Thermal Casimir Effect in the Plane-Sphere Geometry

Canaguier-Durand, Antoine; Neto, Paulo A. Maia; Lambrecht, Astrid; Reynaud, Serge

doi:10.1103/physrevlett.104.040403

Cited by 84 publications

(128 citation statements)

References 28 publications

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“…(The corrections computed previously 65,66 cannot be used in this experiment because they are found for much larger values of a/R.) In the framework of the PFA, the Lifshitz-type formula for the gradient of the Casimir force between a sphere and a plate takes the form…”

Section: 64mentioning

confidence: 99%

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

et al. 2012

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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 separationindependent 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.

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Section: 64mentioning

confidence: 99%

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

et al. 2012

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“…2 correspond to data for T = 300 K, while the dashed lines are for T = 0 K. We also show (solid lines) the result for perfect reflectors at T = 300 K. Thus, the solid lines neglect finite conductivity corrections, while the dashed lines neglect finite temperature corrections. The importance of including both corrections for the leading (PFA) Casimir force has been previously noted 20 . A comparable previous estimate ofθ 1 , for a metal sphere-plate setup at zero temperature, was obtained in Ref.…”

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confidence: 92%

Material dependence of Casimir forces: Gradient expansion beyond proximity

Bimonte

Emig

Kardar

2012

Applied Physics Letters

104

156

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A widely used method for estimating Casimir interactions [H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)] between gently curved material surfaces at short distances is the proximity force approximation (PFA). While this approximation is asymptotically exact at vanishing separations, quantifying corrections to PFA has been notoriously difficult. Here we use a derivative expansion to compute the leading curvature correction to PFA for metals (gold) at room temperature. We derive an explicit expression for the amplitude θ1 of the PFA correction to the force gradient for axially symmetric surfaces. In the non-retarded limit, the corrections to the Casimir free energy are found to scale logarithmically with distance. For gold, θ1 has an unusually large temperature dependence.

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“…Using these methods, we have been able to compute forces between various combinations of planes, spheres, and circular and parabolic cylinders (19)(20)(21)(22)(23)(24) (see also refs. [25][26][27]. Both perfect conductors and dielectrics have been studied.…”

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confidence: 99%

“…Both perfect conductors and dielectrics have been studied. However, with the notable exception of the knife edge (23)(24)(25)(26)(27)(28), which is a limit of the parabolic cylinder geometry, systems with sharp edges have not yet been studied analytically. † In all the above cases, the object corresponds to a surface of constant radial coordinate.…”

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confidence: 99%

Analytical results on Casimir forces for conductors with edges and tips

Maghrebi

Rahi

Emig

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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Casimir forces between conductors at the submicron scale are paramount to the design and operation of microelectromechanical devices. However, these forces depend nontrivially on geometry, and existing analytical formulae and approximations cannot deal with realistic micromachinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically wedges and cones. The Casimir interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of microelectromechanical devices. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe. We find an unexpectedly large temperature dependence of the force in the cone tip which is of immediate relevance to experiments.fluctuations | quantum electrodynamics T he inherent appeal of the Casimir force as a macroscopic manifestation of quantum "zero-point" fluctuations has inspired many studies over the decades that followed its discovery (1). Casimir's original result (2) for the force between perfectly reflecting mirrors separated by vacuum was quickly extended to include slabs of material with specified (frequency-dependent) dielectric response (3). Quantitative experimental confirmation, however, had to await the advent of high-precision scanning probes in the 1990s (4-7). Recent studies have aimed to reduce or reverse the attractive Casimir force for practical applications in micron-sized mechanical machines, where Casimir forces may cause components to stick and the machine to fail. In the presence of an intervening fluid, experiments have indeed observed repulsion due to quantum (8) or critical thermal (9) fluctuations. Metamaterials, fabricated designs of microcircuitry, have also been proposed as candidates for Casimir repulsion across vacuum (10).Although there have been many studies of the role of materials (dielectrics, conductors, etc.), the treatment of shapes and geometry has remained comparatively less investigated. Interactions between nonplanar shapes are typically calculated via the proximity force approximation (PFA), which sums over infinitesimal segments treated as locally parallel plates (11). This approximation represents a serious limitation because the majority of experiments measure the force between a sphere and a plate with precision that is now sufficient to probe deviations from PFA in this and other geometries (12, 13). Practical applications are likely to explore geometries further removed from parallel plates. Several numerical schemes (14, -16), and even an analog computer (17), have recently been developed for computing Casimir forces in general geometries. However, analytical formulae for quick...

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Thermal Casimir Effect in the Plane-Sphere Geometry

Cited by 84 publications

References 28 publications

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using an atomic force microscope in a frequency-shift technique

Material dependence of Casimir forces: Gradient expansion beyond proximity

Analytical results on Casimir forces for conductors with edges and tips

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