Effect of hydrogen-switchable mirrors on the Casimir force

Abstract

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...

Variations of Casimir energy from a superconducting transition

“…For example, Ref. [15] reports on an experiment, based on the technology of hydrogen switchable mirrors. Despite the large modulation of reflectivity in the optical region of the spectrum, which is very relevant for typical submicron separations between the mirrors, no detectable variation in the Casimir force could be seen, possibly due to lack of the necessary sensitivity in force measurements.…”

“…(12)(13)(14)(15) involve the electric permittivities ǫ (iζ) of the various layers at imaginary frequencies iζ. For these functions, we have made the following choices.…”

The Casimir free energy in high- and low-temperature limits

“…force became a subject of systematic experimental investigation [4][5][6][7][8][9][10][11]. The force between ideal metals at zero temperature [1],…”

Reduction of the Casimir force using aerogels

“…Casimir predicted that two neutral parallel plates will attract each other due to a force arising from quantum vacuum fluctuations. The interest in this force arises from the precise measurements between metallic [2,3,4,5,6] and dielectric systems [7,8] that are now possible. The measurements have confirmed the validity of Casimir's theory and Lifshitz formulation [9], that takes into account the dielectric properties of the plates.…”