title: Observation of the spatial distribution of gravitationally bound quantum states of ultracold neutrons and its derivation using the Wigner function.
abstract: 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.
authors.affiliation: Department of Physics, Graduate School of Science, and International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: G
authors.initials: G
authors.lastname: Ichikawa
authors.affiliation: Department of Physics, Graduate School of Science, and International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: S
authors.initials: S
authors.lastname: Komamiya
authors.affiliation: Department of Physics, Graduate School of Science, and International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: Y
authors.initials: Y
authors.lastname: Kamiya
authors.affiliation: Department of Physics, Graduate School of Science, and International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: Y
authors.initials: Y
authors.lastname: Minami
authors.affiliation: Department of Physics, Graduate School of Science, and International Center for Elementary Particle Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Tani
authors.affiliation: Institut Laue-Langevin, BP 156, 6, rue Jules Horowitz, 38042 Grenoble Cedex 9, France.
authors.forename: P
authors.initials: P
authors.lastname: Geltenbort
authors.affiliation: Research Center for Ultra-Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan.
authors.forename: K
authors.initials: K
authors.lastname: Yamamura
authors.affiliation: Research Center for Ultra-Precision Science and Technology, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Nagano
authors.affiliation: Department of Physics, Graduate School of Science, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan.
authors.forename: T
authors.initials: T
authors.lastname: Sanuki
authors.affiliation: High Energy Accelerator Research Organization, Institute of Particle and Nuclear Studies, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan.
authors.forename: S
authors.initials: S
authors.lastname: Kawasaki
authors.affiliation: Kyoto University Research Reactor Institute, 2, Asahiro-Nishi, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Hino
authors.affiliation: Department of Physics, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Kitaguchi