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An examination of the use of wave packets for the calculation of atom diffraction by surface

Bret Jackson, Horia I. Metiu

Published Mar 1, 1985• 0 citations
OpenAlex

Abstract

The authors use analytic models valid for neutron scattering and numerical calculations to examine a method proposed by Drolshagen and Heller for computing atom diffraction from surfaces. Our main concern is the manner in which the use of narrow packets causing a partial coherence of the incident beam, might affect the diffracted intensity. We find that the demands of representing beam coherence correctly conflict with the requirements for the validity of the propagation scheme. We suggest some improvements that should increase the reliability of the method without affecting greatly its remarkable computational and conceptual advantages.

Related papers

Temperature dependence of diffracted-beam intensities in atom-surface scattering. Annual technical report

Bret Jackson, Horia I. Metiu

We develop a new method for the calculation of the atom scattering analog of the Debye-Waller factor. Unlike x-ray and neutron scattering, the properties of an atom scattered by a solid surface cannot be computer by perturbation theory, therefore the simple Debye-Waller theory cannot be applied. Nevertheless the Debye-Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.

•Mar 1, 1985•0 citations

The temperature dependence of diffracted beam intensities in atom–surface scattering

Bret Jackson, Horia I. Metiu

We develop a new method for the calculation of the atom scattering analog of the Debye–Waller factor. Unlike x-ray and neutron scattering the properties of an atom scattered by a solid surface cannot be computed by perturbation theory; therefore the simple Debye–Waller theory cannot be applied. Nevertheless the Debye–Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.

The Journal of Chemical Physics•Aug 15, 1985•44 citations

Semiclassical perturbation theory for diffraction in heavy atom surface scattering

Salvador Miret-Artés, Shauli Daon, Eli Pollak

The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.

The Journal of Chemical Physics•May 28, 2012•7 citations

On coherence and the transverse spatial extent of a neutron wave packet

C. F. Majkrzak, N. F. Berk, Brian B. Maranville +2 more

In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.

arXiv:1911.07974•Nov 18, 2019•0 citations

Decoherence in the Diffraction of Helium at Surfaces

Florian Aigner, N. S. Simonović, Beate Solleder +1 more

Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns (Schuller, Wethekam and Winter 2007, Roisseau et al. 2007). In spite of the impulsive interaction with a surface at elevated temperature, which results in phonon excitation, quantum coherence evidently persists. To quantitatively study this remarkable survival of coherence, we present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 〈110〉 direction and compare with recent experimental diffraction data. Decoherence is analyzed employing a quantum trajectory Monte Carlo method (Minami, Reinhold and Burgdorfer 2003), calculating the ensemble average over solutions of a stochastic linear Schrodinger equation. The evolution of the atomic wavepacket is governed by a sequence of stochastic collisions and continuous propagation in the He-LiF surface potential. We find near-perfect agreement between the resulting diffraction patterns and experimental results (Schuller, Wethekam and Winter 2007) without using any adjustable parameters. The question, whether the LiF surface features “buckling”, (i.e. vertical surface reconstruction where the F atoms are displaced relative to the Li atoms) has been addressed in the past (de Wette, Kress and Schroder 1985). However, experimental uncertainties were of the same order as the displacement amplitude itself. In atom-surface diffraction at a grazing angle, surface reconstruction drastically changes the diffraction patterns. By comparison of numerical and experimental results, the buckling amplitude can be determined with unprecedented accuracy.

Publications de l'Observatoire Astronomique de Beograd•Jul 1, 2008•0 citations

The diraction of atoms by light

Duncan H J O’Dell, H. H. Wills

The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.

•Jan 1, 1998•1 citation
The authors use analytic models valid for neutron scattering and numerical calculations to examine a method proposed by Drolshagen and Heller for computing atom diffraction from surfaces. Our main concern is the manner in which the use of narrow packets causing a partial coherence of the incident beam, might affect the diffracted intensity. We find that the demands of representing beam coherence correctly conflict with the requirements for the validity of the propagation scheme. We suggest some improvements that should increase the reliability of the method without affecting greatly its remarkable computational and conceptual advantages.
We develop a new method for the calculation of the atom scattering analog of the Debye-Waller factor. Unlike x-ray and neutron scattering, the properties of an atom scattered by a solid surface cannot be computer by perturbation theory, therefore the simple Debye-Waller theory cannot be applied. Nevertheless the Debye-Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.
We develop a new method for the calculation of the atom scattering analog of the Debye–Waller factor. Unlike x-ray and neutron scattering the properties of an atom scattered by a solid surface cannot be computed by perturbation theory; therefore the simple Debye–Waller theory cannot be applied. Nevertheless the Debye–Waller phenomenon has a close analog: the elastic intensity is depressed due to the uncorrelated part of the thermal motion of the lattice atoms. To compute this effect we develop a time dependent scattering theory in which the quantum properties of the scattered atom are described by propagating coherently an ensemble of wave packets and lattice motion is simulated by a classical Langevin equation. Applications are made to He and Ne scattering from a surface whose lattice dynamics mimics that of Pt(111) but whose corrugation was slightly increased to enrich the diffraction structure.
The semiclassical perturbation theory formalism of Hubbard and Miller [J. Chem. Phys. 78, 1801 (1983)] for atom surface scattering is used to explore the possibility of observation of heavy atom diffractive scattering. In the limit of vanishing ℏ the semiclassical theory is shown to reduce to the classical perturbation theory. The quantum diffraction pattern is sensitive to the characteristics of the beam of incoming particles. Necessary conditions for observation of quantum diffraction are derived for the angular width of the incoming beam. An analytic expression for the angular distribution as a function of the angular and momentum variance of the incoming beam is obtained. We show both analytically and through some numerical results that increasing the angular width of the incident beam leads to decoherence of the quantum diffraction peaks and one approaches the classical limit. However, the incoherence of the beam in the parallel direction does not destroy the diffraction pattern. We consider the specific example of Ar atoms scattered from a rigid LiF(100) surface.
In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.
Scattering of fast neutral atoms with keV kinetic energies at alkali-halide surfaces under grazing angles displays intriguing diffraction patterns (Schuller, Wethekam and Winter 2007, Roisseau et al. 2007). In spite of the impulsive interaction with a surface at elevated temperature, which results in phonon excitation, quantum coherence evidently persists. To quantitatively study this remarkable survival of coherence, we present an ab initio simulation of the quantum diffraction of fast helium beams at a LiF (100) surface in the 〈110〉 direction and compare with recent experimental diffraction data. Decoherence is analyzed employing a quantum trajectory Monte Carlo method (Minami, Reinhold and Burgdorfer 2003), calculating the ensemble average over solutions of a stochastic linear Schrodinger equation. The evolution of the atomic wavepacket is governed by a sequence of stochastic collisions and continuous propagation in the He-LiF surface potential. We find near-perfect agreement between the resulting diffraction patterns and experimental results (Schuller, Wethekam and Winter 2007) without using any adjustable parameters. The question, whether the LiF surface features “buckling”, (i.e. vertical surface reconstruction where the F atoms are displaced relative to the Li atoms) has been addressed in the past (de Wette, Kress and Schroder 1985). However, experimental uncertainties were of the same order as the displacement amplitude itself. In atom-surface diffraction at a grazing angle, surface reconstruction drastically changes the diffraction patterns. By comparison of numerical and experimental results, the buckling amplitude can be determined with unprecedented accuracy.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.