It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density but rather reaches a limiting value of $n\approx 1.7$. This limit arises purely from electrodynamics, as it occurs at densities far below those where chemical processes become important. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that, regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of the refractive index from a bottom-up, atomic physics perspective, and it also introduces the renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

中文翻译：

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原子介质的最大折射率

有趣的是，所有具有正折射率的光学材料的折射率值均为1数量级。令人惊讶的是，似乎缺少对导致这种普遍行为的机制的深入了解。此外，这种观察很难与以下事实相吻合：已知一个孤立的原子具有巨大的光学响应，其特征是共振散射截面远远超过其物理尺寸。在这里，我们从理论上和数字上研究了理想原子的光学性质随密度的变化，从稀薄的气体极限开始，包括多重散射和近场相互作用的影响。有趣的是，尽管一个孤立的原子产生了巨大的反应，$ñ\approx 1.7$。这个限制纯粹是由电动力学引起的，因为它的发生密度远低于化学过程变得重要的密度。我们提出了一种基于强无序重整化群论的解释，其中近场相互作用与随机原子位置相结合会导致原子共振频率的不均匀扩宽。这种机制可以确保，无论物理原子密度如何，任何给定频率的光仅与每立方波长最多与几个近共振原子相互作用，从而限制了可获得的最大折射率。我们的工作是从自下而上的原子物理学角度了解折射率极限的有希望的第一步，