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Annalen der Physik

A Green's function approach to modeling molecular diffraction in the limit of ultra‐thin gratings

Christian Brand, Johannes Fiedler, Thomas Juffmann, Michele Sclafani, Christian Knobloch, Stefan Scheel, Yigal Lilach, Ori Cheshnovsky, Markus Arndt

Published Oct 1, 2015• 34 citations

Abstract

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

DOI: 10.1002/andp.201500214

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A few years ago, diffraction of atoms by double slits and gratings was achieved for the first time, and standard optical wave-theory provided an excellent description of the experiments. More recently, diffraction of weakly bound molecules and even clusters has been observed. Due to their size and to possible breakup processes optical wave-theory is no longer adequate and a more sophisticated approach is needed. Moreover, surface effects, which can modify the diffraction pattern of atoms and molecules, give rise to further complications. In this article a fully quantum mechanical approach to these questions is discussed.

We investigate effects of a permanent electric dipole moment on matter‐wave diffraction at nanomechanical gratings. Specifically, the diffraction patterns of hypericin at ultra‐thin carbonaceous diffraction masks are compared with those of a polar and a non‐polar porphyrin derivative of similar mass and de Broglie wavelength. We present a theoretical analysis of the diffraction of a rotating dipole highlighting that small local electric charges in the material mask can strongly reduce the interference visibility. We discuss the relevance of this finding for single grating diffraction and multi‐grating interferometry with biomolecules.

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