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arXiv:1806.02409 · Physical Review A

Diffraction of particles in free fall

David Condado, J. Lorenzo Díaz-Cruz, A. Rosado, Emerson Sadurní

Published Oct 15, 2018• 0 citations
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Abstract

The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasitime $\ensuremath{\tau}$ given by a function of the coordinate along the propagation axis in a classical combination ${z}_{0}\ensuremath{-}{t}^{2}F/m$, while the diffraction effects along transverse axes are due solely to $m/\ensuremath{\hbar}$. The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultracold neutrons, Bose-Einstein condensates, and molecular beams are proposed.

DOI
10.1103/physreva.98.043618

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The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the resulting patterns depend on a quasitime \ensuremathτ\ensuremath{\tau}\ensuremathτ given by a function of the coordinate along the propagation axis in a classical combination z0\ensuremath−t2F/m{z}_{0}\ensuremath{-}{t}^{2}F/mz0​\ensuremath−t2F/m, while the diffraction effects along transverse axes are due solely to m/\ensuremathℏm/\ensuremath{\hbar}m/\ensuremathℏ. The consequences on the precision at which the equivalence principle can be tested are discussed. Realizations with ultracold neutrons, Bose-Einstein condensates, and molecular beams are proposed.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments have been explained by some theoretical works. We study electronic double-slit diffraction with a quantum mechanical approach and obtain the following results: (1) When the ratio of ( d + a )/ a = n ( n = 1,2,3,…), orders n ,2 n ,3 n ,… are missing in diffraction pattern. (2) When the ratio of ( d + a )/ a ≠ n ( n = 1,2,3,…), there is not missing order in diffraction pattern. (3) The slit thickness c has a large affect on the electronic diffraction pattern, which is a new quantum effect. We believe that all the predictions in our work can be tested by the electronic double slit diffraction experiment.
The authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons ($\ensuremath{\lambda}\ensuremath{\approx}2$ nm) at single- and double-slit assemblies of dimensions in the 20-100 \ensuremath{\mu}m range. Their experimental results show all predicted features of the diffraction patterns in great detail. Particularly, their double-slit diffraction experiment is its most precise realization hitherto for matter waves.
It is proved that for a double slit diffraction experiment,superposition principle of probability amplitudes means the probability amplitude of the event that an electron passes through a certain slit and falls on somewhere of the screen has nothing to do with the condition whether or not the other slit is open,from which it is concluded that the probability itself does not obey superposition principle.Consequently,the total probability formula as a relation among the measurable probabilities is invalid herein.As a result,it is unnecessary to give up the classical idea that an electron moves along an orbit,and thereby it is unnecessary to distinguish between classical physics and quantum physics.
Phenomena of electron, neutron, atomic and molecular diffraction have been studied in many experiments, and these experiments are explained by many theoretical works. We study neutron single-slit diffraction with a quantum mechanical approach. It is found that the obvious diffraction patterns can be obtained when the single-slit width a is in the range of 3λ~60λ. We also find a new quantum effect of the thickness of single-slit which can make a large impact on the diffraction pattern. The new quantum effect predicted in our work can be tested by the neutron single-slit diffraction experiment.
In the early 1900s more and more experimental evidence was accumulated indicating that microscopic particles show wave-like properties in certain situations. These particle-wave features are very evident, e.g., in measurements where electrons are diffracted from a double slit to propagate toward a screen where they are detected. Based on the classical averaging of particles discussed in Section 1.2.2, one expects that the double slit only modulates the overall intensity, not the spatial distribution. Experimentally, however, one observes a nearly perfect interference pattern at the screen implying that the electrons exhibit wave averaging features such as discussed in Section 2.1.2. This behavior, originally unexpected for particle beams, persists even if the experiment is repeated such that only one electron at a time passes the double slit before it propagates to the detection screen. Thus, the wave aspect must be an inherent property of individual electrons and not an ensemble effect. Another, independent argument for the failure of classical physics is that the electromagnetic analysis of atoms leads to the conclusion that the negatively charged electron(s) should collapse into the positively charged ion because the electron–ion system loses its energy due to the emission of radiation. As we will see, this problem can be solved by including the wave aspects of particles into the analysis. In particular, as discussed in Section 2.3.3, waves can never be localized to a point without increasing their momentum and energy beyond bounds.
We studied electron single-slit,double-slit and three-slit diffraction with a new quantum mechanics approach and obtained the following results.(1) For single-slit diffraction,the thickness of the single-slit can make a large impact on the diffraction intensity and pattern.(2) For double-slit diffraction,when the ratio of(a+d)/a=n(n=1,2,3,…),orders n,2n,3n,… are missing in diffraction pattern,when the ratio of(a+d)/a≠n(n=1,2,3,…),there isn't missing order in diffraction pattern.(3) For double-slit diffraction,it can be found that when the thickness of the double-slit increases,the diffraction intensity and pattern will be changed,and when the thickness of the double-slit increases,the missing order phenomena disappear.(4) For three-slit diffraction,when the thickness of the slit increases,the diffraction intensity and pattern will be changed,and there is one secondary maxima and two minima between the two principle maxima.