COLLECTIVE LIGHT / THE BRIGHT SIDE

Dicke Superradiant Burst

Release an excited ensemble into a common decay channel. Watch the delayed burst grow, compare independent atoms, and record individual photon timestamps from repeated preparations.

Ideal symmetric Dicke decay, with a separate independent-emitter control. A partially excited initial state is a symmetric Dicke state, not randomly selected excited atoms. The angular surface is a dipole radiation diagnostic, not a propagating wavefront or an apparatus. No coherent dipole shifts, pumping, dephasing or specific hardware.

ANGULAR EMISSIONMODEL

EMISSION RATE

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Unconditional ensemble mean

Radius: cube-root intensity · fixed gain within each model

Dots: equal mean excitation, not individual trajectories. Surface: dipole angular intensity; no propagation or physical detector surface.

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REPEAT THE PREPARATION. RECORD THE LIGHT.

How quiet is quiet?

Each trial starts fresh and records the full time window. Ideal full-solid-angle photon counting, followed by the selected efficiency. No-click trials stay in the denominator.

Analyze clicks before this time

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Recorded clicks per trial

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Trials with a click

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Model click probability

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Model excitation at the gate

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01 / PHOTON TIMES

The burst has a shape.

Cyan: efficiency-scaled model rate. Gold: timestamp histogram per trial. Drag the gold gate; arrows move it. Dashed: independent-emitter reference.

$\Gamma_0t$ · $\text{clicks}/(\text{trial}\cdot\Gamma_0t)$

02 / SURVIVAL

Where the excitation went.

Cyan: remaining excitation fraction. Coral: independent-emitter reference. Pale vertical: selected scene time. Gold: analysis gate.

$\Gamma_0t$ · $\langle m\rangle/m_0$

03 / DIRECTIONAL DIAGNOSTIC

Where light can escape.

Equatorial cut of the 3D surface, in the plane perpendicular to the dipoles. Radius is linear here. This is a model diagnostic; the timestamp counter collects all directions.

$\frac{1}{\Gamma_0}\frac{dR}{d\Omega}$

04 / RAW TRIALS

Every row begins again.

Last 40 trials. Each mark is a detected photon; empty rows are retained. The full ledger and all timestamps are exported.

$\Gamma_0t$

Last 20 raw trials

Trial	Clicks	Timestamps · $\Gamma_0t$

Model, units & sources

Time uses the isolated-emitter population lifetime. The counter has full solid-angle coverage and independent detection loss. No background, dead time, timing jitter or technical preparation error. Intervals describe sampling uncertainty only.

\tau=\Gamma_0t,\qquad \lambda_0=2\pi/k_0

The ideal symmetric collective channel is a model limit, not a literal dense cloud with its near-field interactions neglected without consequence. Independent emission is a distinct comparison. Partial initial excitation is rounded to an integer symmetric Dicke state. Uniformization propagates its population probabilities.

r_m/\Gamma_0=m(N-m+1),\qquad R=\sum_mr_mP_m

The default 3D radius uses a cube-root gain and is an angular diagnostic, not a distance. Enlarge shape explicitly normalizes each frame to reveal weak lobes; compare the numerical rate for actual strength. Its fixed intensity reference is the maximum Dicke ladder rate at 32 atoms, or 12 times the single-dipole maximum for the array. The equatorial 2D plot is linearly scaled with its maximum printed. Atom dots are a separate schematic state diagram, not a detector surface.

Actual preparation and numerical diagnostic:

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The diagnostic is the population-normalization error. Photon waiting times are exponential draws, not samples read from the plotted mean curve.

Holzinger et al. — Dicke decay, Eqs. 1–6 & quantum trajectories
Piovella — vector Green tensor, Eqs. 24–27 & 38
Lehmberg — radiation from an N-atom system

Start with the essentials

Focus question: Together, the light arrives in a rush.
One-sentence intuition: The collective ladder accelerates emission near half excitation. A fully inverted ensemble starts at the independent rate and develops a burst later.

Core mathematical model

Collective ladder

r_m=\Gamma_0m(N-m+1)

Each detected or undetected emitted photon lowers the excitation by one.

Population flow

\dot P_m=r_{m+1}P_{m+1}-r_mP_m

The curve averages all ideal emission histories. Photon records are independent realizations of this process.

Common difficulties

A quiet counter is not proof of storage

Typical misconceptionNo click means the excitation is definitely still present.

Better mental modelThe detector may miss an emitted photon. The model survival and observed no-click fraction are separate quantities; only sampling uncertainty is shown.

Run the experiment

01
Compare the cause
Switch between Release together and Emit independently at the same emitter count.
What to observe: The collective pulse rises before it falls. Independent emission falls from the start.
02
Break the effect
Lower the initial Dicke excitation. The fully inverted delayed-burst story no longer applies to every preparation.
What to observe: The result follows the selected state and geometry, not a fixed animation.
03
Count photons
Collect 200 full decay trials. Drag the time gate, pin the data, change the preparation and restore. Export timestamps, including no-click trials.
What to observe: Detection inefficiency can also produce silence. Compare the measured click probability with the efficiency-aware model.