Measurement of the Casimir Force between a Gold Sphere and a Silicon Surface with Nanoscale Trench Arrays

Abstract

We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interacting bodies. The observed deviation, however, is smaller than the calculated values for perfectly conducting surfaces, possibly due to the interplay between finite conductivity and geometry effects. DOI: 10.1103/PhysRevLett.101.030401 PACS numbers: 03.70.+k, 12.20.Fv, 12.20.Ds, 42.50.Lc The Casimir force is the interaction between neutral conductors that can be understood as resulting from the alteration of the zero point energy of the electromagnetic field in the presence of boundaries [1]. For two perfect metallic planar surfaces, the force is attractive and is given by F c 2 @cA=240z4 , where c is the speed of light, @ is the Planck's constant=2, z is the separation between the plates, and A is the area of the plates. There exists a close connection between the Casimir force between conductors and the van der Waals (vdW) force between molecules. For the former, the quantum fluctuations are often associated with the vacuum electromagnetic field, while the latter commonly refers to the interaction between fluctuating dipoles. In simple geometries such as two parallel planes, the Casimir force can be interpreted as an extension of the vdW force in the retarded limit. The interaction between molecules in the two plates is summed to yield the total force. However, such summation of the vdW force is not always valid for extended bodies because the vdW force is not pairwise additive. The interaction between two molecules is affected by the presence of a third molecule. One important characteristic of the Casimir force is its strong dependence on geometry [2]. The Casimir energy for a conducting spherical shell [3] or a rectangular box [4,5] has been calculated to have opposite sign to parallel plates. Whether such geometries exhibit repulsive Casimir forces remains a topic of current interest [6].In recent years, there have been a number of precision measurements of the Casimir force [7][8][9][10][11][12][13][14][15]. These experiments yield agreement with the theoretical calculations to accuracies of better than 1% when nonideal behavior of the metallic surfaces [16][17][18] are taken into account. The vast majority of force measurements were performed between a sphere and a flat plate, two flat plates, or two cylinders. For these simple geometries, the Casimir force is not expected to show significant deviations from the pairwise additive approximation (PAA) at small separations. There has only been one experiment that involved surfaces of other geometries, where the Casimir force is measured between a sphere and a plate with small sinusoidal corrugations [19]. While this measurement shows deviations from PAA, the interpret...

Casimir forces on a silicon micromechanical chip

“…HF also passivates the surfaces to temporarily prevent the reformation of oxide at ambient pressure 16 . The chip is then immediately loaded into a sealed probe that is evacuated and then lowered into a cryostat.…”

“…Metamaterials, with their remarkable optical properties, have been considered as candidates for controlling the Casimir force 9,10 , but initial suggestions that the sign of the force in vacuum could be altered by metamaterials turned out to be unrealistic 11 . With regard to the non-trivial dependence of the Casimir force on the shape of the bodies [12][13][14][15] , experiments involving nanostructured surfaces have demonstrated the nonpairwise additive nature of the Casimir force 16,17 . Recent experiments have also measured the corrections to the Casimir force that arise from the presence of thermal fluctuations, in addition to quantum fluctuations 18 .…”

Design of a Casimir-driven parametric amplifier

“…An integrated MEMS device may enable significant improvements in the sensitivity of Casimir experiments. This could shed light on experiments studying material, surface topology [47,48] and metamaterials [49,50], an understanding of which is crucial for stabilizing nano-structures subjected to the Casimir force. Ultimately, using parametrically driven MEMS may even enable high precision measurements of non-Newtonian forces acting on short length scales [51].…”

Field theoretic approach to roughness corrections

“…However, it should be noted that surfaces with σ > ℓ can be artificially created. In this case a loop expansion of the free energy in σ 2 /ℓ 2 is not applicable [26,27]. .…”