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Physical Review A

Atomic diffraction under oblique incidence: An analytical expression

Maxime Debiossac, P. Roncin

Published Nov 13, 2014• 17 citations
Publisher

Abstract

The semiclassical perturbation method developed by Henkel et al. [J. Phys. II 4, 1955 (1994)] to model cold-atom diffraction by optical standing waves, is applied to the diffraction of fast atoms on crystal surfaces at grazing incidence (GIFAD or FAD). We first show that the interaction time and interaction length embedded in the obliquity factor is well suited to explain the transition from three-dimensional to two-dimensional (2D) diffraction. The situation of a slightly misaligned primary beam, corresponding to oblique incidence in the effective 2D system, is addressed pointing out discrepancies such as the absence of net deflection of the atomic beam. Guided by time-reversal considerations, we propose an arbitrarily symmetrized form significantly improving the agreement with experimental data recorded in oblique incidence.

DOI
10.1103/physreva.90.054701

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The semiclassical perturbation method developed by Henkel et al. [J. Phys. II 4, 1955 (1994)] to model cold-atom diffraction by optical standing waves, is applied to the diffraction of fast atoms on crystal surfaces at grazing incidence (GIFAD or FAD). We first show that the interaction time and interaction length embedded in the obliquity factor is well suited to explain the transition from three-dimensional to two-dimensional (2D) diffraction. The situation of a slightly misaligned primary beam, corresponding to oblique incidence in the effective 2D system, is addressed pointing out discrepancies such as the absence of net deflection of the atomic beam. Guided by time-reversal considerations, we propose an arbitrarily symmetrized form significantly improving the agreement with experimental data recorded in oblique incidence.
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.
Synopsis Grazing incidence fast atom diffraction (GIFAD) uses keV atoms to investigate properties of crystal surfaces. It exists in two flavors; The elastic diffraction is identified by bright spots sitting on the Laue circle of energy conservation. We will focus on inelastic diffraction with a model where the surface atoms are quantum harmonic oscillators and where the successive collisions of the projectile take place in the Lamb-Dicke regime. The model explains observed lines shapes and predicts a drastic dependence of the energy loss ∆E ∝ θ 7 .
Abstract. — We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed. 1. Introduction. The diffraction of atomic de Broglie waves by standing wave light fields [1-4] or mechanical microstructures [5] has recently received considerable interest because of its potential application as an atomic beam splitter, one of the key components for the development of atom optics and interferometry
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed.
We study the diffraction of atoms and weakly bound three-atomic molecules from a transmission grating at non-normal incidence. Due to the thickness of the grating bars, the slits are partially shadowed. Therefore, the projected slit width decreases more strongly with the angle of incidence than the projected period, increasing, in principle, the experimental resolution. The shadowing, however, requires a revision of the theory of atom diffraction. We derive an expression in the style of the Kirchhoff integral of optics and show that the diffraction pattern exhibits a characteristic asymmetry which must be accounted for when comparing with experimental data. We then analyze the diffraction of weakly bound trimers and show that their finite size manifests itself in a further reduction of the slit width by (3∕4)⟨r⟩(3∕4)⟨r⟩(3∕4)⟨r⟩ where ⟨r⟩⟨r⟩⟨r⟩ is the average bond length. The improved resolution at non-normal incidence may in particular allow us to discern, by means of their bond lengths, between the small ground state of the helium trimer [$⟨r⟩\ensuremath{\approx}1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, Barletta and Kievsky, Phys. Rev. A 64, 042514 (2001)] and its predicted Efimov-type excited state ($⟨r⟩\ensuremath{\approx}8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, ibid.), and in this way to experimentally prove the existence of this long-sought Efimov state.
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.