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arXiv:1410.7243 · Physical Review A

Quantum reflection and interference of matter waves from periodically doped surfaces

Benjamin A. Stickler, Uzi Even, Klaus Hornberger

Published Jan 13, 2015• 12 citations
arXivHTMLPDF

Abstract

We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting the fact that charged dopants locally suppress quantum reflection from the Casimir-Polder potential. We present a general quantum scattering theory for reflection off periodically charged surfaces and discuss the requirements for the observation of multiple diffraction peaks.

DOI
10.1103/physreva.91.013614

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We show that periodically doped, flat surfaces can act as reflective diffraction gratings for atomic and molecular matter waves. The diffraction element is realized by exploiting the fact that charged dopants locally suppress quantum reflection from the Casimir-Polder potential. We present a general quantum scattering theory for reflection off periodically charged surfaces and discuss the requirements for the observation of multiple diffraction peaks.
Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.
We demonstrate experimentally that an electric field can be used to control quantum reflection of matter waves off periodically microstructured surfaces. Applying a voltage of alternating polarity between neighboring grating bars induces an electric field which modifies the interaction between the surface and the impinging matter wave so that quantum reflection is gradually reduced. We find that the measured reflectivities are in good agreement with our numerical simulations and that their suppression is well captured by a simple analytic model. This experiment constitutes a step towards electrically tuned reflective diffraction elements for atomic and molecular matter waves.
Abstract Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schrödinger equation as multistep potentials allows us to determine the reflection coefficient by means of a Riccati equation. We introduce a measure for the wave function's characteristic reflection distance and derive an analytical expression for this reflection point in an arbitrary power-law potential. We study the associated QR rate in the context of Casimir-Polder atom surface interactions, revealing its strong dependence on critical parameters such as velocity and interaction duration. As an application, we demonstrate how the matter-wave diffraction of a low-velocity metastable argon beam impinging on a rotated grating facilitates high-precision potential analysis.
Abstract Molecular beams of He and D2 are scattered from a ruled diffraction grating in conical‐mount geometry under grazing‐incidence conditions. Fully resolved diffraction patterns as a function of detection angle are recorded for different grating azimuth angles and for two different kinetic energies of the particle beams. Variations in diffraction peak widths are traced back to different velocity spreads of He and D2 determined by time‐of‐flight measurements. A comprehensive analysis of diffraction intensities confirms universal diffraction, that is, for identical de Broglie wavelengths, the relative diffraction intensities for He and D2 are the same. Universal diffraction results from peculiarities of quantum reflection of the atoms and molecules from the diffraction grating. In quantum reflection particles scatter many nanometers in front of the surface from the long‐range attractive branch of the particle–surface interaction potential without probing the potential well and the short‐range repulsive branch of the potential.
In recent years, matter‐wave diffraction at nanomechanical structures has been used by several research groups to explore the quantum nature of atoms and molecules, to prove the existence of weakly bound molecules or to explore atom‐surface interactions with high sensitivity. The particles' Casimir‐Polder interaction with the diffraction grating leads to significant changes in the amplitude distribution of the diffraction pattern. This becomes particularly intriguing in the thin‐grating limit, i.e. when the size of a complex molecule becomes comparable with the grating thickness and its rotation period comparable to the transit time through the mask. Here we analyze the predictive power of a Green's function scattering model and the constraints imposed by the finite control over real‐world experimental factors on the nanoscale. image
Motivated by recent experiments that demonstrated a strongly enhanced reflection efficiency of atoms on microfabricated, gratinglike surface structures, we develop a detailed description of the scattering of atomic matter waves on such structures. We start with a simple model that describes the ridged surface as an equivalent absorbing medium. This model correctly predicts the experimentally observed scaling and magnitude of the reflection efficiency. We then calculate the accurate solutions for the Fresnel diffraction of waves at grazing incidence at a periodic set of idealized, parallel edges. Both numerical and analytical solutions are presented. The specular reflectivity and its phase, as well as the efficiencies of higher diffraction orders are calculated. We compare our results to experimental data in a wide range of parameters. We extend the model including the finite size of the grating ridges and the van der Waals attraction and suggest a more general estimate of the reflection coefficient.