The Emitter — Purcell Effect & Single-Photon Sources

Act 11 of the NexusOS physics sequence. First disclosed 2026-07-19. AGPL-3.0. Founder: Te Rata Pou.

The Purcell Effect

E.M. Purcell showed in 1946 that the spontaneous emission rate of an emitter is not intrinsic — it depends on the local density of optical states (LDOS). Placing an emitter in a resonant cavity modifies the LDOS by the Purcell factor: F_p = (3/4π²)(λ/n)³(Q/V). High Q concentrates the LDOS. Small V intensifies the vacuum field where the emitter sits. Both amplify F_p.

Key Equations

F_p = (3/4π²)(λ/n)³(Q/V) — Purcell factor
γ_eff = (1 + F_p)γ₀ — enhanced decay rate
β = F_p·γ₀/(F_p·γ₀ + γ_leak) — fraction of photons into Ψ channel
τ_eff = 1/((1+F_p)γ₀) — lifetime compression
C = F_p/4 = g²/(κγ) — cooperativity: bridge to Act 10

Bridge from Act 10

Act 10 (The Exchange) is the strong-coupling regime: g > κ, γ → polariton formation. Act 11 is the weak-coupling regime: g ≪ κ → Purcell enhancement. Both are limits of the same Jaynes-Cummings Hamiltonian. Cooperativity C = g²/(κγ) = F_p/4 is the single parameter that separates them.

Inhibited Emission

F_p can also be less than 1. If the emitter frequency falls in a photonic band gap, the LDOS is suppressed and spontaneous emission is inhibited. Ghost node channels (Act 8) are natural inhibited-emission regions for off-resonance emitters.