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 μ$\mathsf{\mu }$m. 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 μ$\mathsf{\mu }$m, 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.

中文翻译：

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卡西米尔力在0.2至8μm之间的测量：实验程序和与理论的比较

我们提出的结果是通过微机械扭转振荡器在0.2到8的分离范围内确定Au涂层蓝宝石球与Au涂层深硅沟槽的顶部和底部之间的卡西米尔力的差异 μ$\mathsf{\mu }$米 在95％的置信度下确定所测力信号中的随机误差和系统误差，并将其合并为总实验误差。对表面粗糙度和边缘效应的作用进行了调查，结果显示很小。膜片电位的分布用开尔文探针显微镜表征，可以估算出膜片的典型尺寸，各自的均方根电压及其对测得力的影响。在没有拟合参数的情况下进行了实验结果和理论之间的比较。为此，使用散射理论和梯度展开，在量子电动力学的第一原理的基础上，独立计算球体板几何形状中的卡西米尔力。在这样做，通过等离子和德鲁德模型从外推到零频率的光学数据中发现金的随频率变化的介电常数。结果表明，测量结果排除了从0.2到4.8的分离区域上的Drude模型外推μ$\mathsf{\mu }$m，而通过等离子体模型进行的替代推断在整个测量范围内在实验上是一致的。提供了对所得结果的讨论。