What limits the refractive index of a dense atomic gas?
In plain words
Each atom bends light strongly, yet no known material made of atoms has a refractive index far above a few. Packing atoms denser does not help, and the reason is not fully settled.
Precise statement
Randomly positioned two-level atoms at density n with $n \lambda^3 >> 1$, including near-field dipole-dipole interactions and multiple scattering. Determine the maximum $\operatorname{Re}(n_{\mathrm{ref}})$ over detuning and density, whether its saturation near 1.7 is universal for disordered ensembles, and which mechanism sets it. Answer: value and mechanism, with conditions under which ordered or multilevel atoms exceed it.
What would settle it
Large-scale coupled-dipole and multilevel simulations with a closed-form explanation, tested by dense-cloud or lattice measurements.
Status in the literature
Coupled-dipole numerics found a maximum near 1.7 for disordered gases (Andreoli et al., PRX 2021).