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Advances in High Energy Physics

Quantized Ultracold Neutrons in Rough Waveguides: GRANIT Experiments and Beyond

M. Escobar, A. E. Meyerovich

Published Jan 1, 2014• 4 citations
Publisher

Abstract

We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.

DOI
10.1155/2014/185414

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GRAVITATIONAL QUANTUM STATES OF NEUTRONS AND THE NEW GRANIT SPECTROMETER

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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.

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We apply our general theory of transport in systems with random rough boundaries to gravitationally quantized ultracold neutrons in rough waveguides as in GRANIT experiments (ILL, Grenoble). We consider waveguides with roughness in both two and one dimensions (2D and 1D). In the biased diffusion approximation the depletion times for the gravitational quantum states can be easily expressed via each other irrespective of the system parameters. The calculation of the exit neutron count reduces to evaluation of a single constant which contains a complicated integral of the correlation function of surface roughness. In the case of 1D roughness (random grating) this constant is calculated analytically for common types of the correlation functions. The results obey simple scaling relations which are slightly different in 1D and 2D. We predict the exit neutron count for the new GRANIT cell.
We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.
A comprehensive theory of gravitational quantum states of ultracold neutrons in a rough waveguide is presented. The theory covers recent experiments in which the ultracold neutrons were beamed between a mirror and a rough scatterer and absorber. The results are in very good agreement with experimental data. The analysis is based on a recently developed theory of quantum transport in waveguides with rough absorbing and scattering walls. The calculation is done using two methods: an exact transport equation and a simplified model of biased scattering-driven diffusion of neutrons between quantum states. Both sets of results are in excellent agreement with each other. The exit neutron count is sensitive to the amplitude and the correlation radius (lateral size) of surface inhomogeneities and to the overall time of flight (length of the waveguide). The results indicate that it is possible to choose the waveguide parameters in such a way so to observe the quantum size effect in neutron count---the quantum steps that correspond to individual quantum states---even in a weak roughness regime. Away from the obvious limiting cases, the results are not very sensitive to the ratio of the particle energy to the absorption threshold. The main unresolved issue, which is related to a complexity of required calculations for a ``real'' experimental cell, is the lack of accurate information on the occupation numbers of neutrons entering the waveguide. Our analysis indicates that the initial occupancies of all gravitational states are expected to be the same except for the smallest values of the waveguide width.
A theory of gravitational quantum states of ultracold neutrons in waveguides with absorbing/scattering walls is presented. The theory covers recent experiments in which the ultracold neutrons were beamed between a mirror and a rough scatterer/absorber. The analysis is based on a recently developed theory of quantum transport along random rough walls which is modified in order to include leaky (absorbing) interfaces and, more importantly, the low-amplitude high-aperture roughness. The calculations are focused on a regime where the direct transitions into the continuous spectrum above the absorption threshold dominate the depletion of neutrons from the gravitational states and are more efficient than the processes involving the intermediate states. The theoretical results for the neutron count are sensitive to the correlation radius (lateral size) of surface inhomogeneities and to the ratio of the particle energy to the absorption threshold in the weak-roughness limit. The main impediment for observation of the higher gravitational states is the ``overhang'' of the particle wave functions which can be overcome only by using scatterers with strong roughness. In general, strong roughness with high amplitude is preferable if one wants just to detect the individual gravitational states, while strong-roughness experiments with small amplitude and high aperture are preferable for the quantitative analysis of the data. We also discuss ways to further improve the accuracy of calculations and to optimize the experimental regime.
<!--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 bouncing neutron is one of the rare system where gravity can be studied in a quantum framework. To this end it is crucial to be able to select some specific gravitational quantum state (GQS). The GRANIT apparatus is the first physics experiment connected to a superthermal helium UCN source. We report on the methods developed for this instrument showing how specific GQS can be favored using a step between mirrors and an absorbing slit. We explore the increase of GQS separation efficiency by increasing the absorber roughness amplitude, and find it is feasible but requires a high adjustment precision. We also quantify the transmission of the absorbing slit leading to a measurement of the spatial extension of the neutron vertical wave function z0=ℏ2/3(2m2g)−1/3=5.9±0.3 μz_0 = \hbar^{2/3}\left(2m^2g\right)^{-1/3} = 5.9\pm0.3\,μz0​=ℏ2/3(2m2g)−1/3=5.9±0.3μm.
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.