Abstract
Technological progress has made possible precise measurements of the Casimir forces at distances less than 100 nm. It has enabled stronger constraints on the non-Newtonian forces at short separations and improved control of micromechanical devices. Experimental information on the forces below 30 nm is sparse and not precise due to pull-in instability and surface roughness. Recently, a method of adhered cantilever was proposed to measure the forces at small distances, which does not suffer from the pull-in instability. Deviation of the cantilever from a classic shape carries information on the forces acting nearby the adhered end. We calculate the force between a flat cantilever and rough Au plate and demonstrate that the effect of roughness dominates when the bodies approach the contact. Short-distance repulsion operating at the contact is included in the analysis. Deviations from the classic shape due to residual stress, inhomogeneous thickness of the cantilever, and finite compliance of the substrate are analysed. It is found that a realistic residual stress gives a negligible contribution to the shape, while the finite compliance and inhomogeneous thickness give measurable contributions that have to be subtracted from the raw data.
Highlights
Quantum fluctuations of the electromagnetic field manifest themselves in very different physical circumstances such as sticking gecko to walls or evaporation of black holes.Van der Waals attraction between nonpolar molecules is the effect of quantum fluctuations as was explained by London [1]
At very short distances the fluctuation induced forces between bulk bodies decreasing with the distance as h−3 are called the Van der Waals (vdW) forces, while at larger separations the forces behave as h−4 and are called the Casimir forces
There is no physical difference in the origin of these forces, just in the first case retardation of the electromagnetic signal is neglected, but in the second case (CF) it is fully taken into account
Summary
Quantum fluctuations of the electromagnetic field manifest themselves in very different physical circumstances such as sticking gecko to walls or evaporation of black holes. All systems used to measure the forces employ the elastic suspension (torsional pendulum or cantilever with a ball attached) that loses stability at sufficiently short separations. The surface force apparatus that uses much stiffer springs is more stable, but even in this case the smallest distance in vacuum was about 8.5 nm [36] The measurements at these short separations are sparse [35,36,37] and have low precision. To be able to extract information on the CF from the experiment we analyse the influence of the background effects on the classic shape of the cantilever It includes the residual stress in the cantilever, inhomogeneous thickness of the cantilever, and finite compliance of the substrate in the adhered area
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