Casimir Force Experiments Research Articles

Modeling electrostatic patch effects in Casimir force measurements

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 quasilocal 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 thus may be a more important systematic effect than was previously anticipated. Additionally, patches may render the experimental data at distances below 1 $\ensuremath{\mu}$m compatible with theoretical predictions based on the Drude model.

Short-range fundamental forces

We consider theoretical motivations to search for extra short-range fundamental forces as well as experiments constraining their parameters. The forces could be of two types: 1) spin-independent forces; 2) spin-dependent axion-like forces. Different experimental techniques are sensitive in respective ranges of characteristic distances. The techniques include measurements of gravity at short distances, searches for extra interactions on top of the Casimir force, precision atomic and neutron experiments. We focus on neutron constraints, thus the range of characteristic distances considered here corresponds to the range accessible for neutron experiments. Nous considérons les motivations théoriques pour rechercher des forces fondamentales supplémentaires à courte portée ainsi que des expériences contraignant leurs paramètres. Les forces peuvent être de deux types : 1) les forces indépendantes du spin ; 2) les forces dépendant du spin, de type axion. Différentes techniques expérimentales sont sensibles dans des domaines différents de distances caractéristiques. Les expériences incluent des mesures de gravité à courte distance, la recherche dʼinteractions supplémentaires en plus de la force de Casimir, des expériences atomiques et neutroniques de précision. Comme nous mettons lʼaccent sur les contraintes neutroniques, la gamme de distances caractéristiques considérées ici correspond à la plage accessible pour les expériences avec les neutrons.

Chameleons with field-dependent couplings

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for E\"ot-Wash experiments, fifth-force searches and Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.

Tuning the Mass of Chameleon Fields in Casimir Force Experiments

We have calculated the chameleon pressure between two parallel plates in the presence of an intervening medium that affects the mass of the chameleon field. As intuitively expected, the gas in the gap weakens the chameleon interaction mechanism with a screening effect that increases with the plate separation and with the density of the intervening medium. This phenomenon might open up new directions in the search of chameleon particles with future long-range Casimir force experiments.

Contact potentials in Casimir force setups: An experimental analysis

The authors present an extensive study of the contact potential difference, V0, between a gold coated sphere and a gold coated plate kept in air at submicron separation. The data confirm that in ambient conditions, V0 depends on both time and separation. They discuss the origin of the time dependence of V0 and elaborate on its functional dependence on separation, d. The data strongly support a log(d) hypothesis but also show that in air this description is not quite complete. These effects might have important implications in the realm of Casimir force experiments.

Edge effects in electrostatic calibrations for the measurement of the Casimir force

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.

Casimir effect on the brane

We consider the Casimir effect between two parallel plates localized on a brane. We argue that in order to properly compute the contribution to the Casimir energy due to any higher dimensional field, it is necessary to take into account the localization properties of the Kaluza-Klein modes. When the bulk field configuration is such that no massless mode appears in the spectrum, as, for instance, when the higher dimensional field obeys twisted boundary conditions across the branes, the correction to the Casimir energy is exponentially suppressed. When a massless mode is present in the spectrum, the correction to the Casimir energy can be, in principle, sizeable. However, when the bulk field is massless and strongly coupled to brane matter, the model is already excluded without resorting to any Casimir force experiment. The case which is in principle interesting is when the massless mode is not localized on the visible brane. We illustrate a method to compute the Casimir energy between two parallel plates, localized on the visible brane, approximating the Kaluza-Klein spectrum by truncation at the first excited mode. We treat this case by considering a pistonlike configuration and introduce a small parameter, $\ensuremath{\epsilon}$, that takes into account the relative amplitude of the zero-mode wave function on the visible brane with respect to the massive excitation. We find that the Casimir energy is suppressed by two factors: at lowest order in $\ensuremath{\epsilon}$, the correction to the Casimir energy comes entirely from the massive mode and turns out to be exponentially suppressed; the next-to-leading order correction in $\ensuremath{\epsilon}$ follows, instead, a power-law suppression due to the small wave-function overlap of the zero mode with matter confined on the visible brane. Generic comments on the constraints on new physics that may arise from Casimir force experiments are also made.

On the use of the proximity force approximation for deriving limits to short-range gravitational-like interactions from sphere-plane Casimir force experiments

We discuss the role of the proximity force approximation in deriving limits to the existence of Yukawian forces - predicted in the submillimeter range by many unification models - from Casimir force experiments using the sphere-plane geometry. Two forms of this approximation are discussed, the first used in most analyses of the residuals from the Casimir force experiments performed so far, and the second recently discussed in this context in R. Decca et al. [Phys. Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force approximation overestimates the expected Yukawa force and that the relative deviation from the exact Yukawa force is of the same order of magnitude, in the realistic experimental settings, as the relative deviation expected between the exact Casimir force and the Casimir force evaluated in the proximity force approximation. This implies both a systematic shift making the actual limits to the Yukawa force weaker than claimed so far, and a degree of uncertainty in the alpha-lambda plane related to the handling of the various approximations used in the theory for both the Casimir and the Yukawa forces. We further argue that the recently discussed form for the proximity force approximation is equivalent, for a geometry made of a generic object interacting with an infinite planar slab, to the usual exact integration of any additive two-body interaction, without any need to invoke approximation schemes. If the planar slab is of finite size, an additional source of systematic error arises due to the breaking of the planar translational invariance of the system, and we finally discuss to what extent this may affect limits obtained on power-law and Yukawa forces.

Customized silicon cantilevers for Casimir force experiments using focused ion beam milling

Higher sensitivity cantilevers will lead to exploration of new phenomena in the Casimir effect. We have used focused ion beam milling to reduce the width of a commercial single crystal, rectangular-shaped silicon cantilevers with a massive Cr/Au-coated-hollow sphere attached at their free end. Theoretically these milled and modified cantilevers should have better Casimir force sensitivity than their non-milled counterparts. In this preliminary report however only 1 out of 4 modified cantilevers were found to have a higher force sensitivity. Future studies will be needed to determine the general applicability of focused ion beam milling for force sensitivity improvements in comparison to the complete nanofabrication of cantilevers.

Vacuum energy, the cosmological constant, and compact extra dimensions: Constraints from Casimir effect experiments

We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero-point energy of the vacuum. We derive the Casimir force between parallel conducting plates as a function of the following scales: plate separation, radius of the extra dimension and cutoff energy scale. We find that there are critical values of these scales where the Casimir force between the plates changes sign. For the cutoff energy scale required to reproduce the observed value of the cosmological constant, we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation ${d}_{0}=0.6\text{ }\text{ }\mathrm{mm}$, assuming a zero radius of the extra dimension (no extra dimension). This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of 100 nm. For a nonzero extra dimension radius, the critical separation ${d}_{0}$ gets even larger than 0.6 mm and remains inconsistent with Casimir force experiments. We conclude that with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff cannot play the role of the cosmological constant.

Casimir force experiments with quartz tuning forks and an atomic force microscope (AFM)

The aim of the measurement series is to study the Casimir force, specifically the effects of different materials and geometries. The art of measuring sub-nano Newton forces has been engineered to a great extent in the material sciences, especially for the atomic force microscope. In today's scanning microscope technologies there are several common methods used to measure sub-nano Newton forces. While the commercial atomic force microscopes (AFM) mostly work with soft silicon cantilevers, there are a large number of reports from university groups on the use of quartz tuning forks to get high resolution AFM pictures, to measure shear forces or to create new force sensors. The quartz tuning fork based force sensor has a number of advantages over the silicon cantilever, but also has some disadvantages. In this report the method based on quartz tuning forks is described with respect to their usability for Casimir force measurements and compared with other successful techniques. Furthermore, a design for Casimir force measurements that was set up in Berlin will be described and practical experimental aspects will be discussed. A status report on the Casimir experiments in Berlin will be given, including the experimental setup. In order to study the details of the Casimir effect the apparatus and active surfaces have to be improved further. The surfaces have to be flatter and cleaner. For better resolution, cantilevers and tuning forks with a low spring constant have to be employed.

Alpenglow: A signature for chameleons in axionlike particle search experiments

We point out that chameleon field theories might reveal themselves as an afterglow effect in axionlike particle search experiments due to chameleon-photon conversion in a magnetic field. We estimate the parameter space which is accessible by currently available technology and find that afterglow experiments could constrain this parameter space in a way complementary to gravitational and Casimir force experiments. In addition, one could reach photon-chameleon couplings which are beyond the sensitivity of common laser polarization experiments. We also sketch the idea of a Fabry-Perot cavity with chameleons which could increase the experimental sensitivity significantly.

Casimir force on real materials—the slab and cavity geometry

We analyse the potential of the geometry of a slab in a planar cavity for the purpose of Casimir force experiments. The force and its dependence on temperature, material properties and finite slab thickness are investigated both analytically and numerically for the slab and walls made of aluminium and teflon FEP respectively. We conclude that such a setup is ideal for measurements of the temperature dependence of the Casimir force. By numerical calculation it is shown that temperature effects are dramatically larger for dielectrics, suggesting that a dielectric such as teflon FEP whose properties vary little within a moderate temperature range, should be considered for experimental purposes. We finally discuss the subtle but fundamental matter of the various Green's two-point function approaches present in the literature and show how they are different formulations describing the same phenomenon.

Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation

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.

On the use of hydrogen switchable mirrors in Casimir force experiments

Hydrogen switchable mirrors (HSMs) are shiny metals that become optically transparent upon exposure to hydrogen. The Casimir force between HSMs is thus supposed to be stronger in air than in hydrogen. A few years ago, an experiment designed to measure this effect gave an unexpected result (Iannuzzi, Lisanti and Capasso 2004 Proc. Natl Acad. Sci. USA101 4019–23): no change of the force was observed upon hydrogenation. Qualitative arguments show that this result is reasonable if HSMs do not switch at long wavelengths, where no measurements of the dielectric function are available. Because the exact composition of the mirrors used in that experiment is not known, a more quantitative comparison of the data with theory is not possible. Still, calculations of the Casimir force in the presence of similar HSMs of known composition might provide new insights for the interpretation of the experimental result and may suggest precious hints for the development of future analogous experiments. In this paper, we present calculations of the Casimir attraction between Mg2Ni mirrors in air and in hydrogen. Our results clearly indicate that the modulation of the Casimir force with HSMs should be observable with modern set-ups.

Constraints on new interactions from neutron scattering experiments

Constraints for the constants of hypothetical Yukawa-type corrections to the Newtonian gravitational potential are obtained from analysis of neutron scattering experiments. Restrictions are obtained for the interaction range between 10−12 and 10−7 cm, where Casimir force experiments and atomic-force microscopy are not sensitive. Experimental limits are obtained also for nonelectromagnetic inverse-power-law neutron-nucleus potentials. Some possibilities are discussed to strengthen these constraints.

Casimir force between metal plate and dielectric plate

The Casimir effect between metal plate and dielectric plate is discussed with 1 + 1-dimensional potential model without using cut-off method. Calculation shows that the Casimir force between metal plate and dielectric plate is determined not only by the potentialV 0, the dielectric thickness and the distancea between the metal plate and dielectric plate, but also by the dimension of the vessel. Whena is far less than the dimension of the vessel, the Casimir forceF c ∝a -1; converselyF c ∝a -2 This result is significant for Casimir force experiment.