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New Journal of Physics

Coherent diffraction of hydrogen through the 246 pm lattice of graphene

Christian Brand, Maxime Debiossac, Toma Susi, François Aguillon, Jani Kotakoski, P. Roncin, Markus Arndt

Published Feb 11, 2019• 23 citations
Publisher

Abstract

We study the diffraction of neutral hydrogen atoms through suspended single-layer graphene using molecular dynamics simulations based on density functional theory. Although the atoms have to overcome a transmission barrier, we find that the de Broglie wave function for H at 80 eV has a high probability to be coherently transmitted through about 18% of the graphene area, contrary to the case of He. We propose an experiment to realize the diffraction of atoms at the natural hexagon lattice period of 246 pm, leading to a more than 400-fold increase in beam separation of the coherently split atomic wave function compared to diffraction experiments at state-of-the art nano-machined masks. We expect this unusual wide coherent beam splitting to give rise to novel applications in atom interferometry.

DOI
10.1088/1367-2630/ab05ed

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We study the diffraction of neutral hydrogen atoms through suspended single-layer graphene using molecular dynamics simulations based on density functional theory. Although the atoms have to overcome a transmission barrier, we find that the de Broglie wave function for H at 80 eV has a high probability to be coherently transmitted through about 18% of the graphene area, contrary to the case of He. We propose an experiment to realize the diffraction of atoms at the natural hexagon lattice period of 246 pm, leading to a more than 400-fold increase in beam separation of the coherently split atomic wave function compared to diffraction experiments at state-of-the art nano-machined masks. We expect this unusual wide coherent beam splitting to give rise to novel applications in atom interferometry.
Analytic methods based on matter-wave diffraction are a cornerstone in condensed-matter research, providing access to static and dynamic materials properties down to the atomic level. In these experiments, the shape of the diffraction pattern is largely determined by the lattice at equilibrium whereas vibrationally-induced distortions are treated perturbatively. Here, we show that the perturbative approach does not hold for helium diffracted at kiloelectronvolt energy through freestanding single-layer graphene. In this case, we enter a new regime of strong coupling where the projectile strongly interacts with the electron density of several lattice atoms simultaneously, leading to phase shifts of several radians. In consequence, lattice distortions introduce a significant phase spread that cannot be described by the typically employed Debye-Waller factor. We show that the weak-coupling regime is retained for atomic hydrogen diffraction. The experimental results are supported by simulations, providing a regime-independent approach to describe the influence of phonons on atom diffraction phenomena.
We have demonstrated a novel diffraction grating for atoms. A collimated beam of sodium atoms with a de Broglie wavelength of 17 pm was diffracted by transmission through an array of slits with a spatial period of 0.2 \ensuremath{\mu}m formed in a gold membrane. This is the first reported diffraction of atoms by a fabricated periodic structure. Our transmission grating for atoms can divide or recombine an atomic beam coherently, and may provide the easiest route to the realization of an atom wave interferometer.
We have developed a nozzle source that delivers a continuous beam of atomic helium or molecular hydrogen having a high degree of transverse coherence and with adequate optical brightness to enable new kinds of experiments. Using this source we have measured single slit diffraction patterns and the first ever speckle-diffraction patterns using atomic and molecular de Broglie waves. Our results suggest fruitful application of coherent matter beams in dynamic scattering and diffractive imaging at short wavelength and with extreme surface sensitivity.
The photonic graphene in atoms not only has the typical photonic band structures but also exhibits controllable optical properties that are difficult to achieve in the natural graphene. Here, the evolution process of discrete diffraction patterns of a photonic graphene, which is constructed through a three-beam interference, is demonstrated experimentally in a 5 S 1/2 − 5 P 3/2 − 5 D 5/2 85 Rb atomic vapor. The input probe beam experiences a periodic refractive index modulation when traveling through the atomic vapor, and the evolution of output patterns with honeycomb, hybrid-hexagonal, and hexagonal geometric profiles is obtained by controlling the experimental parameters of two-photon detuning and the power of the coupling field. Moreover, the Talbot images of such three kinds of periodic structure patterns at different propagating planes are observed experimentally. This work provides an ideal platform to investigate manipulation the propagation of light in artificial photonic lattices with tunable periodically varying refractive index.
Diffraction of matter waves is a fundamental consequence of quantum mechanics, directly illustrating the core principles of wave-particle duality, quantum superposition, and quantum interference. De Broglie's proposal that particles exhibit wave-like properties has been experimentally confirmed for electrons, neutrons, and composite systems such as helium atoms, molecules and clusters. Here, we report the observation of positronium diffraction using a high-quality, energy-tunable positronium beam transmitted through graphene. Time-of-flight selection and spatially resolved detection reveal a distinct 1st-order diffraction peak at a position consistent with the prediction from matter-wave considerations for positronium. This work provides the direct and definitive evidence of quantum interference in positronium beams and confirms that it behaves as a single quantum entity rather than two independent interfering particles. This groundbreaking experimental milestone marks a major advance in fundamental physics, not only demonstrating positronium's wave nature as a bound lepton-antilepton system but also opening pathways for precision measurements involving positronium.