Signature of Short-Range van der Waals Forces Observed in Poisson Spot Diffraction with Indium Atoms

Nicolas Gack, Christian Reitz, Joshua Leo Hemmerich, Max Könne, Robert Bennett, Johannes Fiedler, Herbert Gleiter, Stefan Yoshi Buhmann, Horst Hahn, and Thomas Reisinger

Phys. Rev. Lett. 125, 050401 – Published 27 July 2020

Abstract

The phase of de Broglie matter waves is a sensitive probe for small forces. In particular, the attractive van der Waals force experienced by polarizable atoms in the close vicinity of neutral surfaces is of importance in nanoscale systems. It results in a phase shift that can be observed in matter-wave diffraction experiments. Here, we observe Poisson spot diffraction of indium atoms at submillimeter distances behind spherical submicron silicon dioxide particles to probe the dispersion forces between atoms and the particle surfaces. We compare the measured relative intensity of Poisson’s spot to theoretical results derived from first principles in an earlier communication and find a clear signature of the atom-surface interaction.

Received 13 December 2019
Revised 29 April 2020
Accepted 6 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.050401

Physics Subject Headings (PhySH)

Atom interferometry Casimir effect & related phenomena Van der Waals interaction

Atomic & molecular beams Atoms

Polarizability

Atomic, Molecular & Optical

Authors & Affiliations

Nicolas Gack ¹, Christian Reitz¹, Joshua Leo Hemmerich², Max Könne², Robert Bennett ^2,3, Johannes Fiedler ^2,4, Herbert Gleiter ¹, Stefan Yoshi Buhmann², Horst Hahn ¹, and Thomas Reisinger ¹

¹Institute of Nanotechnology, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany
²Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg i. Br., Germany
³School of Physics & Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom
⁴Centre for Materials Science and Nanotechnology, Department of Physics, University of Oslo, P.O. Box 1048 Blindern, NO-0316 Oslo, Norway

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Vol. 125, Iss. 5 — 31 July 2020

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Images

Figure 1
Schematic of the Poisson spot experiment. Indium is evaporated in an effusive oven source with the indium atoms emanating from an orifice in the crucible lid [(1) optical micrograph]. They accumulate a phase shift due to the attractive vdW potential when passing the spherical submicron particles [attached to silver nanowires on copper grids: (2), (3) scanning electron micrographs], which are mounted at various detection distances $b$ from a silicon wafer surface. There the Poisson spot diffraction images are recorded by condensation. Note the deposited indium in inset (2).
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Figure 2
Scanning electron micrographs of the indium film deposited on the silicon wafer piece. The shadows cast by the silver nanowires and spherical silicon dioxide particles are visible. Distinct Poisson spots are visible at the centers of the spherical-particle shadows. The right and left insets show the corresponding results of the Fresnel-Kirchhoff diffraction simulation with ( $FK + vdW$ ) and without (FK) the phase shift due to vdW forces, respectively. The transmission electron microscopy grid supporting the wires or particles are mounted at detection distances $b = 0.1 mm$ (a), 0.25 mm (b), and 0.3 mm (c),(d). The diameters of the spheres are (a) 176 nm, (b) 179 nm, (c) 181 nm, (d) 199 nm. The two adjacent pie sections indicated in each image correspond to the integration areas used for the lateral intensity data shown in Fig. 3. The scale bar length is 200 nm.
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Figure 3
Radial relative intensity extracted from the filtered SEM images in Figs. 2–2 (data points; for error bars see text) and images from diffraction models by averaging of the same radial intervals. Shadow shoulders and central peak of (a)–(c) are shifted in steps of (10, 0.5) and (50,0.5) for clarity, respectively. The thick and thin lines are the result of the diffraction model taking and not taking into account a vdW potential, respectively, using the expected distribution of de Broglie wavelengths. The models include the blocking effect of the supporting wires [30 nm width in (a); in (b)–(d) the wire was assumed to be tangential to the sphere], but neglect surface corrugation. The thin pink lines in (c) and (d) show the $FK + vdW$ model for a monochromatic beam at the central wavelength using the above averaging intervals and parallel to the wire’s axis without averaging, respectively.
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Figure 4
Averaged relative intensity within 20 nm of shadow center for the models with (top panel, dotted line) and without (bottom panel, dotted line) taking the vdW interaction into account. The diffraction images of the on-axis spot were computed for $b$ in steps of 0.01 mm at the central wavelength. The small (less than 10%) effect of the wavelength spread was corrected for by extrapolating the relative correction known exactly at the experiment’s $b$ values within each $b$ range. For the data points we averaged over the same regions but using the SEM images in Fig. 2 (see SM [28]). The relative intensities are adapted for the differing shadow minima in the two models. The estimated reduced intensities due to surface corrugation of 1.5 nm, as determined from atomic force microscopy (see SM), are indicated using continuous lines. Within the indicated $b$ ranges the specific sphere and wire parameters associated with the data points have been used. The data points clearly correspond better to the model taking vdW interactions into account.
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