Non-Markovian dynamics of a system of two-level atoms coupled to a structured environment

Abstract

In this work, taking $N$ noninteracting two-level atoms coupled to an anisotropic three-dimensional photonic crystal into account, we study exact non-Markovian dynamics of the atoms with the photonic crystal as an environment. We find that there exists a threshold number ${N}_{\mathrm{CR}}$ for the identical atoms, beyond which the system environment has a bound state regardless of how weak the system-environment coupling is. This means all identical atoms do not dissipate to the ground state. Further, when the whole system has no bound state, we find that the amplitude of collective excitation approaches a limit value $2/3$ as the number of atoms approaches to infinity. For nonidentical atoms with different transition frequencies, there exist $N$ bound states at most that lead to $N$-wave mixing in the system dynamics. The present prediction is possible to observe in the recent circuit QED experiment, and the results suggest that coherence in a many-body system can be maintained in bound states by manipulating the environment.