Precise Calculation of the Casimir Force Between Gold Surfaces

Abstract

We analyse the result of precise measurement of the Casimir force between bodies covered with gold. The values of the parameters used to extrapolate the gold dielectric function to low frequencies are very important and discussed in detail. The finite temperature effect is shown to exceed considerably the experimental errors. The upper limit on the force is found which is smaller than the measured force. Many experimental and theoretical uncertainties were excluded with gold covering and we conclude that, possibly, a new force has been detected at small separations between bodies.12.20. Ds, 12.20.Fv, 03.70.+k, 14.80 c a 4 has been found as change in the zero point energy between two parallel perfectly conducting plates separated by the distance a. For sphere and plate the expression above has to be modified with the proximity force theorem (PFT) [7] to the followingwhere R is the sphere radius. Real metals are not ideal conductors and there is an important correction to (1) taking into account their real properties. In the Lifshitz theory [8], which generalizes the Casimir approach, the force is represented in terms of the metal dielectric function ε (iω) at imaginary frequencies. This theory was applied for description of the experiments in [6,9]. Different but equivalent method has been developed in [10], where detailed calculations were made for Al, Au, and Cu metallization of the bodies using the handbook optical data for these metals. The result for Au is in good agreement with the torsion pendulum experiment [4]. For the atomic force microscope (AFM) experiment [5,6] Al metallization has been used. This metal is oxidized easily and charges can be trapped in the oxide. To prevent influence of these charges on the force, Al was covered with a thin layer (20 or 8 nm thick) of Au/P d. The conclusion has been made [6] that the result of the AFM experiment was in agreement with the theory. However, in all calculations [5,6,11] the role of Au/P d layer was ignored. Importance of this layer was stressed in [12] (see also [13]), where the upper limit on the force has been found using parameters of single-crystalline materials. This limit was smaller than the measured force in both experiments [5,6] and the discrepancy far exceeded the experimental errors. To exclude uncertainties connected with aluminum oxidation, Au/P d layer and clarify the origin of the discrepancy, it was proposed [12] to use Au metallization instead of Al. Very recently the AFM experiment with Au metallization has been carried out [14]. In this experiment the residual potential was reduced to a negligible level so as the surface roughness. The force was measured for smaller separations up to 62 nm with uncertainty 3.5 pN . In the previous experiments the photodiods response on the cantilever deflection was calibrated assuming that the plate-sphere system on the contact behaves as a rigid body. As the new experiment showed this natural assumption was not quite correct and different calibration method was proposed [14]. To all appearance the exc...

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