Demonstration of the asymmetric lateral Casimir force between corrugated surfaces in the nonadditive regime

Abstract

The measurement of the lateral Casimir force between two aligned sinusoidally corrugated Au-coated surfaces has been performed in the nonadditive regime. The use of deeper corrugations also allowed us to demonstrate an asymmetry in the phase dependences of the lateral Casimir force, as predicted earlier. The measurement data are found to be in excellent agreement with the exact theoretical results computed at T = 300 K including effect of real material properties. The deviations between the exact theory and the proximity force approximation are quantified. The obtained results are topical for applications in nanomachines.The most universally known normal Casimir force 1 leads to an attraction between two closely spaced bodies directed perpendicular to their surfaces. This attraction arises due to zero-point and thermal fluctuations of the electromagnetic field. The phenomenon is important for numerous fields ranging from extradimensional physics to nanotechnology and has recently attracted considerable experimental and theoretical attentions ͑see Ref. 2͒. The most intriguing feature of the Casimir force is its nonadditivity and thus the complicated dependence on the shape of the boundary surfaces connected with diffraction effects. The nontrivial behavior of the normal Casimir force was experimentally demonstrated in the configuration of a smooth sphere above a sinusoidally corrugated plate 3 in the additive regime. Recently the normal Casimir force between an Au coated sphere and a Si plate with an array of rectangular corrugations was measured in the nonadditive regime 4 ͑where the corrugation period ⌳ is smaller than the mean separation z between the surfaces 5 ͒. The measurement data were shown to deviate from the additive theoretical results. These deviations, however, are smaller by about 50% than the prediction of Ref. 6 for ideal metals which might be explained by the interplay between nonzero skin depth and geometry effects. 4 Exact calculations performed at T = 0 taking into account the nonzero skin depth 7 favor this conjecture. In the configuration of two sinusoidally corrugated bodies ͑a sphere and a plate͒ there also arises the lateral Casimir force 8,9 which gives the possibility to actuate lateral translations in micromachines by means of the electromagnetic zero-point fluctuations. In Ref. 9 this force was measured in the additive regime ͑⌳ӷz͒. It was shown to oscillate sinusoidally as a function of the phase shift between the two corrugations.In this Rapid Communication we report measurement of the lateral Casimir force between two aligned sinusoidally corrugated surfaces of a sphere and a plate in the nonadditive regime where ⌳ ϳ z. The measurement data are found to be in excellent agreement with the exact computational results at T = 300 K taking into account real material properties. The deviation of both the experimental data and the exact theory from the prediction of the proximity force approximation ͑PFA͒ is quantified. The use here of much deeper corruga-tions than in Ref. 9 enabled the ...

Modifying the Casimir force between indium tin oxide film and Au sphere

“…[45][46][47][48]52 It was claimed that anomalous dependences of the residual potential difference and separation on contact on the separation distance observed in several experiments cast doubts on the measurements of the Casimir force performed to date. It was also suggested that inasmuch electrostatic calibrations are based on a fitting procedure there is no principal difference detween independent measurements of the Casimir force [20][21][22][23][24][25][26][27][28][29][30][35][36][37][39][40][41][42][43][44]71 and deriving the Casimir force by means of a fit from some much larger measured force of hypothetical origin. 31 In this respect we would like to note that the calibration consists in determination of the parameters of a setup using well established physical laws (in our case of electrostatics) and involves only well understood and precisely measured forces.…”

“…First, we briefly consider the preparation of the sphere which was done similar to previous experiments. [20][21][22]27,28,39,40,43,44 We used a polystyrene sphere which was glued with silver epoxy (20 × 20 µm 2 spot) to the tip of a triangular silicon nitride cantilever with a nominal spring constant of order 0.01 N/m. The cantilever-sphere system was then coated with a 10 nm Cr layer followed by 20 nm Al layer and finally with a 105 ± 1 nm Au layer.…”

“…[20][21][22][23][24][25][26][27][28][40][41][42][43][44] The AFM system consists of a head, piezoelectric actuator, an AFM controller and computer. The head includes a diode laser which emits a collimated beam with a waist of tens of micrometers at the focus, an Au-coated cantilever with attached sphere that bends in response to the sphere-plate force, and photodetectors which measure the cantilever deflection through a differential measurement of the laser beam intensity.…”

Constraints on non-Newtonian gravity and light elementary particles from measurements of the Casimir force by means of a dynamic atomic force microscope

“…For λ smaller than a few micrometers the strongest constraints on the Yukawa-type corrections to Newtonian gravity follow from measurements of the Casimir force [14,15] which becomes the dominant background force in place of gravitation at sufficiently short separations between the test bodies (see review [16]). Measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate by means of an atomic force microscope (AFM) [17,18] and the gradient of the Casimir force between smooth surfaces of a sphere and a plate by means of a micromachined oscillator [19,20] have already resulted [21] in up to several orders of magnitude stronger constraints.…”

What Is Credible and What Is Incredible in the Measurements of the Casimir Force

“…2,5 Independent on separation contact potential was also reported in experiments by U. Mohideen. 2,4,5,[23][24][25] It is notable that all these experiments were performed in high vacuum with small spheres of order 100 µm curvature radii.…”