with an atomic transition of wavelength $\lambda_0$ ([Fig. \[fig:scatt\_cross\_sec\]]{}-a), which far exceeds both the physical size of the atom or the typical lattice constant of a solid ($\lambda_0\sim 1\upmu \text{m}$ for a typical optical transition, compared to the Bohr radius $a_0\sim 0.1 \text{nm}$).

Specifically, in standard theories [@Jackson1998ClassicalElectrodynamics; @Grynberg2010IntroductionOptics], the macroscopic index of an atomic medium ([Fig. \[fig:scatt\_cross\_sec\]]{}-b) is constructed from the product of the single-atom polarizability and the atomic density, and around resonance its value $n\sim \sqrt{N\lambda_0^3/V}$ extrapolates to a maximum of $ \sim 10^5$ at solid densities ([Fig. \[fig:scatt\_cross\_sec\]]{}-c). It is well-known that this argument neglects multiple scattering of light and photon-mediated dipole-dipole interactions [@Fleischhauer1999RadiativeFormula; @Javanainen2016LightOptics], and substantial work has been devoted to explore their effects on various optical phenomena, such as collective resonance shifts [@Manassah2012CooperativeShift; @Keaveney2012CooperativeThickness; @Javanainen2014ShiftsSample; @Bromley2016CollectiveMedium; @Jenkins2016OpticalGases; @Dobbertin2020CollectiveNanocavities], cooperative scattering properties [@Schilder2016PolaritonicAtoms; @Schilder2017HomogenizationScatterers; @Schilder2020Near-ResonantAtoms], emergence of sub- and super-radiance [@Dicke1954CoherenceProcesses; @Gross1982Superradiance:Emission; @Roof2016ObservationAtoms; @Araujo2016SuperradianceRegime; @Asenjo-Garcia2017ExponentialArrays; @He2019GeometricEmission], realization of atomic mirrors [@Shahmoon2017CooperativeArrays; @Bettles2016EnhancedArray; @Rui2020ALayer], and Anderson localization of light [@Skipetrov2014AbsenceScatterers; @Skipetrov2019SearchField]. In particular, this includes theoretical and experimental evidence that the optical response of dense gases can be much smaller than standard predictions [@Pellegrino2014ObservationEnsemble; @Schilder2016PolaritonicAtoms; @Jennewein2018CoherentTheory; @Javanainen2016LightOptics; @Guerin2017LightEffects] or even reach limiting values [@Chomaz2012AbsorptionAnalysis; @Zhu2016LightMedia; @Jenkins2016CollectiveExperiment; @Jennewein2016PropagationAtoms; 