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Register a new userCasimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids
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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.
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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.
In this paper we study an archetypical scenario in which repulsive Casimir-Polder forces between an atom or molecule and two macroscopic bodies can be achieved. This is an extension of previous studies of the interaction between a polarizable atom and a wedge, in which repulsion occurs if the atom is sufficiently anisotropic and close enough to the symmetry plane of the wedge. A similar repulsion occurs if such an atom passes a thin cylinder or a wire. An obvious extension is to compute the interaction between such an atom and two facing wedges, which includes as a special case the interaction of an atom with a conducting screen possessing a slit, or between two parallel wires. To this end we further extend the electromagnetic multiple-scattering formalism for three-body interactions. To test this machinery we reinvestigate the interaction of a polarizable atom between two parallel conducting plates. In that case, three-body effects are shown to be small, and are dominated by three- and four-scattering terms. The atom-wedge calculation is illustrated by an analogous scalar situation, described in the Appendix. The wedge-wedge-atom geometry is difficult to analyze because this is a scale-free problem. But it is not so hard to investigate the three-body corrections to the interaction between an anisotropic atom or nanoparticle and a pair of parallel conducting cylinders, and show that the three-body effects are very small and do not affect the Casimir-Polder repulsion at large distances between the cylinders. Finally, we consider whether such highly anisotropic atoms needed for repulsion are practically realizable. Since this appears rather difficult to accomplish, it may be more feasible to observe such effects with highly anisotropic nano particles.
It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir-Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt [Ann. Phys. {bf 395}, 326 (2018)], who find that the energy or self-stress of a homogeneous dielectric ball with permittivity $varepsilon$ begins with a term of order $varepsilon-1$. Here we demonstrate that this cannot be correct. The only possible origin of a term linear in $varepsilon-1$ lies in the bulk energy, that energy which would be present if either the material of the body, or of its surroundings, filled all space. Since Avni and Leonhardt correctly subtract the bulk terms, the linear term they find likely arises from their omission of an integral over the transverse stress tensor.
Polarisable atoms and molecules experience the Casimir-Polder force near magnetoelectric bodies, a force that is induced by quantum fluctuations of the electromagnetic field and the matter. Atoms and molecules in relative motion to a magnetoelectric surface experience an additional, velocity-dependent force. We present a full quantum-mechanical treatment of this force and identify a generalised Doppler effect, the time delay between photon emission and reabsorption, and the Roentgen interaction as its three sources. For ground-state atoms, the force is very small and always decelerating, hence commonly known as quantum friction. For atom and molecules in electronically excited states, on the contrary, both decelerating and accelerating forces can occur depending on the magnitude of the atomic transition frequency relative to the surface plasmon frequency.
We take a closer look at the fundamental Casimir-Polder interaction between quantum particles and dispersive dielectric surfaces with surface polariton or plasmon resonances. Linear response theory shows that in the near field, van der Waals, regime the free energy shift of a particle contains a thermal component that depends exclusively on the population/excitation of the evanescent surface polariton/plasmon modes. Our work makes evident the link between particle surface interaction and near field thermal emission and demonstrates how this can be used to engineer Casimir-Polder forces. We also examine how the exotic effects of surface waves are washed out as the distance from the surface increases. In the case of molecules or excited state atoms, far field approximations result in a classical dipole-dipole interaction which depends on the surface reflectivity and the mean number of photons at the frequency of the atomic/molecular transition. Finally we present numerical results for the CP interaction between Cs atoms and various dielectric surfaces with a single polariton resonance and discuss the implications of temperature and retardation effects for specific spectroscopic experiments.
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