Measurement of the Casimir Force between Dissimilar Metals

The first precise measurement of the Casimir force between dissimilar metals is reported. The attractive force, between a Cu layer evaporated on a microelectromechanical torsional oscillator and an Au layer deposited on an ${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ sphere, was measured dynamically with a noise level of $6\mathrm{f}\mathrm{N}/\sqrt{\mathrm{H}\mathrm{z}}$. Measurements were performed for separations in the $0.2–2\mu \mathrm{m}$ range. The results agree to better than $1\%$ in the $0.2–0.5\mu \mathrm{m}$ range with a theoretical model that takes into account the finite conductivity and roughness of the two metals. The observed discrepancies, which are much larger than the experimental precision, can be attributed to a lack of a complete characterization of the optical properties of the specific samples used in the experiment.

Figure 1

Schematic of the experimental setup showing its main components. The inset shows a schematic of the electronic circuit used for the static measurements.

Figure 2

Electrostatic force as a function of separation for $V_{Au}-V_o=0.24\mathrm{V}$ and 0.30 V. Inset: Scanning electron microscope image of the MTO showing the serpentine spring.

Figure 3

Casimir force as a function of separation. The separation between the metallic layers has been adjusted to account for the roughness: $z=z_{\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{l}}+2{\delta }_o$. (a) Direct measurement of the force. The solid line is a fit using Eq. (4b). (b) Experimental data subtracted from the theoretical model.

Figure 4

(a) Derivative of the Casimir force (see text) as a function of separation. The solid line is a fit using Eq. (4a). (b) Experimental data subtracted from the theoretical model. The deviation with respect to the model at small separations is partially associated with nonlinear terms of Eq. (2).