Knobs
inversion is COMPUTED from the cascade (trapped-field 3p fraction), not a knob — the whole point.
At the probe
local slope
—
= scaling exponent
inversion (computed)
—
n₃ₚ/n from cascade
regime
—
N / cooperative / N²
τ_R
—
cooperative time
τ_E = L/c
—
Arecchi-Courtens
T₂ (min)
—
dephasing
Na₂ fraction
—
free-Na sink
The scaling spectrum: $I_{589}$ vs $n_\text{Na}$ on log-log. The local slope is the regime exponent. slope 1 = incoherent N; slope > 1 = cooperative/pooling; slope → 2 = Dicke N²; slope rolls over (even negative) where the Na₂ dimer sink (∝$n^2$) depletes the free radiating Na. The device walks the ladder; the slope tells you which rung. Superradiance is GATED per-cell by $\tau_R < \min(T_2, )$ and Arecchi-Courtens $\tau_E = L/c < \tau_R$ — earned where the chemiluminescent inversion beats dephasing, absent in the thermalized bulk (Gross-Haroche; Rajabi-Houde).
The ladder (sourced — LITERATURE-CANON.md)
$N^1$ incoherentthermalized bulk — default (Rajabi-Houde: no SR in relaxed gas)
$N^1$ + Holstein trapping$A_\text{eff}=A g_0$ — funnel reservoir builds (M&O; breaks at $n^*/n>10^{-2}$)
partial cooperativeinversion subset, $\tau_R\tau_R$ — the reaction cline
$N^2$ Dicke$\tau_R
pooling $n^2$Na(3p)+Na(3p)→3d — super-linear in density (in the cascade)
3-body recomb $n^3$Na⁺+e+e — runaway seed
ASE $e^{gL}$exponential in path, not polynomial — gain regime
Na₂ dimer rollover∝$n^2$ sink depletes free Na (de Groot; D₀=0.747 eV) — bends slope DOWN