Measurement of the Casimir force in a gas and in a liquid

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Measurement of the Casimir force in a gas and in a liquid

Anne Le Cunuder, Artyom Petrosyan, George Palasantzas, Vitaly Svetovoy, and Sergio Ciliberto

Phys. Rev. B 98, 201408(R) – Published 28 November 2018

Abstract

We present detailed measurements of the Casimir-Lifshitz force between two gold surfaces, performed in both gas (nitrogen) and liquid (ethanol) environments with the same apparatus and on the same spot of the sample. Furthermore, we study the role of double-layer forces in the liquid, and we show that these electrostatic effects are important. The latter contributions are subtracted to recover the genuine Casimir force, and the experimental results are compared with calculations using Lifshitz theory. Our measurements demonstrate that carefully accounting for the actual optical properties of the surfaces is necessary for an accurate comparison with the Lifshitz theory predictions at distances smaller than 200 nm.

Received 12 July 2018
Revised 22 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.201408

Physics Subject Headings (PhySH)

Casimir effect Defects Dielectric properties Electrical conductivity Permittivity Roughness Structural properties

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Anne Le Cunuder^1,*, Artyom Petrosyan¹, George Palasantzas², Vitaly Svetovoy^2,3, and Sergio Ciliberto¹

¹Laboratoire de Physique, CNRS UMR5672, Université de Lyon, École Normale Supérieure, 46 Allée d'Italie, 69364 Lyon, France
²Faculty of Sciences and Engineering, University of Groningen, Nijenborg 4, 9747 AG Groningen, The Netherlands
³A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninsky prospect 31 bld. 4, 119071 Moscow, Russia

^*Present address: Department of Condensed Matter Physics, University of Barcelona, Marti i Franques, 1, 080028 Barcelona, Spain.

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Issue

Vol. 98, Iss. 20 — 15 November 2018

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Images

Figure 1
Experimental setup. A gold-coated polystyrene bead is glued on the cantilever tip which measures the sphere-plane interaction force at distance $d$ . The deflection of the cantilever is detected by an interferometric technique: two laser beams, orthogonally polarized, are focused on the cantilever; the reference one is reflected by the static base and the second one by the cantilever free end. When the cantilever is bent the optical path difference $δ$ between the two beams is measured through an interferometer [19].
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Figure 2
Measurement of the Casimir force between two Au surfaces in a nitrogen atmosphere. (a) Blue points correspond to the mean measured force. Blue circles correspond to a single measurement of the Casimir force. Orange solid curve corresponds to the Lifshitz theory in which the dielectric function $ε$ is evaluated from measured optical data of a real gold film [10]. For the green dashed-dotted line, $ε$ is evaluated using the handbook optical data [34]. Red dashed line corresponds to the theory in the case of ideal conductors. (b) Relative difference between the theoretical and experimental Casimir forces. Same colors as in (a). The error bars include the statistical and the systematic errors due to uncertainties on the separation upon contact $d_{0} = (31 \pm 2) nm$ (using the hydrodynamic estimation), on the stiffness $κ = (0.57 \pm 0.03) N / m$ and on the diameter of the sphere $D = (150.0 \pm 0.5) μ m$ .
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Figure 3
Measurement of the Casimir force in ethanol. (a) Single force measurement (blue points) after subtracting the hydrodynamic force. The distance has been shifted by $d_{0} = 31 nm$ . The red line corresponds to the linear fit of the thermal drift in the range 300– $600 nm$ . (b) Single force measurement (red circles) and mean force measurement (blue points) (averaged over eight measurements) of $F_{cas} + F_{Debye}$ obtained after subtraction of the thermal drift and the hydrodynamic force. The mean measured force is fitted by an exponential in the range $d > 120 nm$ . In this distance range, double-layer forces largely remove the Casimir force. The blue line corresponds to the exponential fit, yielding the Debye length $λ_{D} = (46 \pm 6) nm$ and the surface potential $ψ_{0_{adj}} = (63 \pm 13) mV$ through Eq. (6). (c) Measurement of the Casimir force between two Au surfaces in ethanol, where blue crosses correspond to the mean measured force. The orange solid line corresponds to the Lifshitz theory where the dielectric function $ε$ is evaluated from measured optical data of a real gold film [10]; for the green dashed-dotted line, $ε$ is evaluated using the handbook optical data [34].
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