{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"63d78a2219484916b71b9db84186b23e5d9f906000d02725f07fe4a8a43e79c4","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"0bbb292e9230ed86c57a08b3f34d0c1c282af5f8e24dddc4b24e1288a5ef6dbe","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"amo.collective-emission.max-refractive-index","kind":"phenomenon","literature_status":"partially-resolved","n":"1","parents":[],"plain":"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.","posed_since":"","precise":"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.","problem_ref":null,"references":"","settled_by":"Large-scale coupled-dipole and multilevel simulations with a closed-form explanation, tested by dense-cloud or lattice measurements.","status_note":"Coupled-dipole numerics found a maximum near 1.7 for disordered gases (Andreoli et al., PRX 2021).","title":"What limits the refractive index of a dense atomic 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