Precision measurement of the Casimir force using gold surfaces

Abstract

A precision measurement of the Casimir force using metallic gold surfaces is reported. The force is measured between a large gold-coated sphere and flat plate using an atomic force microscope. The use of gold surfaces removes some theoretical uncertainties in the interpretation of the measurement. The forces are also measured at smaller surface separations. The complete dielectric spectrum of the metal is used in the comparison of theory to the experiment. The average statistical precision remains at the same 1% of the forces measured at the closest separation. These results should lead to the development of stronger constraints on hypothetical forces. PACS number͑s͒: 12.20.Fv The Casimir force ͓1,2͔ has its origin in the zero-point electromagnetic vacuum fluctuations predicted by quantum electrodynamics. If two perfectly reflecting metal plates are held parallel, then the alteration of the zero-point energy by the metal boundaries leads to an attractive force between the plates called the Casimir force ͓1,2͔. Lifshitz ͓3͔ generalized the force to any two infinite dielectric half-spaces as the force between fluctuating dipoles induced by the zero-point electromagnetic fields and obtained the same result as Casimir for two perfectly reflecting ͑infinite conductivity͒ flat plates. The Casimir force has been demonstrated between two flat plates ͓4͔ and a large sphere and a flat plate ͓5,6͔ and its value shown to be in agreement with the theory to an average deviation of 1% ͓7-9͔. For dielectric bodies the resulting force has been measured with reasonable agreement to the theory ͓10͔. Theoretical treatments of the Casimir force have shown that it is a strong function of the boundary geometry and spectrum ͓11-13͔. Experiments with periodically corrugated boundaries have also demonstrated the nontrivial boundary dependence of the Casimir force ͓14͔. Here we report an improved precision measurement of the Casimir force between a metallized sphere of diameter 191.3 m and a flat plate using an atomic force microscope ͑AFM͒. The use of gold surfaces and the related experimental changes are the primary differences between the experiments reported here and the last version of the experiment ͓9͔. In the previous experiments ͓7,9͔, Al surfaces were used due to their high reflectivity and ease of fabrication. However, in order to prevent the effects of oxidation of the Al surfaces, a thin layer of sputtered Au/Pd was used on top of the Al surface. This thin Au/Pd coating was treated in a phenomenological manner in the earlier experiments ͓7-9͔. A more complete theoretical treatment is complicated as nonlocal effects such as spatial dispersion need to be taken into account in the calculation of the Casimir force ͓15͔. Thus it is necessary to use chemically inert materials such as gold for the measurement of the Casimir force that is reported here. The complete dielectric properties of Au is used in the theory. An important application of Casimir force measurements is to develop strong limits on hypothetical long-range forces ...

New developments in the Casimir effect

“…In the experiments on the Casimir force measurements, symmetrical configurations are usually used, i.e., both interacting bodies are made of one and the same material which at times is covered by a thin layers of another material [40][41][42][43][44]. In line with this let us consider the configuration presented in Fig.…”

“…Unfortunately, this can be done only for configurations possessing high symmetry properties. Of particular interest is the configuration of a sphere (lens) above a disk which is used in the modern experiments on the measurement of the Casimir force [40][41][42][43][44]. For this configuration all the variables in the wave equation cannot be separated which makes impossible to obtain the exact expression for the Casimir force starting from the first principles.…”

“…Given that the modern experiments on the Casimir force measurement [40][41][42][43][44] use configurations such as a sphere (lens) above a disk, the approximate methods discussed above are gaining in importance.…”

“…The historical experiments on measuring the Casimir force between metals and dielectrics are presented starting from [20]. The major part of Sec.6 is devoted to the presentation of the results of modern experiments [40][41][42][43][44] and their comparison with the theoretical results for the Casimir force between real media represented in Sec.5. The prospects for further improving the accuracy of Casimir force measurements are outlined.…”

“…In [40] a torsion pendulum was used to measure the force between Cu plus Au coated quartz optical flat, and a spherical lens. In [41][42][43][44] an atomic force microscope was first applied to measure the Casimir force between Al plus Au/Pd and Au coated sapphire disk and polystyrene sphere. Considerable progress has been made towards the improving the accuracy of the Casimir force measurements.…”