The Casimir force between rough metallic plates (original) (raw)
Related papers
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 .
2012
So far there has been no reliable method to calculate the Casimir force at separations comparable to the root-mean-square of the height fluctuations of the surfaces. Statistical analysis of rough gold samples has revealed the presence of peaks considerably higher than the root-mean-square roughness. These peaks redefine the minimum separation distance between the bodies and can be described by extreme value statistics. Here we show that the contribution of the high peaks to the Casimir force can be calculated with a pairwise additive summation, while the contribution of asperities with normal height can be evaluated perturbatively. This method provides a reliable estimate of the Casimir force at short distances, and it solves the significant, so far unexplained discrepancy between measurements of the Casimir force between rough surfaces and the results of perturbation theory. Furthermore, we illustrate the importance of our results in a technologically relevant situation.
Casimir effect with rough metallic mirrors
Physical Review A, 2005
We calculate the second order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the Proximity Force Approximation, which is obtained from our theory as a limiting case (very smooth surfaces).
Comment on “Low-frequency character of the Casimir force between metallic films”
Physical Review E, 2006
In Phys. Rev. E 70, 047102 (2004), J.R. Torgerson and S.K. Lamoreaux investigated for the first time the real-frequency spectrum of finite temperature correction to the Casimir force, for metallic plates of finite conductivity. The very interesting result of this study is that the correction from the TE mode is dominated by low frequencies, for which the dielectric description of the metal is invalid. However, their analysis of the problem, based on more appropriate low-frequency metallic boundary conditions, uses an incorrect form of boundary conditions for TE modes. We repeat their analysis, using the correct boundary conditions. Our computations confirm their most important result: contrary to the result of the dielectric model, the thermal TE mode correction leads to an increase in the TE mode force of attraction between the plates. The magnitude of the correction has a value about twenty times larger than that quoted by them.
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.
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.
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.
Recent Experiments on the Casimir Effect: Description and Analysis
Poincaré Seminar 2002, 2003
After its prediction in 1948 [1], the Casimir force has been observed in a number of 'historic' experiments which confirmed its existence and main properties . The Casimir force has recently been measured with a largely improved experimental precision which allows for an accurate comparison between measured values of the force and theoretical predictions. This comparison is interesting for various reasons.
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.