Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions

We report an improved dynamic determination of the Casimir pressure P^expt between two plane plates obtained using a micromachined torsional oscillator. The main improvements in the current experiment are a significant suppression of the surface roughness of the Au layers deposited on the interacting surfaces, and a decrease by a factor of 1.7 (down to 0.6 nm) in the experimental error in the measurement of the absolute separation. A metrological analysis of all data for P^expt from 15 sets of measurements permitted us to determine both the random and systematic errors, and to find the total experimental error in P^expt as a function of separation at the 95% confidence level. In contrast to all previous experiments on the Casimir effect, where a small relative error was achieved only at the shortest separation, our smallest experimental error (∼0.5%) is achieved over a wide separation range. The theoretical Casimir pressures P^theor in the experimental configuration were calculated by the use of four theoretical approaches suggested in the literature based on the Lifshitz formula at nonzero temperature. All corrections to the Casimir force due to grain structure of the overlying metal layers (including the variation of optical data and patch potentials), surface roughness (including nonmultiplicative and diffraction-type effects), and nonlocal effects, were calculated or estimated. The maximum value of the roughness correction, achieved at the shortest separation of 160 nm, is equal to only 0.65% of the Casimir pressure. All theoretical errors, including those introduced by the proximity force theorem, finite size of the plate area, and uncertainties in the experimental separations, were analyzed and metrologically combined to obtain the total theoretical error at the 95% confidence level. Finally, the confidence interval for (P^theor - P^expt) was obtained as a function of separation. Our measurements are found to be consistent with two theoretical approaches utilizing the plasma model and the surface impedance over the entire measurement region from 160 to 750 nm. Two other approaches to the thermal Casimir force, utilizing the Drude model or a special prescription for the determination of the zero-frequency contribution to the Lifshitz formula, are excluded on the basis of our measurements at the 99 and 95% confidence levels, respectively. Finally, constraints on Yukawa-type hypothetical interactions are strengthened by up to a factor of 20 in a wide interaction range.