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

Abstract

We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involves both an isotropic three-dimensional model and the one-dimensional case. The resonance interaction asymptotically decays faster with distance compared to the free-space case, specifically as $1/r^2$ compared to the $1/r$ free-space dependence in the three-dimensional case, and as $1/r$ compared to the oscillatory dependence in free space for the one-dimensional case. Nonetheless, the interaction energy remains significant and much stronger than dispersion interactions between atoms. On the other hand, spontaneous emission is strongly suppressed by the environment and the correlated state is thus preserved by the spontaneous-decay decoherence effects. We conclude that our configuration is suitable for observing the elusive quantum resonance interaction between entangled atoms.

12 pages, 3 figures

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Cited by in corpus (12)

• Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum
• Extended range of dipole-dipole interactions in periodically structured photonic media
• Vacuum fluctuations and radiation reaction contributions to the resonance dipole-dipole interaction between two atoms near a reflecting boundary
• Resonance energy transfer between two atoms in a conducting cylindrical waveguide
• Dispersion Interaction between Two Hydrogen Atoms in a Static Electric Field
• Resonance dipole-dipole interaction between two accelerated atoms in the presence of a reflecting plane boundary
• Spontaneous emission of an atom near an oscillating mirror
• Resonance interaction of two entangled atoms accelerating between two mirrors
• Strong and long-range radiative interaction between resonant transitions
• Collective spontaneous emission of two entangled atoms near an oscillating mirror
• Time-dependent resonance interaction energy between two entangled atoms under non-equilibrium conditions
• Dynamical atom-wall Casimir-Polder effect after a sudden change of the atomic position