Temperature dependence of the Casimir effect between metallic mirrors

We calculate the Casimir force and free energy for plane metallic mirrors at non-zero temperature. Numerical evaluations are given with temperature and conductivity effects treated simultaneously. The results are compared with the approximation where both effects are treated independently and the corrections simply multiplied. The deviation between the exact and approximated results takes the form of a temperature dependent function for which an analytical expression is given. The knowledge of this function allows simple and accurate estimations at the % level.Comment: 8 pages, 4 figures, uses RevTe

Constraints on non-Newtonian gravity from the Casimir force measurements between two crossed cylinders

Constraints on the Yukawa-type corrections to Newtonian gravitational law are obtained resulting from the measurement of the Casimir force between two crossed cylinders. The new constraints are stronger than those previously derived in the interaction range between 1.5 nm and 11 nm. The maximal strengthening in 300 times is achieved at 4.26 nm. Possible applications of the obtained results to the elementary particle physics are discussed.Comment: An error in the text and in the figure had been corrected. To appear in Phys. Rev.

Sub-millimeter Tests of the Gravitational Inverse-square Law

Motivated by a variety of theories that predict new effects, we tested the gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using two different 10-fold azimuthally symmetric torsion pendulums and rotating 10-fold symmetric attractors. Our work improves upon other experiments by up to a factor of about 100. We found no deviation from Newtonian physics at the 95% confidence level and interpret these results as constraints on extensions of the Standard Model that predict Yukawa or power-law forces. We set a constraint on the largest single extra dimension (assuming toroidal compactification and that one extra dimension is significantly larger than all the others) of R <= 160 microns, and on two equal-sized large extra dimensions of R <= 130 microns. Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of large extra dimensions. We also provide new constraints on power-law potentials V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of pseudoscalars with m <= 10 meV/c^2.Comment: 34 pages, 38 figure

The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for General Permittivities

The Casimir mutual free energy F for a system of two dielectric concentric nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf 63}, 051101 (2001)], in which F was evaluated in full only for the case of ideal metals (refractive index n=infinity). Here, analogous results are presented for dielectrics, for some chosen values of n. Our basic calculational method stems from quantum statistical mechanics. The Debye expansions for the Riccati-Bessel functions when carried out to a high order are found to be very useful in practice (thereby overflow/underflow problems are easily avoided), and also to give accurate results even for the lowest values of l down to l=1. Another virtue of the Debye expansions is that the limiting case of metals becomes quite amenable to an analytical treatment in spherical geometry. We first discuss the zero-frequency TE mode problem from a mathematical viewpoint and then, as a physical input, invoke the actual dispersion relations. The result of our analysis, based upon the adoption of the Drude dispersion relation at low frequencies, is that the zero-frequency TE mode does not contribute for a real metal. Accordingly, F turns out in this case to be only one half of the conventional value at high temperatures. The applicability of the Drude model in this context has however been questioned recently, and we do not aim at a complete discussion of this issue here. Existing experiments are low-temperature experiments, and are so far not accurate enough to distinguish between the different predictions. We also calculate explicitly the contribution from the zero-frequency mode for a dielectric. For a dielectric, this zero-frequency problem is absent.Comment: 23 pages, LaTeX, 7 ps figures; expanded discussion, especially in Sec. 5. To appear in Phys. Rev.

Improved tests of extra-dimensional physics and thermal quantum field theory from new Casimir force measurements

We report new constraints on extra-dimensional models and other physics beyond the Standard Model based on measurements of the Casimir force between two dissimilar metals for separations in the range 0.2--1.2 $\mu$m. The Casimir force between an Au-coated sphere and a Cu-coated plate of a microelectromechanical torsional oscillator was measured statically with an absolute error of 0.3 pN. In addition, the Casimir pressure between two parallel plates was determined dynamically with an absolute error of $\approx 0.6$ mPa. Within the limits of experimental and theoretical errors, the results are in agreement with a theory that takes into account the finite conductivity and roughness of the two metals. The level of agreement between experiment and theory was then used to set limits on the predictions of extra-dimensional physics and thermal quantum field theory. It is shown that two theoretical approaches to the thermal Casimir force which predict effects linear in temperture are ruled out by these experiments. Finally, constraints on Yukawa corrections to Newton's law of gravity are strengthened by more than an order of magnitude in the range 56 nm to 330 nm.Comment: Revtex 4, 35 pages, 14 figures in .gif format, accepted for publication in Phys. Rev.

Constraints on Non-Newtonian Gravity from Recent Casimir Force Measurements

Corrections to Newton's gravitational law inspired by extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newton's gravitational law are reviewed following from the E\"{o}tvos- and Cavendish-type experiments and from the measurements of the Casimir and van der Waals force. We show that the recent measurements of the Casimir force gave the possibility to strengthen the previously known constraints on the constants of hypothetical interactions up to several thousand times in a wide interaction range. Further strengthening is expected in near future that makes Casimir force measurements a prospective test for the predictions of fundamental physical theories.Comment: 20 pages, crckbked.cls is used, to be published in: Proceedings of the 18th Course of the School on Cosmology and Gravitation: The Gravitational Constant. Generalized Gravitational Theories and Experiments (30 April- 10 May 2003, Erice). Ed. by G. T. Gillies, V. N. Melnikov and V. de Sabbata, 20pp. (Kluwer, in print, 2003

New constraints for non-Newtonian gravity in nanometer range from the improved precision measurement of the Casimir force

We obtain constraints on non-Newtonian gravity following from the improved precision measurement of the Casimir force by means of atomic force microscope. The hypothetical force is calculated in experimental configuration (a sphere above a disk both covered by two metallic layers). The strengthenings of constraints up to 4 times comparing the previous experiment and up to 560 times comparing the Casimir force measurements between dielectrics are obtained in the interaction range 5.9 nm$\leq\lambda\leq 115$nm. Recent speculations about the presence of some unexplained attractive force in the considered experiment are shown to be unjustified.Comment: 5 pages, 1 figur

Measurement of the Casimir force between parallel metallic surfaces

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 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 $\mu$m range, and the related force coefficient was determined at the 15% precision level.Comment: 4 Figure

Casimir-like tunneling-induced electronic forces

We study the quantum forces that act between two nearby conductors due to electronic tunneling. We derive an expression for these forces by calculating the flux of momentum arising from the overlap of evanescent electronic fields. Our result is written in terms of the electronic reflection amplitudes of the conductors and it has the same structure as Lifshitz's formula for the electromagnetically mediated Casimir forces. We evaluate the tunneling force between two semiinfinite conductors and between two thin films separated by an insulating gap. We discuss some applications of our results.Comment: 8 pages, 3 figs, submitted to Proc. of QFEXT'05, to be published in J. Phys.

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 non-electromagnetic inverse power law neutron-nucleus potential. Some possibilities are discussed to strengthen these constraints.Comment: 18 pages, 3 figure