Institut für Physik und Astronomie
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This thesis investigates the Casimir effect between plates made of normal and superconducting metals over a broad range of temperatures, as well as the Casimir-Polder interaction of an atom to such a surface. Numerical and asymptotical calculations have been the main tools in order to do so. The optical properties of the surfaces are described by dielectric functions or optical conductivities, which are reviewed for common models and have been analyzed with special weight on distributional properties and causality. The calculation of the Casimir energy between two normally conducting plates (cavity) is reviewed and previous work on the contribution to the Casimir energy due to the surface plasmons, present in all metallic cavities, has been generalized to finite temperatures for the first time. In the field of superconductivity, a new analytical continuation of the BCS conductivity to to purely imaginary frequencies has been obtained both inside and outside the extremely dirty limit of vanishing mean free path. The Casimir free energy calculated from this description was shown to coincide well with the values obtained from the two fluid model of superconductivity in certain regimes of the material parameters. The Casimir entropy in a superconducting cavity fulfills the third law of thermodynamics and features a characteristic discontinuity at the phase transition temperature. These effects were equally encountered in the Casimir-Polder interaction of an atom with a superconducting wall. The magnetic dipole coupling of an atom to a metal was shown to be highly sensible to dissipation and especially to the surface currents. This leads to a strong quenching of the magnetic Casimir-Polder energy at finite temperature. Violations of the third law of thermodynamics are encountered in special models, similar to phenomena in the Casimir-effect between two plates, that are debated controversely. None of these effects occurs in the analog electric dipole interaction. The results of this work suggest to reestablish the well-known plasma model as the low temperature limit of a superconductor as in London theory rather than use it for the description of normal metals. Superconductors offer the opportunity to control the dissipation of surface currents to a great extent. This could be used to access experimentally the low frequency optical response of metals, which is strongly connected to the thermal Casimir-effect. Here, differently from corresponding microwave experiments, energy and momentum are independent quantities. A measurement of the total Casimir-Polder interaction of atoms with superconductors seems to be in reach in today’s microchip-based atom-traps and the contribution due to magnetic coupling might be accessed by spectroscopic techniques