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

Abstract

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.

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Physics Department, Wabash College, Crawfordsville, Indiana 47933 (United States)
  2. (United States)
  3. Department of Physics, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202 (United States)
  4. Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974 (United States)
  5. Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States)
Publication Date:
OSTI Identifier:
20955406
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevLett.98.050403; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; CASIMIR EFFECT; GEOMETRY; GOLD; OSCILLATORS; PLATES; SPHERES; TORSION

Citation Formats

Krause, D. E., Department of Physics, Purdue University, West Lafayette, Indiana 47907, Decca, R. S., Lopez, D., and Fischbach, E. Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.050403.
Krause, D. E., Department of Physics, Purdue University, West Lafayette, Indiana 47907, Decca, R. S., Lopez, D., & Fischbach, E. Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation. United States. doi:10.1103/PHYSREVLETT.98.050403.
Krause, D. E., Department of Physics, Purdue University, West Lafayette, Indiana 47907, Decca, R. S., Lopez, D., and Fischbach, E. Fri . "Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation". United States. doi:10.1103/PHYSREVLETT.98.050403.
@article{osti_20955406,
title = {Experimental Investigation of the Casimir Force beyond the Proximity-Force Approximation},
author = {Krause, D. E. and Department of Physics, Purdue University, West Lafayette, Indiana 47907 and Decca, R. S. and Lopez, D. and Fischbach, E.},
abstractNote = {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.},
doi = {10.1103/PHYSREVLETT.98.050403},
journal = {Physical Review Letters},
number = 5,
volume = 98,
place = {United States},
year = {Fri Feb 02 00:00:00 EST 2007},
month = {Fri Feb 02 00:00:00 EST 2007}
}
  • We argue that the appropriate variable to study a nontrivial geometry dependence of the Casimir force is the lateral component of the Casimir force, which we evaluate between two corrugated metallic plates outside the validity of the proximity-force approximation. The metallic plates are described by the plasma model, with arbitrary values for the plasma wavelength, the plate separation, and the corrugation period, the corrugation amplitude remaining the smallest length scale. Our analysis shows that in realistic experimental situations the proximity-force approximation overestimates the force by up to 30%.
  • The lateral Casimir force between two corrugated metallic plates makes possible a study of the nontrivial interplay of geometry and Casimir effect appearing beyond the regime of validity of the proximity-force approximation. Quantitative evaluations can be obtained by using scattering theory in a perturbative expansion valid when the corrugation amplitudes are smaller than the three other length scales: the mean separation distance L of the plates, the corrugation period {lambda}{sub C}, and the plasma wavelength {lambda}{sub P}. Within this perturbative expansion, evaluations are obtained for arbitrary relative values of L, {lambda}{sub C}, and {lambda}{sub P} while limiting cases, some ofmore » them already known, are recovered when these values obey some specific orderings. The consequence of these results for comparison with existing experiments is discussed at the end of the paper.« less
  • We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio {epsilon}. This correction is of order {epsilon}. Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, {epsilon}ln{epsilon} and {epsilon}(ln{epsilon}){sup 2}. We compare this result with the available findings of numerical and experimental approaches.
  • 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 Yukawamore » 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.« less
  • We compute Casimir interaction energies for the sphere-plate and cylinder-plate configuration induced by scalar-field fluctuations with Dirichlet boundary conditions. Based on a high-precision calculation using world-line numerics, we quantitatively determine the validity bounds of the proximity-force approximation (PFA) on which the comparison between all corresponding experiments and theory are based. We observe the quantitative failure of the PFA on the 1% level for a curvature parameter a/R>0.00755. Even qualitatively, the PFA fails to predict reliably the correct sign of genuine Casimir curvature effects. We conclude that data analysis of future experiments aiming at a precision of 0.1% must no longermore » be based on the PFA.« less