Recently W. J. Kim, M. Brown-Hayes, D. A. R. Dalvit, J. H. Brownell, and R. Onofrio [Phys. Rev. A, v.78, 036102(R) (2008)] performed electrostatic calibrations for a plane plate above a centimeter-size spherical lens at separations down to 20-30 nm and observed "anomalous behavior". It was found that the gradient of the electrostatic force does not depend on separation as predicted on the basis of a pure Coulombian contribution. Some hypotheses which could potentially explain the deviation from the expected behavior were considered, and qualitative arguments in favor of the influence of patch surface potentials were presented. We demonstrate that for the large lenses at separations of a few tens nanometers from the plate, the electrostatic force law used by the authors is not applicable due to possible deviations of the mechanically polished and ground lens surface from a perfect spherical shape. A model is proposed which explains the observed "anomalous behavior" using the standard Coulombian force.
A number of experimental measurements of the Casimir force have observed a logarithmic distance variation of the voltage that minimizes electrostatic force between the plates in a sphere-plane geometry. We show that this variation can be simply understood from a geometric averaging of surface potential patches together with the Proximity Force Approximation.
In a recent paper (Phys.Rev.A78, 020101(R) (2008)), Kim at al. have reported a large anomaly in the scaling law of the electrostatic interaction between a sphere and a plate, which was observed during the calibration of their Casimir force set-up. Here we experimentally demonstrate that in proper electrostatic calibrations the scaling law follows the behavior expected from elementary electrostatic arguments, even when the electrostatic voltage that one must apply to minimize the force (typically ascribed to contact potentials) depends on the separation between the surfaces.
The imperfect termination of static electric fields at semiconducting surfaces has been long known in solid state and transistor physics. We show that the imperfect shielding leads to an offset in the distance between two surfaces as determined by electrostatic force measurements. The effect exists even in the case of good conductors (metals) albeit much reduced.
It is well known that residual electrostatic forces create significant difficulties to precise measurements of the Casimir force and to wide use of Casimir-operated microdevices. We experimentally demonstrate that with the help of Ar-ion cleaning of the surfaces it is possible to make electrostatic effects negligibly small as compared to the Casimir interaction. Our experimental setup consists of the dynamic atomic force microscope supplemented with an Ar-ion gun and argon reservoir. The residual potential difference between the Au-coated surfaces of a sphere and a plate was measured both befo…
We report on measurements performed on an apparatus aimed to study the Casimir force in the cylinder-plane configuration. The electrostatic calibrations evidence anomalous behaviors in the dependence of the electrostatic force and the minimizing potential upon distance. We discuss analogies and differences of these anomalies with respect to those already observed in the sphere-plane configuration. At the smallest explored distances we observe frequency shifts of non-Coulombian nature preventing the measurement of the Casimir force in the same range. We also report on measurement performed in t…
The existence of a monotonic distance dependent contact potential between two plates in a Casimir experiment leads to an additional electrostatic force that is significantly different from the case of a constant potential. Such a varying potential can arise if there is a uniform gradient in the work function or contact potential across a plate, as opposed to random microscopic fluctuations associated with patch potentials. A procedure to compensate for this force is described for the case of an experiment where the electrostatic force is minimized at each measurement distance by applying a vol…
In this work, we present detailed measurements of the Casimir-Lifshitz force between two gold surfaces (a sphere and a plate) immersed in ethanol and study the effect of residual electrostatic forces, which are dominated by static fields within the apparatus and can be reduced with proper shielding. Electrostatic forces are further reduced by Debye screening through the addition of salt ions to the liquid. Additionally, the salt leads to a reduction of the Casimir-Lifshitz force by screening the zero-frequency contribution to the force; however, the effect is small between gold surfaces at the…
Several new experiments have extended studies of the Casimir force into new and interesting regimes. This recent work will be briefly reviewed. With this recent progress, new issues with background electrostatic effects have been uncovered. The myriad of problems associated with both patch potentials and electrostatic calibrations are discussed and the remaining open questions are brought forward.
We compare the results of capacitance measurements in the lens-plane and sphere-plane configurations with theoretical predictions from various models of a spherical surface. It is shown that capacitance measurements are incapable of discriminating between models of perfect and modified spherical surfaces in an experiment demonstrating the anomalous scaling law for the electric force. Claims to the contrary in the recent literature are explained by the use of irregular comparison. The data from capacitance measurements in an experiment measuring the Casimir force using a micromechanical torsion…
We present an overview of the validity of the Proximity Force Approximation (PFA) in the calculation of Casimir forces between perfect conductors for different geometries, with particular emphasis for the configuration of a cylinder in front of a plane. In all cases we compare the exact numerical results with those of PFA, and with asymptotic expansions that include the next to leading order corrections. We also discuss the similarities and differences between the results for Casimir and electrostatic forces.
We have performed numerical simulations to evaluate the effect on the capacitance of finite size boundaries realistically present in the parallel plane, sphere-plane, and cylinder-plane geometries. The potential impact of edge effects in assessing the accuracy of the parameters obtained in the electrostatic calibrations of Casimir force experiments is then discussed.
We have performed precision electrostatic calibrations in the sphere-plane geometry and observed anomalous behavior. Namely, the scaling exponent of the electrostatic signal with distance was found to be smaller than expected on the basis of the pure Coulombian contribution and the residual potential found to be distance dependent. We argue that these findings affect the accuracy of the electrostatic calibrations and invite reanalysis of previous determinations of the Casimir force.
Electrostatic patch potentials give rise to forces between neutral conductors at distances in the micrometer range and must be accounted for in the analysis of Casimir force experiments. In this paper we develop a quasi-local model for describing random potentials on metallic surfaces. In contrast to some previously published results, we find that patches may provide a significant contribution to the measured signal, and may render the experimental data at distances below 1 micrometer compatible with theoretical predictions based on the Drude model.
We report on measurements of forces acting between two conducting surfaces in a spherical-plane configuration in the 35 nm-1 micrometer separation range. The measurements are obtained by performing electrostatic calibrations followed by a residual analysis after subtracting the electrostatic-dependent component. We find in all runs optimal fitting of the calibrations for exponents smaller than the one predicted by electrostatics for an ideal sphere-plane geometry. We also find that the external bias potential necessary to minimize the electrostatic contribution depends on the sphere-plane dist…
In a recent Comment, Decca et al. [Phys. Rev. A 79, 026101 (2009); arXiv:0809.3576] discussed the origin of the anomalies recently reported by us in Phys. Rev. A 78, 036102(R) (2008); arXiv:0812.0028 . Here we restate our view, corroborated by their considerations, that quantitative geometrical and electrostatic characterizations of the conducting surfaces (a topic not discussed explicitly in the literature until very recently) are critical for the assessment of precision and accuracy of the demonstration of the Casimir force and for deriving meaningful limits on the existence of Yukawian comp…
Measurements of the Casimir force require the elimination of electrostatic interactions between the surfaces. However, due to electrostatic patch potentials, the voltage required to minimize the total force may not be sufficient to completely nullify the electrostatic interaction. Thus, these surface potential variations cause an additional force, which can obscure the Casimir force signal. In this paper, we inspect the spatially varying surface potential (SP) of e-beamed, sputtered, sputtered and annealed, and template stripped gold surfaces with Heterodyne Amplitude Modulated Kelvin Probe Fo…
We have reviewed the Comment of Geyer et al. [arXiv:0708.1548] concerning our recent work [Phys. Rev. A 75, 060102 (R) (2007)], and while we disagree with their criticisms, we acknowledge them for giving us the opportunity to add interesting addition material and a more detailed description of our experiment. We describe further our calculation and explain why a more sophisticated model is not warranted. We also present detailed experiments on the effects of electrostatic forces in our measurements and show that the contribution due to work function differences is small and that the residual e…
The Casimir force is the ultimate background in ongoing searches of extra-gravitational forces in the micrometer range. Eccentric cylinders offer favorable experimental conditions for such measurements as spurious gravitational and electrostatic effects can be minimized. Here we report on the evaluation of the exact Casimir interaction between perfectly conducting eccentric cylinders using a mode summation technique, and study different limiting cases of relevance for Casimir force measurements, with potential implications for the understanding of mechanical properties of nanotubes.
We present calculations of contact potential surface patch effects that simplify previous treatments. It is shown that, because of the linearity of Laplace's equation, the presence of patch potentials does not affect an electrostatic calibration (of force and/or distance) of a two-plate Casimir measurement apparatus. Using models that include long-range variations in the contact potential across the plate surfaces, a number of experimental observations can be reproduced and explained. For these models, numerical calculations show that if a voltage is applied between the plates which minimizes …
By considering the effect of diffusion on the external electric field response of charge carriers in metals and semiconductors, it is shown that the finite temperature correction proposed Bostrom and Sernelius requires substantial modification, and there is no large correction as suggested for good conductors. The apparent violation of the Third Law of Thermodynamics of the various proposed temperature corrections to the Casimir force is also resolved. Finally, the effect of Debye screening on electrostatic calibrations between pure germanium surfaces is calculated
The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of Micro- and NanoElectroMechanical Systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the us…
We show that graphene-dielectric multilayers give rise to an unusual tunability of the Casimir-Lifshitz forces, and allow to easily realize completely different regimes within the same structure. Concerning thermal effects, graphene-dielectric multilayers take advantage from the anomalous features predicted for isolated suspended graphene sheets, even though they are considerably affected by the presence of the dielectric substrate. They can also archive the anomalous non-monotonic thermal metallic behavior by increasing the graphene sheets density and their Fermi energy. In addition to a stro…
We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasi-static magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.
Assuming the conventional Casimir setting with two thick parallel perfectly conducting plates of large extent with a homogeneous and isotropic medium between them, we discuss the physical meaning of the electromagnetic field energy $W_{\rm disp}$ when the intervening medium is weakly dispersive but nondissipative. The presence of dispersion means that the energy density contains terms of the form $d[ωε(ω)] /dω$ and $d[ωμ(ω)] /dω$. We find that, as $W_{\rm disp}$ refers thermodynamically to a non-closed physical system, it is {\it not} to be identified with the internal thermodynamic energy $U$…
This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in EPL 91, 60003 (2010), which was restricted to a pair of particles with longitudinal polarization only. For…
Zero-frequency Casimir theory is analyzed from different viewpoints, focusing on the Drude-plasma issue that turns up when one considers thermal corrections to the Casimir force. The problem is that the plasma model, although leaving out dissipation in the material, apparently gives the best agreement with recent experiments. We consider a dielectric plate separated from a dielectric half-space by a vacuum gap, both media being similar. We consider the following categories: (1) Making use of the statistical mechanical method developed by Høye and Brevik (1998), implying that the quantized elec…
Casimir-electrostatic pull-in in nanoelectromechanical actuators: Differentiable design sensitivities and the damping-dependent collapse boundary
Nantong University（南通大学）；Kuban State University（库班国立大学）；Joint-Stock Company “Center for Research and Development”（联合股份公司“研发中⼼”）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）
Isoelectronic differential force measurements provide a unique opportunity to probe controversial features of the thermal Casimir effect, that are still much debated in the current literature. Isolectronic setups offer two major advantages over conventional Casimir setups. On one hand they are immune from electrostatic forces caused by potential patches on the plates surfaces, that plague present Casimir experiments especially for separations in the micron range. On the other hand they can strongly enhance the discrepancy between alternative theoretical models that have been proposed to estima…
The exact critical Casimir force between periodically deformed boundaries of a 2D semi-infinite strip is obtained for conformally invariant classical systems. Only two parameters (conformal charge and scaling dimension of a boundary changing operator), along withthe solution of an electrostatic problem, determine the Casimir force, rendering the theory practically applicable to any shape and arrangement. The attraction between any two mirror symmetric objects follows directly from our general result. The possibility of purely shape induced reversal of the force, as well as occurrence of stable…
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the te…
We describe an isoelectronic differential apparatus designed to observe the influence on the Casimir force of the Mott-Anderson metal-insulator transition in doped semiconductors. Alternative theories of dispersion forces lead to different predictions for this effect. The investigation of this problem by standard apparatus, based on absolute measurements of the Casimir force, is very difficult because the effect is small in the region of sub-micron separations, where the Casimir force can be measured precisely. The differential apparatus described here is immune by design to several sources of…
We describe a Casimir setup consisting of two aligned sinusoidally corrugated Ni surfaces, one of which is "hidden" by a thin opaque layer of gold with a flat exposed surface. The gold layer acts as a low-pass filter that allows for a clean observation of the controversial thermal Casimir force between the corrugations, with currently available Casimir apparatuses. The proposed scheme of measurement, based on the phase-dependent modulation of the Casimir force, requires no electrostatic calibrations of the apparatus, and is unaffected by uncertainties in the knowledge of the optical properties…
Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro- and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here, by integrating a force-sensing micromechanical beam and an electrostatic act…
We report on a proposal aimed at measuring the Casimir force in a cylinder-plane configuration. The Casimir force is evaluated including corrections due to finite parallelism, conductivity, and temperature. The range of validity of the proximity force approximation is also discussed. An apparatus to test the feasibility of a precision measurement in this configuration has been developed, and we describe both a procedure to control the parallelism and the results of the electrostatic calibration. Finally, we discuss the possibility of measuring the thermal contribution to the Casimir force and …
We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. …
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 3x10^{-8} Torr with hollow glass sphere of 41.3 mcm 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 way…
We report on measurements of the Casimir force in a sphere-plane geometry using a cryogenic force microscope to move the force probe in situ over different materials. We show how the electrostatic environment of the interacting surfaces plays an important role in weak force measurements and can overcome the Casimir force at large distance. After minimizing these parasitic forces, we measure the Casimir force between a gold-coated sphere and either a gold-coated or a heavily doped silicon surface in the 100-400 nm distance range. We compare the experimental data with theoretical predictions and…
In the current work we present the complete results for the measurement of normal Casimir force between shallow and smooth sinusoidally corrugated gold coated sphere and a plate at various angles between the corrugations using an atomic force microscope. All measured data were compared with the theoretical approach using the proximity force approximation and theory based on derivative expansion. In both cases real material properties of the surfaces and non-zero temperature were taken into account. Special attention is paid to the description of electrostatic interactions between corrugated su…
Using the measured optical response and surface roughness topography as inputs, we perform realistic calculations of the combined effect of Casimir and electrostatic forces on the actuation dynamics of micro-electromechanical systems (MEMS). In contrast with the expectations, roughness can influence MEMS dynamics even at distances between bodies significantly larger than the root-mean-square roughness. This effect is associated with statistically rare high asperities that can be locally close to the point of contact. It is found that, even though surface roughness appears to have a detrimental…
We present complete results of the experiment on measuring the Casimir force between an Au-coated sphere and an untreated or, alternatively, UV-treated indium tin oxide film deposited on a quartz substrate. Measurements were performed using an atomic force microscope in a high vacuum chamber. The measurement system was calibrated electrostatically. Special analysis of the systematic deviations is performed, and respective corrections in the calibration parameters are introduced. The corrected parameters are free from anomalies discussed in the literature. The experimental data for the Casimir …
We describe a Casimir apparatus based on a differential force measurement between a Au-coated sphere and a planar slab divided in two regions, one of which is made of high-resistivity (dielectric) Si, and the other of Au. The crucial feature of the setup is a semi-transparent plane parallel conducting over-layer, covering both regions. The setup offers two important advantages over existing Casimir setups. On one hand it leads to a large amplification of the difference between the Drude and the plasma prescriptions that are currently used to compute the thermal Casimir force. On the other hand…
Quantum theory predicts the existence of the Casimir force between macroscopic bodies, due to the zero-point energy of electromagnetic field modes around them. This quantum fluctuation-induced force has been experimentally observed for metallic and semiconducting bodies, although the measurements to date have been unable to clearly settle the question of the correct low-frequency form of the dielectric constant dispersion (the Drude model or the plasma model) to be used for calculating the Casimir forces. At finite temperature a thermal Casimir force, due to thermal, rather than quantum, fluct…
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 $P_{\rm res}(D)$ 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 o…
A quite straightforward approximation for the electrostatic interaction between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the characteristic lengths associated to their shapes. Indeed, in the so called "proximity force approximation" the electrostatic force is evaluated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contribution of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied to differen…
The Casimir effect between metal surfaces has now been well-verified at the few-percent level experimentally. However, the temperature dependence has never been observed in the laboratory, since all experiments are conducted at room temperature. The temperature dependence for the related Casimir-Polder force between an atom and a bulk material has, in contrast, been observed between a BEC and a silica substrate, with the environment and the silica held at different temperatures. There is a controversy about the temperature dependence for the force between metals, having to do with the magnitud…
Recently J.N. Munday and F. Capasso [Phys. Rev. A {\bf 75}, 060102(R) (2007); arXiv:0705.3793] claimed that they have performed a precision measurement of the Casimir force between a sphere and a plate coated with Au, both immersed in ethanol. The measurement results were claimed to be consistent with the Lifshitz theory. We demonstrate that the calculation of the Casimir force between the smooth bodies following the authors prescription has a discrepancy up to 25% with respect to authors result. We show also that the attractive electrostatic force only due to the surface potential differences…
We performed measurements of the gradient of the Casimir force between Au-coated surfaces of a sphere and a plate by means of significantly upgraded dynamic atomic force microscope (AFM) based technique. By introducing combined cleaning procedure of interior surfaces of the vacuum chamber and the test bodies by means of UV light and Ar ions, we reached higher vacuum and eliminated the role of electrostatic patches. Furthermore, the use of much softer cantilever allowed a sixfold decrease of the systematic error in measuring the force gradient. The experimental data are compared with theoretica…
Differential force measurements between spheres coated with either nickel or gold and rotating disks with periodic distributions of nickel and gold are reported. The rotating samples are covered by a thin layer of titanium and a layer of gold. While titanium is used for fabrication purposes, the gold layer (nominal thicknesses of 21, 37, 47 and 87 nm) provides an isoelectronic environment, and is used to nullify the electrostatic contribution but allow the passage of long wavelength Casimir photons. A direct comparison between the experimental results and predictions from Drude and plasma mode…
We report measurements of the short-range forces between two macroscopic gold-coated plates using a torsion pendulum. The force is measured for separations between 0.7 $μ$m and 7 $μ$m, and is well described by a combination of the Casimir force, including the finite-temperature correction, and an electrostatic force due to patch potentials on the plate surfaces. We use our data to place constraints on the Yukawa-type "new" forces predicted by theories with extra dimensions. We establish a new best bound for force ranges 0.4 $μ$m to 4 $μ$m, and, for forces mediated by gauge bosons propagating i…
Short-range forces have important real-world relevance across a range of settings in the nano world, from colloids and possibly for protein folding to nano-mechanical devices, but also for detection of weak long-range forces, such as gravity, at short distances and of candidates to solve the problem of dark energy. Short-range forces, such as Casimir-Polder or van der Waals are in general difficult to calculate as a consequence of their non-additive nature, and challenging to measure due to their small magnitude - especially for charged particles where dispersion forces are normally many order…
