The Observer — QND Dispersive Readout and the Non-Demolition Ψ Channel Register
Act 13 of the NexusOS physics sequence. First disclosed 2026-07-19. AGPL-3.0. Founder: Te Rata Pou.
The Problem of Observation
Measuring a quantum state generically destroys it. A photon detector absorbs the photon; the measurement result is yes or no but the photon is gone. For the Ψ channel network (Act 12), this is fatal: routing decisions must read channel state without removing the information carrier.
Dispersive Limit of the Jaynes-Cummings Hamiltonian
The full Jaynes-Cummings Hamiltonian: H = ω_c a†a + ω_q/2 σ_z + g(a†σ⁻ + aσ⁺). In the dispersive limit Δ = ω_q − ω_c ≫ g: H_disp = (ω_c + χ σ_z) a†a + ω̃_q/2 σ_z, where χ = g²/Δ is the dispersive shift and ω̃_q = ω_q + g²/Δ is the Lamb-shifted qubit frequency. The cavity frequency splits: ω± = ω_c ± χ for qubit |↑⟩ or |↓⟩.
Measurement Rate and Quantum Back-Action
Measurement rate: Γ_meas = 4χ²n̄/κ. Qubit dephasing: Γ_φ = Γ_meas/2 (Heisenberg limit). Critical photon number: n_crit = Δ²/(4g²). Purcell decay: Γ_P = (g/Δ)² κ. Validity condition: g/|Δ| ≪ 1.
WNSP Connection
Each SNIC node integrates a dispersive readout circuit adjacent to the WGM resonator. Target parameters: χ/2π ~ 5 MHz, κ/2π ~ 10 MHz, n̄ ~ 5 photons → Γ_meas/2π ~ 50 kHz → T_meas ~ 20 μs. Compatible with photon lifetimes in high-Q (Q ~ 10⁸) WGM resonators.
The 13-Act Sequence