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Casimir-Polder interaction energies between a point anisotropicallypolarizable atom and an annular dielectric are shown to exhibit localizedrepulsive long-range forces in specific configurations. We show that when theatom is positioned at the center of the annular dielectric, it is energeticallyfavorable for the atom to align its polarizability with respect to that of thedielectric. As the atom moves away from, but along the symmetry axis of theannular dielectric, it encounters a point where the polarizable atomexperiences no torque and the energy is free of orientation dependence. At thisheight, abruptly, the atom prefers to orient its polarizability perpendicularto that of the dielectric. For certain configurations, it encounters anothertorsion-free point a larger distance away, beyond which it prefers to againpoint its polarizability with respect to that of the dielectric. We find whenthe atom is close enough, and oriented such that the energy is close tomaximum, the atom could be repelled. For certain annular polarizations,repulsion can happen below or above the torsion-free height. Qualitativefeatures differ when the atom is interacting with a ring, versus a plate ofinfinite extent with a hole. In particular, the atom can prefer to orientperpendicular to the polarizability of the plate at large distances, instriking contrast to the expectation that it will orient parallel. To gaininsight of this discrepancy, we investigate an annular disc, which captures theresults of both geometries in limiting cases. These energies are too weak forimmediate applications, nevertheless, we elaborate an interesting applicationon a prototype of a Casimir machine using these configurations.

Geometrical dependence in Casimir-Polder repulsion: Anisotropically polarizable atom and anisotropically polarizable annular dielectric