Cavity quantum electrodynamics for a cylinder: Inside a hollow dielectric and near a solid dielectric cylinder
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We calculate the atomic energy-level shift and the modified dipolar radiation rate inside a hollow dielectric cylinder and outside a solid cylinder using a quantum-mechanical linear-response formalism in the dipole approximation. We first derive the electromagnetic fields scattered by the cylindrical surface for an oscillating dipole inside and outside the cylinder. When an atom is located on the axis of the cylindrical hollow, we obtain analytic expressions of the atomic level shifts in two limiting cases: when [Formula Presented] (radius of hollow) is very small, the level shift is proportional to [Formula Presented] which is associated with the kinetic-energy change of the atomic electron, whereas when [Formula Presented] is very large, the shift is proportional to [Formula Presented] which is identified as the retarded (Casimir-Polder) interaction energy. Moreover, we calculate the atomic potentials as a function of the position of atoms in the hollow region, which is important for the atom-guiding experiment. We also calculate the decay rates and find enhanced rates inside and outside the cylinder. In particular, we compare the radiative properties of an atom inside the hollow cylinder with those between two plates, and those near a cylinder with near a single surface. 1997 The American Physical Society.