We argue that the appropriate variable to study a non trivial 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 (PFA). 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%.Considerable experimental progress has been achieved [1] in the measurement of the Casimir force, opening the way for various applications in nano-science [2], particularly in the development of nano-or micro-electromechanical systems (NEMS or MEMS). Calculations are much simpler in the original Casimir geometry of two plane plates [3] which obeys a symmetry with respect to lateral translations and thus allows to derive the expression of the Casimir force from the reflection amplitudes which describe specular scattering on the plates [4].More general geometries open a far richer physics with a variety of extremely interesting theoretical predictions [5]. Up to now the experimental studies of the effect of geometry have been restricted to simple configurations which can be calculated with the help of the Proximity Force Approximation (PFA). This approximation is essentially equivalent to an averaging over plane-plane geometries and its result can be deduced from the force known in this geometry [6]. For example, it allows to evaluate the force between a plane and a sphere [7] provided the radius R of the sphere is much larger than the mirror separation R ≫ L. It is also valid for the description of the effect of roughness when the wavelengths associated with the plate deformations are large enough [8]. However PFA relies heavily on assuming some additivity of Casimir forces which is known to be generally not valid except for very smooth geometrical perturbations [9].The aim of the present paper is to study a configuration allowing a new test of QED theoretical predictions outside the PFA domain and independent of those already performed in the plane-plane geometry. The idea is to look for the lateral component of the Casimir force which appears, besides the usual normal component, when periodic corrugations with the same period are imprinted on the two metallic plates. This configuration contrasts with other ones, for example the normal Casimir force in the plane-sphere geometry or roughness corrections to it. There PFA can also be invalid, but this leads only to small corrections of the dominant normal Casimir force, which do not seem accessible experimentally at the moment. The lateral component of the Casimir force has recently been measured and analyzed within the PFA [10,11]. We find for experimentally realizable parameters that PFA overestimates the force by as much as 30%, which should allow for a ...
Theory of quantized fields. PACS. 68.35.Ct -Interface structure and roughness.Abstract. -We study the torque arising between two corrugated metallic plates due to the interaction with electromagnetic vacuum. This Casimir torque can be measured with torsion pendulum techniques for separation distances as large as 1µm. It allows one to probe the nontrivial geometry dependence of the Casimir energy in a configuration which can be evaluated theoretically with accuracy. In the optimal experimental configuration, the commonly used proximity force approximation turns out to overestimate the torque by a factor 2 or larger.
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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 C , and the plasma wavelength P . Within this perturbative expansion, evaluations are obtained for arbitrary relative values of L, C , and P while limiting cases, some of 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.
We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position.
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