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Title: Quantum motion of a neutron in a waveguide in the gravitational field

Abstract

We study theoretically the quantum motion of a neutron in a horizontal waveguide in the gravitational field of the Earth. The waveguide in question is equipped with a mirror below and a rough surface absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are determined mainly by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing waveguide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in the Earth's gravitational field.

Authors:
; ; ; ; ; ;  [1];  [2];  [2];  [3];  [4];  [5]
  1. P.N. Lebedev Physical Institute, 53 Leninsky prospekt, 119991, Moscow (Russian Federation)
  2. (Germany)
  3. (ILL), 6 rue Jules Horowitz, F-38042, Grenoble (France)
  4. (LPSC), IN2P3-CNRS, UJFG, 53, Avenue des Martyrs, F-38026, Grenoble (France)
  5. (Italy)
Publication Date:
OSTI Identifier:
20776767
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044029; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FILTERS; GRAVITATIONAL FIELDS; MIRRORS; NEUTRONS; POTENTIALS; SURFACES; WAVEGUIDES

Citation Formats

Voronin, A.Yu., Abele, H., Baessler, S., Nesvizhevsky, V.V., Petukhov, A.K., Protasov, K.V., Westphal, A., Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg, Institut of Physics, University of Mainz, 55099 Mainz, Institut Laue-Langevin, Laboratoire de Physique Subatomique et de Cosmologie, and ISAS-SISSA and INFN, Via Beirut 2-4, I-34014 Trieste. Quantum motion of a neutron in a waveguide in the gravitational field. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.044029.
Voronin, A.Yu., Abele, H., Baessler, S., Nesvizhevsky, V.V., Petukhov, A.K., Protasov, K.V., Westphal, A., Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg, Institut of Physics, University of Mainz, 55099 Mainz, Institut Laue-Langevin, Laboratoire de Physique Subatomique et de Cosmologie, & ISAS-SISSA and INFN, Via Beirut 2-4, I-34014 Trieste. Quantum motion of a neutron in a waveguide in the gravitational field. United States. doi:10.1103/PhysRevD.73.044029.
Voronin, A.Yu., Abele, H., Baessler, S., Nesvizhevsky, V.V., Petukhov, A.K., Protasov, K.V., Westphal, A., Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg, Institut of Physics, University of Mainz, 55099 Mainz, Institut Laue-Langevin, Laboratoire de Physique Subatomique et de Cosmologie, and ISAS-SISSA and INFN, Via Beirut 2-4, I-34014 Trieste. Wed . "Quantum motion of a neutron in a waveguide in the gravitational field". United States. doi:10.1103/PhysRevD.73.044029.
@article{osti_20776767,
title = {Quantum motion of a neutron in a waveguide in the gravitational field},
author = {Voronin, A.Yu. and Abele, H. and Baessler, S. and Nesvizhevsky, V.V. and Petukhov, A.K. and Protasov, K.V. and Westphal, A. and Physikalisches Institut der Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg and Institut of Physics, University of Mainz, 55099 Mainz and Institut Laue-Langevin and Laboratoire de Physique Subatomique et de Cosmologie and ISAS-SISSA and INFN, Via Beirut 2-4, I-34014 Trieste},
abstractNote = {We study theoretically the quantum motion of a neutron in a horizontal waveguide in the gravitational field of the Earth. The waveguide in question is equipped with a mirror below and a rough surface absorber above. We show that such a system acts as a quantum filter, i.e. it effectively absorbs quantum states with sufficiently high transversal energy but transmits low-energy states. The states transmitted are determined mainly by the potential well formed by the gravitational field of the Earth and the mirror. The formalism developed for quantum motion in an absorbing waveguide is applied to the description of the recent experiment on the observation of the quantum states of neutrons in the Earth's gravitational field.},
doi = {10.1103/PhysRevD.73.044029},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 73,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • No abstract prepared.
  • Observation of neutron gravitational quantum states E{sub n}=mgz{sub n} in the peV energy range (z{sub 1} is about 10 {mu}m in the vertical direction) in the experiment conducted at Laue-Langevin Institute, Grenoble, with ultracold neutrons was recently reported in a series of publications. The purpose of the present work is to analyze the experiment. The experimental apparatus is designed to measure a transmission function T(z{sub a}), namely, a horizontal flux of relatively fast neutrons (k>>k{sub z} in wavelength terms) passing through a slit of variable height z{sub a} of upper absorbing wall. The quantum states in question are defined bymore » the so-called Airy functions, which are solutions to the stationary 1D equation for a neutron 'bouncing' above the perfect mirror in a linear potential field. The Airy functions describe the quantum bouncer (QB), the concept of which is subject to theoretical study of toy 1D models of gravitationally bound particles in nonrelativistic quantum mechanics (QM). This is essentially different from the 3D nonstationary QM object, 'the running QB', investigated in the experiment. The authors assume that there is a connection between T(z{sub a}) and the probability density distribution P(z,z{sub a}) for QB states. They devised the 'phenomenological model', in which the quantum pattern should be visible in the transmission curve. We argue, however, that the measured curve T(z{sub a}) is not sensitive to QB states. Instead, it is sensitive to dynamics of neutron horizontal transport inside the absorbing slit for neutrons of energy values about 10{sup 5} times greater than eigenvalues E{sub n}. The latter are related to the neutron transverse mode k{sub z} and cannot be termed ''energies of neutron gravitational quantum states.'' We conclude that the experiment setup and real conditions are not adequate to the claimed objective, and the methodology of measured data treatment is flawed. The authors' claim that 'neutron gravitational quantum states are observed' is neither theoretically nor experimentally substantiated. Final, statistically significant results of the experiment are consistent with our physical reasoning that the experiment is not sensitive to 'neutron gravitational quantum states' (in terms of Airy mode) and does not prove even their existence in rigorous quantum-mechanical terms.« less
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