No abstract

The possibility to modify the strength of the Casimir effect by tailoring the dielectric functions of the interacting surfaces is regarded as a unique opportunity in the development of micro- and nanoelectromechanical systems. In air, however, one expects that, unless noble metals are used, the electrostatic force arising from trapped charges overcomes the Casimir attraction, leaving no room for exploitation of Casimir force engineering at ambient conditions. Here we show that, in the presence of a conductive oxide, the Casimir force can be the dominant interaction even in air, and that the use of conductive oxides allows one to reduce the Casimir force up to a factor of 2 when compared to noble metals.

We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a piston-like geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic "lateral" force from the walls.

We present systematic measurements of the Casimir force between a gold-coated plate and a sphere coated with a hydrogen-switchable mirror. Hydrogen-switchable mirrors are shiny metals that can become transparent upon hydrogenation. Despite such a dramatic change of the optical properties of the sphere, we did not observe any significant decrease of the Casimir force after filling the experimental apparatus with hydrogen. This counterintuitive result can be explained by the Lifshitz theory that describes the Casimir attraction between metallic and dielectric materials. O ne of the most spectacular consequences of quantum electrodynamics is that it does not leave room for an empty vacuum. Even in the absence of electromagnetic sources, quantum fluctuations of electric and magnetic fields give rise to a zero-point energy that never vanishes (for a general introduction to quantum electrodynamics, see, for example, ref. 1).At first one might think that the zero-point energy is only a constant background to every experimental situation, and, as such, that it has no observable consequences. On the contrary, there are several phenomena in which quantum fluctuations of the electromagnetic field play a very important role, such as the Lamb shift, the anomalous magnetic moment of the electron, spontaneous emission, and the Casimir effect. The latter has received a lot of attention since 1948, when H. B. G. Casimir predicted an attractive force between two perfectly conducting, electrically neutral parallel plates (2). The plates act as a cavity where only the electromagnetic modes that have nodes on both the walls can exist. The zero-point energy when the plates are kept at a distance d is thus smaller than the zero-point energy of free space. Following Casimir's calculation, it is possible to show that, when the plates are brought from infinity to a distance d, the energy decreases bywhere A is the area of the plates, and ប and c are the usual fundamental constants. The Casimir force is thus given byIt is worth mentioning that the attraction, although negligible at macroscopic distances, increases rapidly as the distance between the plates decreases. At d Ӎ 100 nm, the Casimir pressure is as high as Ӎ10 N͞m 2 . For this reason, the Casimir effect recently received considerable attention in the context of the development of Micro-and NanoElectroMechanical Systems (MEMS and NEMS) (see, for example, refs. 3-5). Casimir's theory was generalized to the case of dielectrics by E. M. Lifshitz (6), who derived an analytical expression for the attraction between two uncharged parallel plates with arbitrary dielectric functions. The calculated force reduces to the Casimir result (Eq. 1) in the limit of ideal metals (i.e., with infinite plasma frequency).The literature on the Casimir force experiments spans almost 50 years, covering the results of a series of measurements of increasing precision (4,5,(7)(8)(9)(10)(11)(12)(13)(14)(15). (For a description of the earliest experiments, see, for example, refs. 16 and 17. See also refs. 18...

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a piston-like problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate non-additive and non-monotonic changes in the force due to these lateral walls. PACS numbers:Casimir forces arise between macroscopic objects due to changes in the zero-point energy associated with quantum fluctuations of the electromagnetic field [1]. This spectacular effect has been subject to many experimental validations, as reviewed in Ref. 2. All of the experiments reported so far have been based on simple geometries (parallel plates, crossed cylinders, or spheres and plates). For more complex geometries, calculations become extremely cumbersome and often require drastic approximations, a limitation that has hampered experimental and theoretical work beyond the standard geometries.In this letter, we present a method to compute Casimir forces in arbitrary geometries and materials, with no uncontrolled approximations, that can exploit the efficient solution of well-studied problems in classical computational electromagnetism. Using this method, which we first test for geometries with known solutions, we predict a non-monotonic change in the force arising from lateral side walls in a less-familiar piston-like geometry (Fig. 2). Such a lateral-wall force cannot be predicted by "additive" methods based on proximity-force or other purely two-body-interaction approximations, due to symmetry, and it is difficult to find a simple correction to give a non-monotonic force. We are able to compute forces for both perfect metals and arbitrary dispersive dielectrics, and we also obtain a visual map of the stress tensor that directly depicts the interaction forces between objects.The Casimir force was originally predicted for parallel metal plates, and the theory was subsequently extended to straighforward formulas for any planar-multilayer dielectric distribution ε(x, ω) via the generalized Lifshitz formula [3]. In order to handle more arbitrary geometries, two avenues have been pursued. First, one can employ approximations derived from limits such as that of parallel plates; these methods include the proximity-force approximation (PFA) and its refinements [4], renormalized Casimir-Polder [5] or semi-classical interactions [6], multiple-scattering expansions [7], classical ray optics [8], and various perturbative techniques [9,10]. Such methods, however, involve uncontrolled approximations when applied to arbitrary geometries outside their range of applicability, and have even been observed to give qualitatively incorrect results [11,12]. Therefore, re...