{"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 gas?","topic_ref":"e89b5829665c5226a1b9e82a61b53f49c5a98f82161048d6d268249e6935de97"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e2013cb812d6d711637301b3a69eccdf636cf595e2985533a6ec2e92557a440d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"863185a965fc3d782dfa2e727d2c21b521eeb725ce90ab60d869bc59550c7e19","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"pLX89Lu66snown5960_VK55mhQSQ6Hd38-JYv0tykBYNgUv1c2DDFvt-b6nJhKk16CpjRsA6jkyBy2rrdieqAA"},"schema":"pubphys.envelope/1"},"record_hash":"e2013cb812d6d711637301b3a69eccdf636cf595e2985533a6ec2e92557a440d","leaf_index":389}