Spontaneous Radiation of a Two-Level System Confined in a Reflective Spherical Shell Quantum Dot

Using a first-order time-dependent perturbation theory, we calculate the spontaneous emission rate of a two-level system trapped between perfectly reflecting concentric spheres. The emitter is represented by a two-level monopole coupled to a Hermitian massless scalar field satisfying Dirichlet boundary conditions in such quantum-confined low-dimensional structure. We obtained the appropriate Green’s function evaluated in worldline of the atom which incorporates contributions from an infinite set of variable image charges. We provide an analytical expression for the decay rate to investigate the radiation process of the trapped atomic system. We perform a broad analysis of the dependence of the decay rate for different relations between the radii of spheres and the emitted radiation energy. We unveil regimes of strong suppression of the spontaneous emission rate as well as the development of irregular oscillations as a function of the quantum of emitted energy.