Causal trajectories description of atom diffraction by surfaces

Europhysics Letters (EPL), 2001

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.

The striking observation of interference structures produced by grazing impact of fast atoms on crystal surfaces reported a few years ago [1,2] has given rise to the development of a powerful surface analysis technique. This article gives a brief account of the main features of the process, using the Surface Eikonal (SE) approximation as a theoretical tool to analyze the different mechanisms responsible for the quantum interference. The SE approach is a semiclassical method based on the use of the eikonal wave function, which takes into account the coherent superposition of transition amplitudes for different axially channeled trajectories. It has proved to provide a quite good description of experimental diffraction patterns for different collision systems.

Journal of Physics: Condensed Matter, 2002

Diffraction and interference of matter waves are key phenomena in quantum mechanics. Here we present some results on particle diffraction in a wide variety of situations, ranging from simple slit experiments to more complicated cases such as atom scattering by corrugated metal surfaces and metal surfaces with simple and isolated adsorbates. The principal novelty of our study is the use of the so-called Bohmian formalism of quantum trajectories. These trajectories are able to satisfactorily reproduce the main features of the experimental results and, more importantly, they provide a causal intuitive interpretation of the underlying dynamics. In particular, we will focus our attention on: (a) a revision of the concepts of near and far field in undulatory optics; (b) the transition to the classical limit, where it is found that although the quantum and classical diffraction patterns tend to be quite similar, some quantum features are maintained even when the quantum potential goes to zero; and (c) a qualitative description of the scattering of atoms by metal surfaces in the presence of a single adsorbate. Contents 1. Introduction 6109 2. The causal interpretation of quantum mechanics 6111 2.1. The wavefunction and equations of motion 6112 2.2. The quantum potential 6113 2.3. The hydrodynamical interpretation of quantum mechanics 6114 2.4. Quantum vortices 6116 2.5. The classical limit 6117 3. Computational methods 6119 3.1. Quantum trajectories propagation 6119 3.2. Wavepacket propagation-Heller's method 6120 3.3. Wavepacket propagation-grid methods 6121

Surface Science, 1978

Atomic beam scattering from surfaces is rapidly evolving as a valuable technique for exploring atom-surface interactions, manifested in both elastic and inelastic processes. We review this field with emphasis on the regime of elastic scattering of low mass particles, where quantum effects are apparent. The discussion focuses on recent developments including both experimental and theoretical methods and results. Information about the potential that can be deduced from selective adsorption observations is described.

Journal of Electron Spectroscopy and Related Phenomena, 2003

A calculation of the inelastic scattering rate of Xe atoms on Cu(111) is presented. We focus in the regimes of low and intermediate velocities, where the energy loss is mainly associated to the excitation electron-hole pairs in the substrate. We consider trajectories parallel to the surface and restrict ourselves to the Van der Waals contribution. The decay rate is calculated within a self-energy formulation. The effect of the response function of the substrate is studied by comparing the results obtained with two different approaches: the Specular Reflection Model and the Random Phase Approximation. In the latter, the surface is described by a finite slab and the wave functions are obtained from a one-dimensional model potential that describes the main features of the surface electronic structure while correctly retains the imagelike asymptotic behaviour. We have also studied the influence of the surface state on the calculation, finding that it represents around 50% of the total probability of electron-hole pairs excitation.

arXiv: Atomic Physics, 2018

Grazing incidence fast atom diffraction (GIFAD or FAD) is a sensitive tool for surface analysis, which strongly relies on the quantum coherence of the incident beam. In this article the influence of the incidence conditions and the projectile mass on the visibility of the FAD patterns is addressed. Both parameters determine the transverse coherence length of the impinging particles, which governs the general features of FAD distributions. We show that by varying the impact energy, while keeping the same collimating setup and normal energy, it is possible to control the interference mechanism that prevails in FAD patterns. Furthermore, we demonstrate that the contribution coming from different positions of the focus point of the incident particles, which gives rise to the spot-beam effect, allows projectiles to explore different zones of a single crystallographic channel when a narrow surface area is coherently lighted. In this case the spot-beam effect gives also rise to a non-coherent background, which contributes to the gradual quantum-classical transition of FAD spectra. Present results are compared with available experimental data, making evident that the inclusion of focusing effects is necessary for the proper theoretical description of the experimental distributions.

Journal of Physics: Condensed Matter, 2012

A strictly quantum mechanical derivation of the energy and parallel momentum resolved scattering spectrum formula that combines the effects of the diffraction of atoms from corrugated surfaces and multiple inelastic scattering by dispersive phonons is presented. The final result is expressed in the compact and numerically tractable form of a Fourier transform of a cumulant expansion in which each term embodies an interplay between the processes of projectile diffraction and multiphonon scattering to all orders in the respective interaction potentials. The Debye-Waller reduction of the intensities of diffraction peaks is explicitly formulated.

Physical Review B, 1984

The reduction of the specular-beam intensity in the scattering of thermalized He atoms from densely packed surfaces of metals is irivestigated in terms of nonadiabatic multiple excitation of low-energy surface electronic density fluctuations. Their effect on the atom-scattering spectra is studied within the time-dependent approach developed by Doniach and Muller-Hartmann, Ramakrishnan, and Toulouse to treat localized perturbations in metals. This mechanism may explain the peculiar coexistence of the unitarity defect with the absence of diffractive peaks as reported recently for the system He/Cu(100).

The Journal of Chemical Physics, 2004

In this work, a full quantum study of the scattering of He atoms off single CO molecules, adsorbed onto the Pt͑111͒ surface, is presented within the formalism of quantum trajectories provided by Bohmian mechanics. By means of this theory, it is shown that the underlying dynamics is strongly dominated by the existence of a transient vortitial trapping with measurable effects on the whole diffraction pattern. This kind of trapping emphasizes the key role played by quantum vortices in this scattering. Moreover, an analysis of the surface rainbow effect caused by the local corrugation that the CO molecule induces on the surface, and its manifestation in the corresponding intensity pattern, is also presented and discussed.

Chemical Physics, 1984

Exact quantum-mechanical calculations are reported on atom scattering from a crystalline surface with isolated impurities. The calculations are for He scattering from a one-dimensronal model of a Cu surface with adsorbed Ar atoms. The difficulties of carrying out calculations on scattering from extended but non-penodic structures are overcome by using a time-dependent wavepacket approach. A recently developed method for solving the time-dependent Schrodinger equation IS employed. Scattering intensities are given for several energies and incidence angles. Detailed insight IS obtained on impurity effects on surface scattering. The main features are-(1) Broad Intensity tails are superimposed on each diffraction spike. The width of the tails decreases with increasing dtffraction order; (2) Shallow rainbow peaks arise, due to impurity induced local corrugation; (3) Weak intensrty maxlIIla arise due to interference between surface and impurity scattering_ The intensities are somewhat sensitive to the position of the impunty within the surface unit cell. Physical interpretation of the effects is provided from exact calculations, and from a simple sudden approximation for the scattering intensitres. It IS argued that He scattrnng can be used to determine impurity locations on surfaces.