Casimir torque between nanostructured plates

We investigate in detail the Casimir torque induced by quantum vacuum fluctuations between two nanostructured plates. Our calculations are based on the scattering approach and take into account the coupling between different modes induced by the shape of the surface which are neglected in any sort of proximity approximation or effective medium approach. We then present an experimental setup aiming at measuring this torque.Comment: 7 pages, 7 figure

Casimir torque between corrugated metallic plates

We consider two parallel corrugated plates and show that a Casimir torque arises when the corrugation directions are not aligned. We follow the scattering approach and calculate the Casimir energy up to second order in the corrugation amplitudes, taking into account nonspecular reflections, polarization mixing and the finite conductivity of the metals. We compare our results with the proximity force approximation, which overestimates the torque by a factor 2 when taking the conditions that optimize the effect. We argue that the Casimir torque could be measured for separation distances as large as 1 $\mu{\rm m}.$Comment: 7 pages, 3 figures, contribution to QFEXT07 proceeding

Casimir energy and geometry : beyond the Proximity Force Approximation

We review the relation between Casimir effect and geometry, emphasizing deviations from the commonly used Proximity Force Approximation (PFA). We use to this aim the scattering formalism which is nowadays the best tool available for accurate and reliable theory-experiment comparisons. We first recall the main lines of this formalism when the mirrors can be considered to obey specular reflection. We then discuss the more general case where non planar mirrors give rise to non-specular reflection with wavevectors and field polarisations mixed. The general formalism has already been fruitfully used for evaluating the effect of roughness on the Casimir force as well as the lateral Casimir force or Casimir torque appearing between corrugated surfaces. In this short review, we focus our attention on the case of the lateral force which should make possible in the future an experimental demonstration of the nontrivial (i.e. beyond PFA) interplay of geometry and Casimir effect.Comment: corrected typos, added references, QFEXT'07 special issue in J. Phys.

The Scattering Approach to the Casimir Force

We present the scattering approach which is nowadays the best tool for describing the Casimir force in realistic experimental configurations. After reminders on the simple geometries of 1d space and specular scatterers in 3d space, we discuss the case of stationary arbitrarily shaped mirrors in electromagnetic vacuum. We then review specific calculations based on the scattering approach, dealing for example with the forces or torques between nanostructured surfaces and with the force between a plane and a sphere. In these various cases, we account for the material dependence of the forces, and show that the geometry dependence goes beyond the trivial {\it Proximity Force Approximation} often used for discussing experiments.Comment: Proceedings of the QFEXT'09 conference (Oklahoma, 2009

Casimir forces and non-Newtonian gravitation

The search for non-relativistic deviations from Newtonian gravitation can lead to new phenomena signalling the unification of gravity with the other fundamental interactions. Various recent theoretical frameworks indicate a possible window for non-Newtonian forces with gravitational coupling strength in the micrometre range. The major expected background in the same range is attributable to the Casimir force or variants of it if dielectric materials, rather than conducting ones, are considered. Here we review the measurements of the Casimir force performed so far in the micrometre range and how they determine constraints on non-Newtonian gravitation, also discussing the dominant sources of false signals. We also propose a geometry-independent parameterization of all data in terms of the measurement of the constant c. Any Casimir force measurement should lead, once all corrections are taken into account, to a determination of the constant c which, in order to assess the accuracy of the measurement, can be compared with its more precise value known through microscopic measurements. Although the last decade of experiments has resulted in solid demonstrations of the Casimir force, the situation is not conclusive with respect to being able to discover new physics. Future experiments and novel phenomenological analysis will be necessary to discover non-Newtonian forces or to push the window for their possible existence into regions of the parameter space which theoretically appear unnatural.Comment: Also available at http://www.iop.org/EJ/abstract/1367-2630/8/10/23

Effet de la température sur la force de Casimir entre miroirs réels

Les tests récents de l'effet Casimir affichent une précision de l'ordre du pour-cent. Pour rendre compte des différences entre ces expériences réelles et la situation idéale de Casimir il faut disposer d'une théorie précise. C'est à cette fin que nous calculons la force et l'énergie de Casimir où les effets correctifs de la conductivité finie des miroirs et des fluctuations thermiques sont pris en compte simultanément. Ceci contraste avec l'approximation usuelle qui considèrent ces deux effets indépendamment l'un de l'autre en multipliant simplement entre elles leurs corrections respectives. Il s'avère que cette approximation, comparée à notre résultat exact, induit justement une erreur de l'ordre du pour-cent

L'effet Casimir : théorie et expériences

L'existence de fluctuations irréductibles de champ dans le vide est une prédiction importante de la théorie quantique. Ces fluctuations ont de nombreuses conséquences observables comme l'effet Casimir, qui est maintenant mesuré avec une bonne précision et un bon accord avec la théorie, pourvu que celle-ci tienne compte des différences entre les expériences rélles et la situation idéale considérée par H.G.B. Casimir. Nous présenterons quelqu'unes des expériences récentes et discuterons les principales corrections à la force de Casimir liées à la situation expérimentale