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 ...

The lateral Casimir force between a sinusoidally corrugated gold coated plate and large sphere was measured for surface separations between 0.2 µm to 0.3 µm using an atomic force microscope. The measured force shows the required periodicity corresponding to the corrugations. It also exhibits the necessary inverse fourth power distance dependence. The obtained results are shown to be in good agreement with a complete theory taking into account the imperfectness of the boundary metal. This demonstration opens new opportunities for the use of the Casimir effect for lateral translation in microelectromechanical systems.PACS numbers: 12.20. Fv, 42.50.Lc, 61.16.Ch The archetypical Casimir force [1] leads to an attraction between two neutral metal plates placed in vacuum. The force results from the alteration by the metal boundaries of the zero point electromagnetic energy which is present in empty space. Uniquely the Casimir force is independent of the electric charge and other interaction constants. As a result, it is strongly dependent on geometry and topology of the boundary and can be both attractive as well as repulsive (for a review of different aspects of the Casimir effect see monographs [2,3]).The normal Casimir force which leads to an attraction perpendicular to the two surfaces has been demonstrated first between flat plates [4] and between a flat plate and a lens [5,6]. Recently extensive experimental research on the normal Casimir force between a large sphere and a flat plate has been performed with increased precision [7][8][9]. Also the non-trivial boundary dependence of the Casimir force acting between a large sphere and plate with periodic uniaxial sinusoidal corrugations was demonstrated in Ref. [10]. This has led to extensive theoretical study of the corrections to the Casimir effect due to various factors as finite conductivity of the boundary metal, surface roughness, and nonzero temperature. Also the combined effect of these factors was investigated (new experimental and theoretical developments are presented in review [11]). Even more importantly, the Casimir effect is finding new applications in fundamental science and engineering. Thus, with the advent of modern unified theories involving compact dimensions, precision measurements of the Casimir force have been used to set limits on the presence of hypothetical forces [12][13][14]. With regard to technological applications, both static and dynamic microelectromechanical machines have been created actuated by the normal Casimir force [15,16]. Also, adhesion and sticking of moving parts in microelectromechanical systems due to the Casimir effect were investigated [17].In this letter we report the first demonstration of the lateral Casimir force. It acts between two aligned corrugated surfaces and leads to a mechanical force acting tangential to the surfaces. Similar to the normal Casimir force, the lateral Casimir force also originates from the modifications of electromagnetic zero point oscillations. The possibility of a lateral Casimir force...

The experimental demonstration of the modification of the Casimir force between a gold coated sphere and a single-crystal Si membrane by light pulses is performed. The specially designed and fabricated Si membrane was irradiated with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of the charge-carrier density. The difference in the Casimir force in the presence and in the absence of laser radiation was measured by means of an atomic force microscope as a function of separation at different powers of the absorbed light. The total experimental error of the measured force differences at a separation of 100 nm varies from 10 to 20% in different measurements. The experimental results are compared with theoretical computations using the Lifshitz theory at both zero and laboratory temperatures. The total theoretical error determined mostly by the uncertainty in the concentration of charge carriers when the light is incident is found to be about 14% at separations less than 140 nm. The experimental data are consistent with the Lifshitz theory at laboratory temperature, if the static dielectric permittivity of high-resistivity Si in the absence of light is assumed to be finite. If the dc conductivity of high-resistivity Si in the absence of light is included into the model of dielectric response, the Lifshitz theory at nonzero temperature is shown to be experimentally inconsistent at 95% confidence. The demonstrated phenomenon of the modification of the Casimir force through a change of the charge-carrier density is topical for applications of the Lifshitz theory to real materials in fields ranging from nanotechnology and condensed matter physics to the theory of fundamental interactions.

We report the first experiment on the optical modulation of dispersion forces through a change of the carrier density in a Si membrane. For this purpose a high-vacuum based atomic force microscope and excitation light pulses from an Ar laser are used. The experimental results are compared with two theoretical models. The modulation of the dispersion force will find applications in optomechanical micromachines.

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology. PACS numbers: 12.20.Fv, 12.20.Ds, 68.37.Ps, 73.25.+i The Casimir effect [1] implies that there is a force acting between closely spaced neutral bodies determined by the zero-point oscillations of the electromagnetic field. In the last few years the Casimir force was extensively investigated experimentally (see, e.g., Refs,[2,3,4,5,6,7,8] and review [9]). It has found many diverse applications ranging from Bose-Einstein condensation [10], carbon nanotubes [11], and to the testing of predictions of new physics beyond the standard model [7,8,9]. One of the most important applications of the Casimir effect is in the design, fabrication and function of MEMS and NEMS such as micromirrors, nanotweezers and nanoscale actuators [12,13,14]. The combined action of the Casimir and electrostatic forces can result in nonlinear dynamics, bistable phenomena and even cause device failure by the abrupt "pull-in" and attachment of one surface to the other [12,13,14]. The Casimir force also changes the operation bandwidth and tunability of MEMS. The actuation of MEMS using the Casimir force has been demonstrated [14].The modification of the Casimir force by changing parameters of the system other than the separation is a complicated problem since it requires modification of the optical properties of materials within a relatively wide frequency region. The attempt to modify the Casimir force due to a coating with a hydrogen-switchable mirror did not lead to any observed effect [15]. We pioneer the demonstration of the difference Casimir force between a gold coated sphere and two Si samples which possess different resistivities and charge carrier densities. We use a high vacuum (2 × 10 −7 Torr) based AFM to measure the Casimir force between a gold coated polystyrene sphere with a diameter 2R = 201.8 ± 0.6 µm and two 4 × 7 mm 2 size Si plates placed next to each other. The thickness of gold coating on the sphere was measured to be 96 ± 2 nm. The details of the setup were described [16] in the previous experiment with one Si plate. For this experiment two identical polished, single crystal, 100 orientation Si plates were chosen, 500 µm thick and with a resistivity 0.1−1 Ω cm. They were n-type and doped with P. The resistivity of the plates was measured using the 4-probe technique to beρ ≈ 0.43 Ω cm leading to the concentration of charge carriersñ ≈ 1.2 × 10 16 cm −3 . One of these samples was used as the first Si plate in the experiment. The other one was subjected to thermal diffusion doping to prepare the second, lower resistivity, plate. A phosphorous based...