{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"bbe28a6ce19dfe4c938eea9993169a22a82f107ea76ab20b410cbdc9952d089e","created":"2026-10-03T07:17:56Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"37ff3ded2b4dc6a852dcc51918b5dbba1a8bd2e848e28e7d0c2cbf2c3a43a6b8","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"beams.fel-physics.quantum-fel-regime","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"If one photon's recoil is enough to knock an electron out of resonance, the laser behaves like a two-level quantum system with a much narrower spectrum; this regime has not been reached.","posed_since":"","precise":"With $\\rho$ the FEL Pierce parameter and $k_r$ the resonant wavenumber, the quantum FEL parameter is $\\rho_{\\mathrm{bar}} = \\rho \\gamma m c/(\\hbar k_r)$; the quantum regime $\\rho_{\\mathrm{bar}} < 1$ also requires relative energy spread below $\\hbar k_r/(\\gamma m c)$. Determine whether any configuration (optical undulator driven by a laser, crystal or other short-period undulator) reaches $\\rho_{\\mathrm{bar}} < 1$ with gain length shorter than the interaction length, and observe the predicted single-line spectrum.","problem_ref":null,"references":"","settled_by":"Measurement of a spectrum showing the narrowing and line structure predicted for $\\rho_{\\mathrm{bar}} < 1$.","status_note":"","title":"Observing the quantum regime of a free-electron laser","topic_ref":"62fcdc9c8f916869de7ec88dba711f39f0c92f912f69f270978376119dc0bcaa"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"585043f3fda45d5eae950f3aa90c57f901c1c0483ed4f42902b28a09dda50894","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"e2e8263043fff97f5be7226b0a1dcfc9a19e24220837043a000627dc38e8ccb5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"4swGTaS8hFAOV6SreM_asqV3ipUL9-FK_6YVfAXigKYz6jNv204Xs2yAZi3Jxd_X6gNx87xjmotUQsV4weQiAQ"},"schema":"pubphys.envelope/1"},"record_hash":"585043f3fda45d5eae950f3aa90c57f901c1c0483ed4f42902b28a09dda50894","leaf_index":665}