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Physics-Uspekhi

Near-surface quantum states of neutrons in the gravitational and centrifugal potentials

Валерий Викторович Несвижевский

Published Oct 11, 2010• 44 citations
Publisher

Abstract

Two related physical phenomena have recently been observed: quantum states of ultracold neutrons (UCN) in the gravitational field above a flat mirror, and quantum states of cold neutrons (CN) in an effective centrifugal potential in the vicinity of a concave mirror. The two phenomena are similar in terms of their associated experimental methods and mathematical representations as well as in terms of their applications in particle physics, quantum optics, and surface physics.

DOI
10.3367/ufne.0180.201007a.0673

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Two related physical phenomena have recently been observed: quantum states of ultracold neutrons (UCN) in the gravitational field above a flat mirror, and quantum states of cold neutrons (CN) in an effective centrifugal potential in the vicinity of a concave mirror. The two phenomena are similar in terms of their associated experimental methods and mathematical representations as well as in terms of their applications in particle physics, quantum optics, and surface physics.
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.
<!--HTML-->We will discuss the scientific program to be studied in a new gravitational spectrometer GRANIT in a broad context of quantum states (quantum behaviour) of ultracold neutrons (UCN) in gravitational [1] and centrifugal [2] potentials, as well as applications of these phenomena/spectrometer to various domains of physics, ranging from studies of fundamental short-range interactions and symmetries to neutron quantum optics and reflectometry using UCN. All these topics, as well as related instrumental and methodical developments have been discussed during dedicated GRANIT-2010 Workshop [3]. The GRANIT spectrometer has been recently installed at the Institut Laue-Langevin, Grenoble, France [4] and could become operational in near future. 1. V.V. Nesvizhevsky et al (2002), Nature 415, 297. 2. V.V. Nesvizhevsky et al (2010), Nature Physics 6, 114. 3. GRANIT-2010, Les Houches, 14-19 february 2010. 4. M. Kreuz et al (2009), NIM 611, 326.
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 ..
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.
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.