{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e17fbb265dba07876ae1796cfd1fa3cba720350293c64ac0a898ded1ee060743","created":"2026-10-03T07:17:53Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"088ce4fa33f26485a1d39c11fcd8457ef8645bded766969ad3c9458180a17411","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"amo.cavity-photon-matter.equilibrium-superradiance","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Simple models predict that enough atoms in a cavity will spontaneously fill it with light in their lowest energy state. General theorems forbid this, yet loopholes have been proposed.","posed_since":"1975","precise":"$N$ atoms or electrons coupled to a cavity field with full minimal coupling, including the $A^{2}$ term, in thermal equilibrium. Determine whether the ground state can have $\\langle a\\rangle/\\sqrt{N} \\ne 0$ in the thermodynamic limit, given no-go theorems for uniform fields (Rzazewski et al. 1975; Andolina et al. 2019). Answer: yes for a specific realizable setting, or a general no-go proof covering spatially varying and magnetic couplings.","problem_ref":null,"references":"","settled_by":"A proof covering all gauge-invariant multimode couplings, or a model and experiment showing an equilibrium photon condensate.","status_note":"No-go theorems hold for uniform fields; photon condensation is permitted for spatially varying fields as a magnetostatic instability (Andolina et al., PRB 2020); an equilibrium magnonic analog was reported in ErFeO3 (Kim et al., Science Advances 2025), while a photonic equilibrium superradiant phase is unobserved.","title":"Does an equilibrium superradiant phase transition exist in cavity QED?","topic_ref":"8df59b7655cdc4331866853909e22dff07fb2d661e37f2a43fdc664ddd9f7dda"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0dc16ba0ceacd872d5cf73607f23aa0867d4fc3bf520ec82b05ce9303ef63a0d","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"e660adad8f55014b2d7418994edb0e3b2a417843351950438baf2c3938f07b17","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"qrmkuzBTOEh61CwrhmELok2I9DNWlRc9Y5051r7HIrbdk5MpImMQxZPiEjTHnYngGsVwuXm0Q-a2GMgNntzSCA"},"schema":"pubphys.envelope/1"},"record_hash":"0dc16ba0ceacd872d5cf73607f23aa0867d4fc3bf520ec82b05ce9303ef63a0d","leaf_index":384}