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/r2 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.
展开▼
机译:我们考虑两个相同的纠缠原子之间的共振相互作用能,其中一个处于激发态,另一个处于基态。它们在真空状态下与量子电磁场相互作用,并被置于光子带隙环境中,其色散关系在间隙边缘附近呈二次方,对于低频呈线性关系,而原子跃迁频率被假定为在光子间隙内部且在附近它的下边缘。这个问题与外部环境中原子之间的相干共振能量转移严格相关。分析涉及各向同性的三维模型和一维情况。与自由空间相比,共振相互作用随距离渐近衰减,特别是在三维情况下,与1 / r自由空间相关性为1 / r 2 sup>。 r与一维情况下自由空间中的振荡依赖性相比。但是,相互作用能仍然很重要,并且比原子之间的色散相互作用要强得多。另一方面,环境强烈地抑制了自发发射,因此通过自发衰变退相干效应保持了相关状态。我们得出的结论是,我们的配置适合观察纠缠原子之间难以捉摸的量子共振相互作用。
展开▼