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arXiv:0806.3871 · Physical Review A

Centrifugal quantum states of neutrons

Валерий Викторович Несвижевский, Alexander K. Petukhov, Konstantin V. Protasov, Alexei Yu. Voronin

Published Sep 23, 2008• 41 citations
arXivHTMLPDF

Abstract

We propose a method for observation of the quasistationary states of neutrons localized near a curved mirror surface. The bounding effective well is formed by the centrifugal potential and the mirror Fermi potential. This phenomenon is an example of an exactly solvable ``quantum bouncer'' problem that can be studied experimentally. It could provide a promising tool for studying fundamental neutron-matter interactions, as well as quantum neutron optics and surface physics effects. We develop a formalism that describes quantitatively the neutron motion near the mirror surface. The effects of mirror roughness are taken into account.

DOI
10.1103/physreva.78.033616

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We propose a method for observation of the quasistationary states of neutrons localized near a curved mirror surface. The bounding effective well is formed by the centrifugal potential and the mirror Fermi potential. This phenomenon is an example of an exactly solvable ``quantum bouncer'' problem that can be studied experimentally. It could provide a promising tool for studying fundamental neutron-matter interactions, as well as quantum neutron optics and surface physics effects. We develop a formalism that describes quantitatively the neutron motion near the mirror surface. The effects of mirror roughness are taken into account.
Two related physical phenomena have recently been observed: quantum states of neutrons in the gravitational field above a flat mirror, and quantum states of neutrons in an effective centrifugal potential in the vicinity of a concave mirror. It is curious that the measurement of the near-surface quantum states of these two types is the first direct demonstration of the weak equivalence principle for a massive object in a quantum state. These two phenomena and their application to various domains of science will be explored using a new GRANIT spectrometer, which is under commissioning in the Institut Laue-Langevin, Grenoble, France. Most recent advances in these domains are mentioned.
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 SiO 2 concave mirror using a pulsed cold neutron beam. The measured results agree with theoretical calculations within 1.9% for the centrifugal acceleration a ≈ 7 × 10 7 m / s 2 , 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 1 × 10 − 4 , which is two orders of magnitude better than the above agreement.
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.
Neutrons not only fall classically in the gravitational field of the Earth as potatoes and other normal objects do; at certain conditions, they reveal quantum behavior, or even form well­ defined gravitational quantum states. Due to the relative simplicity of quantum mechanical rules for solving this problem, we could predict analytically the motion of a neutron in a grav­ itational field in the vicinity of a reflecting surface. Such a bouncing neutron can have only certain, discrete values of energy. These extremely small energy values turn out to be very sensitive probes to the presence of even tiny extra interactions, in particular those between the neutron and the mirror. Moreover, several emerging fields of research profit from experi­ ence and knowledge gained in the recent experimental observation of gravitational quantum states of ultracold neutrons, and extend the developed methods to atoms and anti-atoms, to whispering-gallery effect and other domains, thus providing more and more application for the method. Quantum bouncing particles could play their role in quantum tests of the equivalence principle, in explorations of gravitational properties of antimatter, in searching for new funda­ mental short-range and other interactions beyond the Standard Model of particle physics, in surface and thin-layer physics, in chemistry, and so on. In this short note we mention results of a few previous years and project nearest developments ..
The ‘whispering gallery’ effect has been known since ancient times for sound waves in air, later in water and more recently for a broad range of electromagnetic waves: radio, optics, Roentgen and so on. It is intensively used and explored due to its numerous crucial applications. It consists of wave localization near a curved reflecting surface and is expected for waves of various natures, for instance, for neutrons and (anti)atoms. For (anti)matter waves, it includes a new feature: a massive particle is settled in quantum states, with parameters depending on its mass. In this talk, we present the first observation of the quantum whispering-gallery effect for matter particles (cold neutrons) 1-2. This phenomenon provides an example of an exactly solvable problem analogous to the ‘quantum bouncer’; it is complementary to recently discovered gravitational quantum states of neutrons3. These two phenomena provide a direct demonstration of the weak equivalence principle for a massive particle in a quantum state. Deeply bound long-living states are weakly sensitive to surface potential; highly excited short-living states are very sensitive to the wall nuclear potential shape. Therefore, they are a promising tool for studying fundamental neutron–matter interactions, quantum neutron optics and surface physics effects. Analogous phenomena could be measured with atoms and anti-atoms 4-5.