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Like Casimirs original force between conducting plates in vacuum, Casimir forces are usually attractive. But repulsive Casimir forces can be achieved in special circumstances. These might prove useful in nanotechnology. We give examples of when repulsive quantum vacuum forces can arise with conducting materials.
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Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general Lifshitz configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capassos group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on recent developments will be surveyed. Here, stress will be placed on analytic developments, especially of Casimir-Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.
We study the zero and finite temperature Casimir force acting on a perfectly conducting piston with arbitrary cross section moving inside a closed cylinder with infinitely permeable walls. We show that at any temperature, the Casimir force always tends to move the piston away from the walls and towards its equilibrium position. In the case of rectangular piston, exact expressions for the Casimir force are derived. In the high temperature regime, we show that the leading term of the Casimir force is linear in temperature and therefore the Casimir force has a classical limit. Due to duality, all these result also hold for an infinitely permeable piston moving inside a closed cylinder with perfectly conducting walls.
Recently, the topic of Casimir repulsion has received a great deal of attention, largely because of the possibility of technological application. The general subject has a long history, going back to the self-repulsion of a conducting spherical shell and the repulsion between a perfect electric conductor and a perfect magnetic conductor. Recently it has been observed that repulsion can be achieved between ordinary conducting bodies, provided sufficient anisotropy is present. For example, an anisotropic polarizable atom can be repelled near an aperture in a conducting plate. Here we provide new examples of this effect, including the repulsion on such an atom moving on a trajectory nonintersecting a conducting cylinder; in contrast, such repulsion does not occur outside a sphere. Classically, repulsion does occur between a conducting ellipsoid placed in a uniform electric field and an electric dipole. The Casimir-Polder force between an anisotropic atom and an anisotropic dielectric semispace does not exhibit repulsion. The general systematics of repulsion are becoming clear.
We study the Casimir interaction energy due to the vacuum fluctuations of the Electromagnetic (EM) field in the presence of two mirrors, described by $2+1$-dimensional, generally nonlocal actions, which may contain both parity-conserving and parity-breaking terms. We compare the results with the ones corresponding to Chern-Simons boundary conditions, and evaluate the interaction energy for several particular situations.
We review new constraints on the Yukawa-type corrections to Newtonian gravity obtained recently from gravitational experiments and from the measurements of the Casimir force. Special attention is paid to the constraints following from the most precise dynamic determination of the Casimir pressure between the two parallel plates by means of a micromechanical torsional oscillator. The possibility of setting limits on the predictions of chameleon field theories using the results of gravitational experiments and Casimir force measurements is discussed.
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