The Quantum Choir: Why an Extra Soloist Doesn't Boost Volume express
A choir where every singer hits the notes precisely sounds louder than you'd expect from a simple sum of voices. A hundred singers aren't just a hundred times louder than one: they're ten thousand times louder. In the world of atoms, something similar happens. In collective behavior discovered by Robert H. Dicke, synchronously emitted photons amplify each other. The brightness grows with the square of the number of atoms.
But a choir is easily ruined. Slight stochastic modeling in rhythm or off-key notes blur the overall harmony. To understand exactly how noise destroys collective emission, physicists included two effects in their model: local loss of synchronization (decoherence) and spontaneous emission by individual atoms. It turned out that depending on their strength, the system can be in three regimes: fully collective, partially collective, and independent loners.
What proved far more interesting was the boundary between these regimes. The transition from full collectivity to partial resembles the moment a choir loses its conductor: a second ago the singers held the line, and now each is singing on their own. If noise is strong, adding more atoms does not boost the light — the system works as a sum of loners. entropy imposes hard limits. Even increasing the number of atoms won't bring back the collective power.
Original abstract
as written by the authors arXiv:2607.28034v1
The survival of many-body coherence depends on the competition between correlation buildup and decoherence. In Dicke superradiance, collective emission builds up correlations, producing a peak intensity scaling as $$N^2$$ for $$N$$ emitters. We develop a scaling theory including local dephasing and spontaneous emission and obtain fully collective, partially collective, and independent-emitter scaling regimes. The boundary of the fully collective regime defines a continuous phase transition in a transient observable. Local decoherence can prevent $$N^2$$ scaling despite increasing $$N$$.
Collective emission was first observed in the 1970s in sodium vapors. It required temperatures just millionths of a degree above absolute zero — otherwise thermal noise destroyed the synchrony.