Control of the spontaneous emission rate of atoms trapped in spherical shell cavities

Abstract

Within a first-order time-dependent perturbation approach, we compute the spontaneous decay rate of a two-level system placed in the vicinity of a perfectly refecting spherical surface (exterior and interior) as well as the spontaneous emission rate of a two-level system trapped between two perfectly reflecting concentric spheres. We consider a model system in which the emitter is represented by a two-level monopole coupled to a Hermitian massless scalar field. Using the method of images, we determine the appropriate Wightman's function evaluated in the world line of the atom. For the atom trapped between the radii of the concentric spheres, Wightman's function of the atom incorporates contributions from an innite set of variable image charges, satisfying Dirichlet boundary conditions. We provide analytical expressions for the decay rate to investigate the radiation process of the atomic system near a single sphere and trapped between the concentric spheres. We provide a detailed analysis on the dependence of the decay rate on a sphere radius, atom's location, and emitted radiation frequency. What is more, on the case of spherical shells, we analyze the decay rate on different relationships between the radii of spheres and the radiation energy emitted. As it turns, we reveal regimes of strong suppression of the spontaneous emission rate, and development of irregular oscillations as function of quantum emitted energy.