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arXiv:2108.06565 · American Journal of Physics

Single-, double-, and triple-slit diffraction of molecular matter waves

Christian Brand, Stephan Troyer, Christian Knobloch, Ori Cheshnovsky, Markus Arndt

Published Nov 22, 2021• 16 citations
arXivHTMLPDF

Abstract

Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, a double, and a triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, which can be modified by rotating the nanomechanical mask with respect to the molecular beam. The text is meant to introduce students and teachers to the concepts of molecule diffraction, supported by problems and solutions that can be discussed in class.

DOI
10.1119/5.0058805

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Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, a double, and a triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, which can be modified by rotating the nanomechanical mask with respect to the molecular beam. The text is meant to introduce students and teachers to the concepts of molecule diffraction, supported by problems and solutions that can be discussed in class.
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.
The chapter discusses advances in matter-wave optics with complex molecules, generalizing Young’s double slit to high masses. The quantum wave-particle duality is visualized by monitoring the arrival patterns of molecules diffracted at nanomechanical masks. Each molecule displays particle behavior when it is localized on the detector; however, the overall interference pattern requires their delocalization in free flight. Internal particle properties influence the de Broglie waves in the presence of surfaces or fields—even in interaction with atomically thin gratings. To probe the quantum nature of high-mass molecules, universal beam splitters are combined in a multi-grating interferometer to observe high-contrast matter-wave fringes even for 500 K hot molecules, containing 810 atoms with a mass of 10 000 amu. The high sensitivity of the nanoscale interference fringes to deflection in external fields enables non-invasive measurements of molecular properties. The chapter concludes by discussing research on beam techniques that extend molecular quantum optics to large biomolecules.
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.
This paper reports on a study of student understanding of the wave nature of matter in the context of the pattern produced by the diffraction and interference of particles. Students in first-year, second-year, and third-year physics courses were asked to predict and explain how a single change in an experimental setup would affect the pattern produced when electrons or other particles are incident on a single slit, double slit, or crystal lattice. The errors made by students after standard instruction indicated the presence of similar conceptual and reasoning difficulties at all levels. Among the most serious was an inability to interpret diffraction and interference in terms of a basic wave model. Other errors revealed a lack of a functional understanding of the de Broglie wavelength. Students often treated it as a fixed property of a particle, not as a function of the momentum. An important goal of this investigation was to provide a research base for the design of instruction to help students develop and apply a basic wave model for matter.
These lecture notes emerged from a contribution to the "Les Houches Summer School, Session CVII - Current Trends in Atomic Physics, July 2016". It is meant to serve students as a guide to a selection of topics that are currently at the focus of molecular quantum optics and complements an earlier lecture on related topics [Arndt et al., 2014]. In this review we discuss recent advances in molecular quantum optics with large organic molecules. In particular, we present successful experiments of molecules of biological importance, such as neurotransmitters and map out the route towards interferometry of large bio-matter such as proteins. The interaction of internally complex molecules with various beam splitters is discussed for both far-field diffraction at a single nanomechanical grating and the Kapitza-Dirac Talbot-Lau near-field interferometer - addressing recent progress, experimental challenges, and prospects for quantum enhanced metrology of highly complex systems in the gas phase. A central part of this review deals with the preparation of slow beams of neutral biomolecules, ranging from a single amino acid to proteins or peptides in a micro-environment.