Dicke Superradiance Ladder: Exact Quantum Master Equation

This simulator is the exact-quantum counterpart to the 3D Dicke superradiance simulator, which visualizes atoms in space animated by the mean-field Bloch-vector approximation. Here the same collective-decay physics is solved a genuinely different way: the full permutation-symmetric N-atom state is represented as a probability distribution over the Dicke ladder — the birth-death chain of "how many atoms have already emitted" — and its exact master equation is integrated numerically every frame with fourth-order Runge–Kutta, with no closed-form shortcut and no classical-vector reduction. The top graph plots the resulting exact radiated intensity against the same mean-field prediction used by the 3D sim, so the two can be compared directly; the bottom panel animates the population cascading down the ladder itself, visually explaining exactly where and why the burst forms. A mode toggle swaps the cooperative Dicke rate for the independent-atom rate, collapsing the burst into ordinary exponential fluorescence as a control case.