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

TL;DR

This paper investigates how a photonic bandgap environment affects the resonance interaction energy between two entangled atoms, showing that the environment modifies decay rates and enhances interaction strength, facilitating observation of quantum effects.

Contribution

It provides a detailed analysis of resonance interactions in photonic bandgap environments, revealing modified distance dependence and suppressed spontaneous emission, which aids in observing quantum resonance phenomena.

Findings

Interaction decays faster than in free space

Spontaneous emission is strongly suppressed

Interaction remains significantly stronger than dispersion forces

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.