near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.*'
author:
- Francesco Andreoli
- 'Michael J. Gullans'
- 'Alexander A. High'
- Antoine Browaeys
- 'Darrick E. Chang'
bibliography:
- 'main.bib'
title: The maximum refractive index of an atomic medium
---

One interesting observation is that all the optical materials that we know of, with a positive index of refraction at visible wavelengths, universally have an index of order unity, $n\sim \mathcal O(1)$. While we typically utilize materials far from their natural electronic resonances, this even holds true close to resonance [@Rustgi1961OpticalEv; @Philipp1963OpticalSemiconductors; @Walker1964UltravioletDiamond; @Lamy1977OpticalUltraviolet; @Aspnes1983DielectricEV; @Warren1984OpticalMicrowave; @Papadopoulos1991OpticalDiamond; @Kitamura2007OpticalTemperature]. Yet, despite the profound implications that an ultra-high index material would have for optical technologies, a deep understanding of the origin of this apparently universal behavior seems to be lacking. Furthermore, this property of real materials is not readily reconciled with the fact that a single, isolated atom exhibits a giant scattering cross-section $\sigma_{\text{sc}} \sim\lambda_0^2$ for photons resonant 