correct description of the phenomena in the regime of classical, weak gravitation, one should observe the forming of quantized bound states in the vertical direction above a mirror. Already in a simplified view, the data of the experiment provides strong evidence for the existence of such gravitationally bound quantized states. A successful quantum-mechanical description would then provide a convincing argument, that the socalled first quantization can be used for gravitation as an interaction potential, as this is widely expected. Furthermore, looking at the characteristic length scales of about 10 mikron of such bound states formed by UCN, one sees, that a complete quantum mechanical description of this experiment additionally would enable one to check for possible modifications of Newtonian gravitation on distance scales being one order of magnitude below currently available tests [Ad00]. The work presented here deals mainly with the development of a quantum mechanical description of the experiment.
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.