Cooperative decay rate and cooperative Lamb shift from a nanospherical configuration of two adjoining atomic species

Abstract

The eigenmodes of a nanosphere configuration where the core is an ensemble of two-level atoms with resonance frequency ${\ensuremath{\omega}}_{C}$, and the shell is an ensemble of two-level atoms but with shifted resonant frequency ${\ensuremath{\omega}}_{B}$ are obtained for different values of the ratio of the core radius to the shell outer radius as function of $({\ensuremath{\omega}}_{C}\ensuremath{-}{\ensuremath{\omega}}_{B})$. I show that the eigenmodes belong to one of two branches. The dominant decay mode for superradiant emission may belong to either branch, depending on the system's parameters. In instances of configurations where the cooperative decay rate values for the two branches become equal, the cooperative exponential amplification (decay) is accompanied by temporal oscillations.