Vacuum induced torque between corrugated metallic plates

– 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. The Casimir effect [1] plays a major role in microand nano-electromechanical systems (MEMS and NEMS) [2]. Besides the normal Casimir force between metallic or dielectric plates [3], the observation of the lateral Casimir force between corrugated plates [4] opens novel possibilities of micro-mechanical control. The lateral force results from breaking the translational symmetry along directions parallel to the plates by imprinting periodic corrugations on both metallic plates. As rotational symmetry is also broken by this geometry, a Casimir torque should also arise when the corrugations are not aligned. In the present letter, we study this effect which provides one with a new mechanism of micro-mechanical control to be exploited in the design of MEMS and NEMS. From the point of view of fundamental physics, this effect makes possible an accurate investigation of the non-trivial geometry dependence of the Casimir energy. Tests of this geometry dependence performed up to date have often been limited by the use of the proximityforce approximation (PFA) in the calculations [5]. Within this approximation, the energy is evaluated by simply averaging the Casimir energy between two planes over the distribution of local distances, which is certainly insufficient except for the limiting case of large corrugation wavelengths [6]. Other calculations [7] have gone farther than PFA while using a model of perfect reflection, which limited their validity to experiments performed with metallic mirrors at distances larger than a few μm. Here we use the scattering approach [8, 9] extended to treat non-planar surfaces [10, 11]. This perturbative approach is restricted by the assumption that corrugation amplitudes are (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]