任意原子晶格的Fano-Hopfield模型和光子带隙
Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice
摘要：
本文研究了Fano Hopfield模型（原子偶极用谐振子模型）中固定位置的周期原子系综中的光色散关系。与早期的工作相比，我们不限于立方晶格，我们不规范的理论，但我们重整化它在一个系统的方式使用高斯截止动量空间。虽然没有全向光谱间隙是已知的布拉维原子晶格中的光，我们发现，在很宽的参数范围内，全向间隙发生在金刚石原子晶格，这可能是实现在超冷原子的实验。该理论的长波长极限也为任意晶格提供了洛伦兹-洛伦兹（或克劳修斯-莫索蒂）关系。
英文摘要：
We study the light dispersion relation in a periodic ensemble of atoms at fixed positions in the Fano-Hopfield model (the atomic dipole being modeled with harmonic oscillators). Compared to earlier works, we do not restrict to cubic lattices, and we do not regularize the theory by hand but we renormalize it in a systematic way using a Gaussian cut-off in momentum space. Whereas no omnidirectional spectral gap is known for light in a Bravais atomic lattice, we find that, for a wide range of parameters, an omnidirectional gap occurs in a diamond atomic lattice, which may be realized in an experiment with ultra-cold atoms. The long-wavelength limit of the theory also provides a Lorentz-Lorenz (or Clausius-Mossotti) relation for an arbitrary lattice.
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