Resonant Interaction Energy between Two Identical Atoms in a Photonic Crystal

We consider the resonant interaction energy between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. We consider two different models of a photonic crystal: a one-dimensional crystal and an isotropic three-dimensional crystal. The two atoms, having the same orientation of their transition dipole moment, are supposed prepared in their entangled symmetrical state and interacting with the quantum electromagnetic field in the multipolar coupling scheme. We consider both the case of an atomic transition frequency outside the photonic band gap and the case of a transition frequency inside the gap. When the transition frequency is ou…