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

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.

On the role of the electric dipole moment in the diffraction of biomolecules at nanomechanical gratings

“…Given that the gratings were milled with a focused gallium ion beam, which is known to deposit surface charges, it is likely that charges were implanted into the membrane during the patterning process. This is also consistent with discrepancies that were found between the observed and predicted Casimir‐Polder interactions at nanomechanical silicon nitride gratings . In the following section, we present a theory that evaluates the possible role of residual charges in the diffraction of polar molecules.…”

“…In a more realistic description of the interaction between molecule and grating, one would add the dispersive Casimir‐Polder interaction to the potential , which is not included in the present model. The electrostatic field can be calculated from Coulomb's law applied to a thin grating with surface charge density σ 0 , period d , opening fraction f and width .…”

Matter-wave physics with nanoparticles and biomolecules

“…Any remaining discrepancy between theory and experiment provides a hint on additional interactions, such as charges inside the thin dielectric membrane. Our experiments with PcH 2 diffracted at a FIB written grating showed an attractive potential 5-8 times stronger than expected based on the CP-interaction alone [27]. This effect was greatly reduced for masks that were generated in photo-lithography and reactive ion etching at low energies.…”

“…The model can be based on a perturbative approach, where it is often sufficient to include only the scattering of a virtual photon from the molecule to the grating, and back. Even scattering inside the material can be corrected for [27]. Any remaining discrepancy between theory and experiment provides a hint on additional interactions, such as charges inside the thin dielectric membrane.…”

In search of multipath interference using large molecules

“…Deviations in the slit morphology alter the position-dependent Casimir-Polder interaction between individual molecules and the mask. This has been studied in detail for matter-wave diffraction at material gratings, including the effect of thermally populated rotational and vibrational states on far-field diffraction ( 46 , 47 ). For each slit, the interference pattern recorded is the ensemble average over the entire phase-space distribution of the molecular beam and the mask.…”