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arXiv:1008.2546 · The Journal of Chemical Physics

Communication: Heavy atom quantum diffraction by scattering from surfaces

Jeremy M. Moix, Eli Pollak

Published Jan 6, 2011• 12 citations
arXivHTMLPDF

Abstract

Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass usually assures that the coherence length of the incident particle in the direction of the propagation of the particle (the parallel direction) will be much shorter than the characteristic lattice length of the surface, thus leading to a classical description. Recent work on molecular interferometry has shown that extreme collimation of the beam creates a perpendicular coherence length which is sufficiently long so as to observe interference of very heavy species passing through a grating. Here we show, using quantum mechanical simulations, that the same effect will lead to quantum diffraction of heavy particles colliding with a surface. The effect is robust with respect to the incident energy, the angle of incidence, and the mass of the particle.

DOI
10.1063/1.3528120

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Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass usually assures that the coherence length of the incident particle in the direction of the propagation of the particle (the parallel direction) will be much shorter than the characteristic lattice length of the surface, thus leading to a classical description. Recent work on molecular interferometry has shown that extreme collimation of the beam creates a perpendicular coherence length which is sufficiently long so as to observe interference of very heavy species passing through a grating. Here we show, using quantum mechanical simulations, that the same effect will lead to quantum diffraction of heavy particles colliding with a surface. The effect is robust with respect to the incident energy, the angle of incidence, and the mass of the particle.
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 conventional notion of elastic, coherent atom-surface scattering originates from the scattering particles acting as a quantum-mechanical matter wave, which coherently interfere to produce distinct Bragg peaks which persist at finite temperature. If we introduce inelastic scattering to this scenario, the result is that the surface particles become displaced by the scattering atoms, resulting in emission or absorption of phonons that shift the final energy and momentum of the scatterer. As the lowest-lying phonons are gapless excitations, the ability to measure these phonons is very difficult and this difficulty is exacerbated by the roughly 1-eV resolution found in high-energy helium scattering experiments. Even though the surface has in effect measured the presence of the scatterer which decoheres the particle, we retain the diffraction spots which are referred to as coherent scattering. How do we reconcile these disparate viewpoints? We propose an experiment to more precisely examine the question of coherence in atom-surface scattering. We begin with an initially coherent superposition of helium particles with equal probabilities of interacting with the surface or not interacting with the surface. The beams are directed so that after the scattering event, the atoms are recombined so that we can observe the resulting interference pattern. The degree to which phonons are excited in the lattice by the scattering process dictates the fringe contrast of the interference pattern of the resulting beams. We use semiclassical techniques to simulate and test the viability of this experiment and show that for a wide range of conditions, despite the massive change in the momentum perpendicular to the surface, we can still expect to have coherent (in the superposition sense) scattering.
Diffraction of fast helium atoms at alkali-halide surfaces under grazing angles of incidence shows intriguing diffraction patterns. The persistence of quantum coherence is remarkably strong, even though high surface temperatures and high (keV) kinetic energies of the incident atoms would strongly suggest the dominance of dissipative and decohering processes. The main source of decoherence is the excitation or absorption of surface vibrations upon impact. The momentum transfer between the surface and the incident helium atom depends on the amplitude of the thermal vibrations of the surface atoms and the energy of the incident particle. 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.
The influence of the collimating conditions of the incident beam on diffraction patterns produced by grazing scattering of fast atoms off crystal surfaces is studied within a semiquantum approach, called the surface initial value representation (SIVR) approximation. In this approach we incorporate a realistic description of the incident particle in terms of the collimating parameters, which determine the surface area that is coherently illuminated. The model is applied to He atoms colliding with a LiF(001) surface after passing through a rectangular aperture. As was experimentally observed [Nucl. Instrum. Methods Phys. Res., Sect. B 350, 99 (2015)], SIVR spectra as a function of the azimuthal angle are very sensitive to the width of the collimating slit. We also found that the length of the collimating aperture affects polar angle distributions, introducing additional interference structures for the longer collimating slits.
The transition to the classical limit in atom-surface diffraction is studied using the de Broglie-Bohm causal formalism. In particular, we focus on rainbow scattering, which is a well-defined effect in classical mechanics and has a clear counterpart in quantum mechanics. In order to achieve this limit, we consider the scattering of particles with increasing masses off a Cu(110) surface. Although the classical limit seems strictly unreachable, quantum trajectories mimic the characteristics of the classical intensity distribution, and their use allows to unveil the mechanism by which the quantum rainbow condition takes place.
Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.