Measurement of the Casimir Force between 0.2 and 8 μm: Experimental Procedures and Comparison with Theory

Giuseppe Bimonte,Benjamin Spreng,Vladimir M Mostepanenko,Gert-Ludwig Ingold,Galina L Klimchitskaya,Paulo A Maia Neto,Ricardo S Decca

doi:10.3390/universe7040093

Abstract

We present results on the determination of the differential Casimir force between an Au-coated sapphire sphere and the top and bottom of Au-coated deep silicon trenches performed by means of the micromechanical torsional oscillator in the range of separations from 0.2 to 8 μm. The random and systematic errors in the measured force signal are determined at the 95% confidence level and combined into the total experimental error. The role of surface roughness and edge effects is investigated and shown to be negligibly small. The distribution of patch potentials is characterized by Kelvin probe microscopy, yielding an estimate of the typical size of patches, the respective r.m.s. voltage and their impact on the measured force. A comparison between the experimental results and theory is performed with no fitting parameters. For this purpose, the Casimir force in the sphere-plate geometry is computed independently on the basis of first principles of quantum electrodynamics using the scattering theory and the gradient expansion. In doing so, the frequency-dependent dielectric permittivity of Au is found from the optical data extrapolated to zero frequency by means of the plasma and Drude models. It is shown that the measurement results exclude the Drude model extrapolation over the region of separations from 0.2 to 4.8 μm, whereas the alternative extrapolation by means of the plasma model is experimentally consistent over the entire measurement range. A discussion of the obtained results is provided.

Highlights

The Casimir attraction [1] between two uncharged closely spaced bodies is a macroscopic quantum effect which is caused by the zero-point and thermal fluctuations of the electromagnetic field
A metal-coated sapphire sphere is glued to a high mechanical quality factor Q polysilicon microelectromechanical torsional oscillator (MTO), which serves as a sensitive force transducer
Underneath the plate two electrodes located to each side of the axis of rotation allow to determine the relative motion of the plate with respect to the substrate by means of the capacitive signal between them and the MTO’s plate

Summary

Introduction

The Casimir attraction [1] between two uncharged closely spaced bodies is a macroscopic quantum effect which is caused by the zero-point and thermal fluctuations of the electromagnetic field. Precise measurements of the Casimir force have been made possible only during the last 20 years thanks to microtechnology achievements These measurements gave the possibility of quantitatively checking the theoretical predictions of the Lifshitz theory [3,4] which generalizes the original Casimir prediction (made for two parallel ideal metal planes at zero temperature) for the case of thick plates described by their frequency-dependent dielectric permittivities in thermal equilibrium with the environment. The first experiment of this kind used an atomic force microscope where the sharp tip was replaced with the sphere of about 100 μm radius [5] This experiment made it possible to demonstrate corrections to the famous Casimir expression due to the finite conductivity of the boundary metal. After experimental improvements [8], micromechanical torsional oscillators were used in the most precise measurements of the Casimir interaction between an Au-coated sapphire sphere of 150 μm radius and an Au-coated polysilicon plate [9,10,11,12]

Methods

Results

Discussion

Conclusion