Resonance interaction energy between two entangled atoms in a photonic bandgap environment

摘要

We consider the resonance interaction energy between two identical entangledatoms, one excited and the other in the ground state, interacting with thequantum electromagnetic field in the vacuum state and placed in aphotonic-bandgap environment with a quadratic dispersion relation. This problemis also strictly related to the coherent resonant energy transfer between atomsin external environments. We assume the atomic transition frequency inside thephotonic gap and near its lower edge. We consider both an isotropicthree-dimensional and a one-dimensional system. We find that the resonanceinteraction asymptotically decays faster with the distance compared to thefree-space case, specifically as $1/r^2$ compared to the $1/r$ free-spacedependence in the three-dimensional case, and as $1/r$ compared to theoscillatory dependence in free space for the one-dimensional case. Nonethelessit remains significant and much stronger than dispersion interactions betweenatoms. On the other hand, spontaneous emission is strongly suppressed by theenvironment and the correlated state is thus preserved by the spontaneous-decaydecoherence effects. A physical interpretation of this result is also discussedin detail. We conclude that our configuration is a suitable one for observingthe elusive quantum resonance interaction between entangled atoms.