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

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.