Contact potentials in Casimir force setups: An experimental analysis (original) (raw)
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Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation
Physical Review Letters, 2007
The analysis of all Casimir force experiments using a sphere-plate geometry requires the use of the proximity-force approximation (PFA) to relate the Casimir force between a sphere and a flat plate to the Casimir energy between two parallel plates. Because it has been difficult to assess the PFA's range of applicability theoretically, we have conducted an experimental search for corrections to the PFA by measuring the Casimir force and force gradient between a gold-coated plate and five gold-coated spheres with different radii using a microelectromechanical torsion oscillator. For separations z < 300 nm, we find that the magnitude of the fractional deviation from the PFA in the force gradient measurement is, at the 95% confidence level, less than 0:4z=R, where R is the radius of the sphere.
Investigation of the Casimir force between metal and semiconductor test bodies
Physical Review A, 2005
The measurement of the Casimir force between a large gold coated sphere and single crystal silicon plate is performed with an atomic force microscope. A rigorous statistical comparison of data with theory is done, without use of the concept of root-mean-square deviation, and excellent agreement is obtained. The Casimir force between metal and semiconductor is demonstrated to be qualitatively different than between two similar or dissimilar metals which opens new opportunities for applications in nanotechnology.
Measurement of the Casimir force between a spherical gold tip and Si(111)-(7 × 7) surfaces
Japanese Journal of Applied Physics, 2016
We have performed the measurement of Casimir force between a spherical Au tip and an atomically flat Si(111)-(7×7) surface at tip-sample distances ranging from 15 to 50 nm in an ultrahigh vacuum of 1.5 × 10 −8 Pa by frequency-modulation atomic force microscopy. Atomically flat Si(111) surfaces provided by the ultrahigh-vacuum condition and a degassed Au tip reduce the contact potential difference that must be compensated. These experimental conditions led to the elucidation of the distance dependence of the Casimir force down to the distance of 15 nm. The observed distance dependence still follows a theory provided by Chen et al.[Phys. Rev. A 74, 022103 (2006)] within these distances.
Measurement of the Casimir Force between Dissimilar Metals
Physical Review Letters, 2003
The first precise measurement of the Casimir force between dissimilar metals is reported. The attractive force, between a Cu layer evaporated on a microelectromechanical torsional oscillator, and an Au layer deposited on an Al 2 O 3 sphere, was measured dynamically with a noise level of 6 fN/ √ Hz. Measurements were performed for separations in the 0.2-2 µm range. The results agree to better than 1% in the 0.2-0.5 µm range with a theoretical model that takes into account the finite conductivity and roughness of the two metals. The observed discrepancies, which are much larger than the experimental precision, can be attributed to a lack of a complete characterization of the optical properties of the specific samples used in the experiment.
The Casimir force between real materials: Experiment and theory
Reviews of Modern Physics, 2009
The physical origin of the Casimir force is connected with the existence of zero-point and thermal fluctuations. The Casimir effect is very general and finds applications in various fields of physics. This review is limited to the rapid progress at the intersection of experiment and theory that has been achieved in the last few years. It includes a critical assessment of the proposed approaches to the resolution of the puzzles arising in the applications of the Lifshitz theory of the van der Waals and Casimir forces to real materials. All the primary experiments on the measurement of the Casimir force between macroscopic bodies and the Casimir-Polder force between an atom and a wall that have been performed in the last decade are reviewed, including the theory needed for their interpretation. The methodology for the comparison between experiment and theory in the force-distance measurements is presented. The experimental and theoretical results described here provide a deeper understanding of the phenomenon of dispersion forces in real materials and offer guidance for the application of Lifshitz theory for the interpretation of the measurement results.
Physical Review B, 2012
We present measurement results for the gradient of the Casimir force between an Au-coated sphere and an Au-coated plate obtained by means of an atomic force microscope operated in a frequency shift technique. This experiment was performed at a pressure of 3 × 10 −8 Torr with hollow glass sphere of 41.3 µm radius. Special attention is paid to electrostatic calibrations including the problem of electrostatic patches. All calibration parameters are shown to be separation-independent after the corrections for mechanical drift are included. The gradient of the Casimir force was measured in two ways with applied compensating voltage to the plate and with different applied voltages and subsequent subtraction of electric forces. The obtained mean gradients are shown to be in mutual agreement and in agreement with previous experiments performed using a micromachined oscillator. The obtained data are compared with theoretical predictions of the Lifshitz theory including corrections beyond the proximity force approximation. An independent comparison with no fitting parameters demonstrated that the Drude model approach is excluded by the data at a 67% confidence level over the separation region from 235 to 420 nm. The theoretical approach using the generalized plasma-like model is shown to be consistent with the data over the entire measurement range. Corrections due to the nonlinearity of oscillator are calculated and the application region of the linear regime is determined. A conclusion is made that the results of several performed experiments call for a thorough analysis of the basics of the theory of dispersion forces.
Influence of random roughness on the Casimir force at small separations
Physical Review B, 2008
The influence of random surface roughness of Au films on the Casimir force is explored with atomic force microscopy in the plate-sphere geometry. The experimental results are compared to theoretical predictions for separations ranging between 20 and 200 nm. The optical response and roughness of the Au films were measured and used as input in theoretical predictions. It is found that at separations below 100 nm, the roughness effect is manifested through a strong deviation from the normal scaling of the force with separation distance. Moreover, deviations from theoretical predictions based on perturbation theory can be larger than 100%. PACS numbers: 68.55.Jk, 68.37.Ps, 85.85.+j, 78.68.+m * Corresponding author: g.palasantzas@rug.nl 2 When the proximity between material objects becomes of the order of nanometers up to a few microns, a regime is entered where forces quantum mechanical in nature, namely, van der Waals and Casimir forces, become operative [1]. Historically, the Casimir force has been considered to result from the perturbation of zero point vacuum fluctuations by conducting plates [1]. Because of its relatively short range, the Casimir force is now starting to take on technological importance in the operation of micro/nanoelectromechanical systems (MEMS/NEMS) at separations <200 nm, e.g., micro oscillator devices, micro/nano switches, nanoscale tweezers or actuators [2-9]. Moreover, from a fundamental point of view the Casimir force plays important role in the search of hypothetical forces beyond the standard model [6]. The early force measurements by Sparnaay and van Blockland and Overbeek [1] gave evidense on the existence of the Casimir force. Higher accuracy measurements by Lamoreaux with the use of torsion pendulum [7] initiated further detailed investigations of the Casimir force. It was also measured accurately by other groups in the plate-sphere setup with the Atomic Force Microscope (AFM), and micro oscillator devices . Other geometries were also investigated, e.g., crossed cylinders [10], and parallel plates .
A recent experiment [J. L. Garrett, D. A. T. Somers, and J. N. Munday, Phys. Rev. Lett 120, 040401 (2018)] measured for the first time the gradient of the Casimir force between two gold spheres in vacuum at room temperature, and placed a bound on the magnitude of the deviation of the measured force from the proximity force approximation (PFA). The present work extends a previous theoretical analysis of this experiment [G. Bimonte, Phys. Rev. D 97, 085011 (2018)], by analyzing in detail how the magnitude of the deviation from PFA is affected by the inclusion or neglect of ohmic dissipation at zero frequency, a much debated issue in the current Casimir literature, which goes by the name of the Drude vs plasma controversy. We analyze as well the effect of connecting the plates to charge reservoirs, which is the standard configuration used in Casimir experiments. We describe a simple and effective decimation procedure, allowing for a faster computation of the Casimir force for large aspect ratios of the system.
Kelvin probe force microscopy of metallic surfaces used in Casimir force measurements
Kelvin probe force microscopy at normal pressure was performed by two different groups on the same Au-coated planar sample used to measure the Casimir interaction in a sphere-plane geometry. The obtained voltage distribution was used to calculate the separation dependence of the electrostatic pressure P res (D) in the configuration of the Casimir experiments. In the calculation it was assumed that the potential distribution in the sphere has the same statistical properties as the measured one, and that there are no correlation effects on the potential distributions due to the presence of the other surface. The result of this calculation, using the currently available knowledge, is that P res (D) does not explain the magnitude or the separation dependence of the difference P (D) between the measured Casimir pressure and the one calculated using a Drude model for the electromagnetic response of Au. We discuss in the conclusions the points which have to be checked out by future work, including the influence of pressure and a more accurate determination of the patch distribution, in order to confirm these results.
Measurement of the Casimir Force between Parallel Metallic Surfaces
Physical Review Letters, 2002
We report on the measurement of the Casimir force between conducting surfaces in a parallel configuration. The force is exerted between a silicon cantilever coated with chromium and a similar rigid surface and is detected by looking at the shifts induced in the cantilever frequency when the latter is approached. The scaling of the force with the distance between the surfaces was tested in the 0.5 3.0 mm range, and the related force coefficient was determined at the 15% precision level.