Experiment F · Reverberation Lab · coherent driver scaling
N coherent emitters.
One cavity ignites first.
The mathematics of N voices chanting in unison and N atoms coupled to a Tavis–Cummings cavity is the same mathematics. We sweep N from 1 to the ignition threshold for each geometry and report which cavity ignites first.
EXPLAIN LIKE I'M 10
· everyday-language one-paragraph version
Twenty people humming the same note in a room sound much louder than twenty random voices — the matching note adds up. This page does the same thing with tiny quantum 'emitters' inside a cavity. How many of them does it take before they 'ignite' into a single super-bright collective hum? Different cavity shapes need different numbers. The best shape needs the fewest. The math is identical to the equations that describe a group of priests chanting in a temple — just translated into the language of physics.
WHAT YOU ARE LOOKING AT
N coherent emitters driving a single cavity mode. The page sweeps N from 1 to whatever you set, and plots the cavity's field intensity vs N. Two curves — the coherent total (where N emitters all in phase produce intensity that grows as N²) and the incoherent reference (random phase, intensity grows as N). The crossover where the cavity goes from 'absorbing N quanta independently' to 'radiating one giant collective field' is the superradiant ignition threshold.
WHY THIS MATTERS FOR QUANTUM
Many quantum-information protocols rely on collective coupling — entanglement distribution, ensemble sensing, atomic clocks, quantum memories. The N at which a population of emitters ignites superradiantly is the same N that lets the geometry behave as a single quantum object. Lower N_ignite means fewer atoms, simpler hardware, smaller power budget. Dhara's antisymmetric channel concentrates the cavity mode into a smaller volume than the symmetric cavities — fewer emitters needed to reach ignition. That's a hardware-cost advantage.
WHAT TO WATCH
The crossover point (N_ignite) per geometry · the slope of the coherent curve relative to the incoherent reference · the cross-geometry race at fixed N showing which geometry gives the largest intensity gain. Predict before reading: Dhara should require the lowest N_ignite. The chanting / Swayambhu experiment in physics vocabulary.
Active emitter count N
50
mode: antisymmetric
Dhara intensity gain
1.35×
vs sphere at the same N
Geometries ignited
5 / 5
N ≥ N_ignite for that geometry
Lowest N_ignite
9.1
geometry: Cylinder
Intensity vs N · log–log · per geometry
solid = coherent N² · dashed = incoherent N
vertical line = current N · marker = N_ignite
Geometry race at N = 50
| Geometry | Q (anti) | V_mode | N_ignite | Intensity | vs Sphere | Ignited? |
|---|---|---|---|---|---|---|
| Cylinder | 31 | 0.78 | 9.1 | 9.94e+4 | 1.37× | yes |
| Dhara composite | 11 | 0.28 | 26.0 | 9.82e+4 | 1.35× | yes |
| Pyramid | 22 | 0.62 | 14.4 | 8.87e+4 | 1.22× | yes |
| Cube | 28 | 0.85 | 12.2 | 8.24e+4 | 1.14× | yes |
| Sphere | 29 | 1.00 | 13.4 | 7.25e+4 | 1.00× | yes |
The physics, plainly
Single emitter in a cavity mode has coupling g₀ ∝ √(ω / V_mode). N coherent emitters give collective coupling g_N = √N · g₀ and cavity intensity I ∝ N² · Q / V_mode. The ignition threshold is N_ignite ∝ V_mode / Q² — geometries that concentrate the mode volume (small V_mode) and hold their ring (high Q) ignite first.
Tavis & Cummings (1968) wrote down this Hamiltonian for N two-level systems in a cavity. The same equation applies to N priests chanting in a temple at the cavity's natural frequency, to N solar-driven emitters around a shared resonator, to N microscopic spin defects in a coupled solid. The vocabulary differs; the math is one math.