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arXiv:2507.03055 · Europhysics Letters (EPL)

Quantum reflection effects in the diffraction of matter waves (a)

Johannes Fiedler, F. Spallek, A. Vega, Eivind Kristen Osestad, Quentin Bouton, G. Dutier

Published Jul 1, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schrödinger equation as multistep potentials allows us to determine the reflection coefficient by means of a Riccati equation. We introduce a measure for the wave function's characteristic reflection distance and derive an analytical expression for this reflection point in an arbitrary power-law potential. We study the associated QR rate in the context of Casimir-Polder atom surface interactions, revealing its strong dependence on critical parameters such as velocity and interaction duration. As an application, we demonstrate how the matter-wave diffraction of a low-velocity metastable argon beam impinging on a rotated grating facilitates high-precision potential analysis.

DOI
10.1209/0295-5075/adebae

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Europhysics Letters (EPL)•Jul 1, 2025•2 citations
Abstract Among the fundamental quantum effects, quantum reflection (QR) is one of the most notable phenomena. Approximating arbitrary potentials in the Schrödinger equation as multistep potentials allows us to determine the reflection coefficient by means of a Riccati equation. We introduce a measure for the wave function's characteristic reflection distance and derive an analytical expression for this reflection point in an arbitrary power-law potential. We study the associated QR rate in the context of Casimir-Polder atom surface interactions, revealing its strong dependence on critical parameters such as velocity and interaction duration. As an application, we demonstrate how the matter-wave diffraction of a low-velocity metastable argon beam impinging on a rotated grating facilitates high-precision potential analysis.
Collisions between ultracold atoms and material surfaces are characterized by the reflection of the atomic matter wave from the attractive Casimir-Polder potential. This quantum reflection is particularly relevant to experiments such as GBAR, which will determine the gravitational acceleration of a cold antihydrogen atom by timing its fall onto a detection plate. In this thesis, the Casimir-Polder potential is computed from the electromagnetic scattering properties of the atom and surface and it is found to depend notably on the dielectric response, thickness and density of the medium. We show that reflection on this potential is associated with a breakdown of the semiclassical approximation and that it is enhanced for slow atoms and weak potentials. Liouville transformations relate Schrödinger equations with different potential landscapes but identical scattering properties. We gain new insights on the problem of quantum reflection on a potential well by mapping it onto an equivalent problem of tunneling through a wall. We also discuss the effect of gravity on the atomic wavepacket and its implications for free fall experiments with atoms. When combined with quantum reflection from a horizontal mirror, gravity can be used to trap particles in long lived states with promising applications for metrology. In particular, we suggest a scheme to improve the precision of the GBAR experiment by reducing the velocity dispersion of the falling atoms.
We show that an attractive potential created by an evanescent wave quantum mechanically reflects an atom with nonzero probability if the atom’s incident de Broglie wavelength is larger than the decay length of the evanescent wave. The amplitude reflection coefficient is calculated by use of an analytical solution of the corresponding Schrödinger equation. We also discuss electromagnetic wave analog of the effect, the partial reflection of light at an exponentially increasing index. We interpret the quantum reflection in terms of a virtual turning point, by means of a complex stationary phase approximation. If the potential remains exponential until it becomes as deep as several hundred recoil energies, the reflection coefficient for a low-energy de Broglie wave is independent of the details of the potential far from the virtual turning point. This means that, if the evanescent wave is strong enough, interactions between the atom and the glass surface at which the evanescent wave is created can be neglected.
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.
Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements require simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.
Abstract Atomic diffraction through a nanograting is a powerful tool to probe the Casimir-Polder potential. Achieving precise measurements requires simulations to bridge theory and experiment. In this context, we present various approximations and methods of Casimir-Polder potentials, and we analyze their impact on matter-wave diffraction patterns. Our analysis includes the pairwise summation approach, the proximity force approximation, and multiple scattering expansion method. Furthermore, we demonstrate that the influence of Casimir-Polder interactions extends up to 25 nm before and after the nanograting slit, highlighting the importance of accounting for this effect in any accurate analysis.