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.
Quantum states in the Earth's gravitational field were observed, when ultra-cold neutrons fall under gravity. The experimental results can be described by the quantum mechanical scattering model as it is presented here. We also discuss other geometries of the experimental setup which correspond to the absence or the reversion of gravity. Since our quantum mechanical model describes, particularly, the experimentally realized situation of reversed gravity quantitatively, we can practically rule out alternative explanations of the quantum states in terms of pure confinement effects.
In the paper by Nesvizhevsky et al. [Phys. Rev. D 67, 102002 (2003)], it is argued that the lowest quantum state of neutrons in the Earth's gravitational field has been experimentally identified. While this is most likely correct, it is imperative to investigate all alternative explanations of the result in order to close all loopholes, as it is the first experiment ever claimed to have observed gravitational quantum states. Here we show that geometrical effects in the experimental setup can mimic the results attributed to gravity. Modifications of the experimental setup to close these possible loopholes are suggested.
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.
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.