Atom-atom interaction at the edge of a photonic band gap

We present the first model calculation for two atoms in a photonic band gap material with transition frequencies near the edge of the gap. We derive nonperturbative expressions for the amplitudes of the atoms without resorting to the pole-approximation which is necessary due to the strongly modified density of modes at the band gap edge. The system is found to exhibit rich dynamics. For a wide range of parameters we find beating and population trapping in the long time limit although the system is coupled to a dissipative environment.