The existence of quantum states of matter in a gravitational field was demonstrated recently in the Institut Laue–Langevin (ILL), Grenoble, in a series of experiments with ultra cold neutrons (UCN). UCN in low quantum states is an excellent probe for fundamental physics, in particular for constraining extra short-range forces; as well as a tool in quantum optics and surface physics. The GRANIT is a follow-up project based on a second-generation spectrometer with ultra-high energy resolution, permanently installed in ILL. It has been constructed in framework of an ANR grant; and will become operational in 2011.
The review covers recent developments on gravitational quantum states of neutrons and the new GRANIT spectrometer, discussed during the Workshop GRANIT-2010 in Les Houches.1The GRANIT facility2includes the spectrometer and the infrastructure needed for its operation. It is constructed at Institut Laue-Langevin (ILL)3in Grenoble for studies of/with gravitational quantum states of neutrons, and for related topics. New methodical developments4are discussed for future upgrades of this facility. An important motivation for this activity consists in constraining fundamental short-range forces.5Other quantum phenomena in gravitational field,6and centrifugal quantum states of neutrons,7were discussed as well. A detailed presentation of all these topics could be found in Workshop-2010 presentations.8We will focus here on instrumental developments and on options for studying neutron gravitational states.
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.
The experiment performed with ultra-cold neutrons at the Laue-Langevin Institute, Grenoble, is analyzed in view of the claim that ``neutron quantum states in Earth gravitational field'' are observed. Our conclusion is that the above claim is neither theoretically nor experimentally substantiated. We also criticize the statement that ``observation of the gravitationally bound quantum states of neutrons and the related experimental techniques provide a unique tool for a broad range of investigations in fundamental physics of particles and fields''.
Observation of neutron gravitational quantum states
En=mgzn in the peV energy range (
z1 is about $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ 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(za), namely, a horizontal flux of relatively fast neutrons ($k\ensuremath{\gg}{k}_{z}$ in wavelength terms) passing through a slit of variable height
za of upper absorbing wall. The quantum states in question are defined by 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(za) and the probability density distribution
P(z,za) 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(za) 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
105 times greater than eigenvalues
En. The latter are related to the neutron transverse mode
kz 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.