Casimir Attraction Research Articles

Effect of hydrogen-switchable mirrors on the Casimir force.

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.

The temperature effect in the Casimir attraction of a thin metal film

The Casimir effect for conductors at arbitrary temperatures is theoretically studied. By using the analytical properties of the Green functions and applying the Abel-Plan formula to Lifshitz's equation, the Casimir force is presented as sum of a temperature dependent and vacuum contributions of the fluctuating electromagnetic field. The general results are applied to the system consisting of a bulk conductor and a thin metal film. It is shown that a characteristic frequency of the thermal fluctuations in this system is proportional to the square root of a thickness of the metal film. For the case of the sufficiently high temperatures when the thermal fluctuations play the main role in the Casimir interaction, this leads to the growth of the effective dielectric permittivity of the film and to a disappearance of the dependence of Casimir's force on the sample thickness.

Temperature effects on the Casimir attraction between a pair of quantum wells

We present calculations of the free energy of attraction between two quantum wells in which the wells are treated as strictly two-dimensional metallic sheets. The van der Waals force exhibits fractional separation dependence in this system. This is in contrast to the usual integer separation dependence. We have performed numerical calculations at different temperatures and with different carrier densities. Except at very low temperatures thermal effects will be a dominating source of attraction. We have determined temperature criteria that must be fulfilled for the fractional separation dependence to be observable. Thermal corrections will be important already at temperatures less than 1 K. We further make some comments on a recent measurement of the Casimir force.

Comment on “Calculation of the Casimir force between imperfectly conducting plates”

In a recent paper [Phys. Rev. A 59, R3149 (1999)] Lamoreaux reported calculations of the Casimir force. The experimentally found permittivity was used in the calculations. Large deviations were found between numerically evaluated forces and forces derived from a series expanded plasma model. We would like to comment on a few results presented in this work. First, we claim that important features of the imaginary component of the permittivity of copper, presented in Fig. 1(a) are due to the interpolation procedure and are not caused by physical phenomena. These features influence the calculated permittivity for imaginary frequencies, which is the quantity used to calculate the Casimir attraction. Second, we discuss the extrapolation procedure used for low frequencies. The results depend substantially on how this extrapolation is performed.

Phenomenological model for Casimir attraction of a metal film

The force of surface interaction (Casimir effect) between a bulk conductor and a metal film deposited on a dielectric substrate is studied by the method of quantum field theory. The film thickness is assumed to be much smaller than the skin depth at characteristic frequencies of fluctuation fields. The equations for one-particle Green’s function of the electromagnetic field in the metal film are solved on the basis of a simple phenomenological model. Namely, complex macroscopic electrodynamic properties of the film are described by introducing the surface permittivity determined by the conductivity 〈σ〉 averaged over sample thickness. The dependence of the Casimir attractive force on the specularity parameter ρ characterizing the interaction of conduction electrons with the film surface is predicted. The results of investigations demonstrate that the electronic and surface properties of metal films can in principle be studied experimentally by measuring the force of their Casimir attraction.

On Casimir pressure, the Lorentz force and black body radiation

It is shown that the Casimir attraction, including the temperature dependence, between two metallic plates can be derived from the Lorentz force acting on the surfaces of the plates. The force per unit area acting on a surface turns out to be a pressure, i.e. directed toward the bulk of the metal, and infinite in magnitude for a perfect conductor. The Casimir formula for the attraction between the plates can be obtained when we consider the pressure acting on the other side of the plates. It is then concluded that any conductor, at least in the shape of a plate, experiences a compression; the better the conductor, the greater that compression is. It is also noticed that there should be a repulsion between two semi-infinite metallic slabs separated by a planar gap. The relation of these results to the Lifshitz general theory of attraction between solids is also discussed.