Spontaneous formation of a macroscopically extended coherent state.

It is a straightforward result of electromagnetism that $N$ dipole oscillators radiate more strongly when they are synchronized, and that the overall emitted intensity scales with $N^2$. In his seminal work \cite{Dicke:1954aa}, Dicke found that such an enhanced radiative property is emergent in a system of $N$ excited two-level systems when correlations are imposed among the radiators during decay. He named it "superradiance", and its spatial extension is the "superfluorescence" \cite{Bonifacio:1975aa}. First demonstrated in a gas \cite{Skribanowitz:1973} and later in condensed matter systems \cite{Florian:1984}, its potential is currently investigated in the fields of ultranarrow laser development for fundamental tests in physics \cite{Meiser:2009,Meiser:2010,Bohnet:2012aa,Norcia:2016, Norcia:2018}, and for the development of devices enabling entangled multi-photon quantum light sources \cite{Raino:2018aa} and of quantum technologies \cite{Angerer:2018aa}. A barely developed aspect in superradiance is related to the properties of the dipole array sourcing the pulsed radiation field. In this work we establish the experimental conditions for formation of a macroscopic dipole via superfluorescence, involving the remarkable number of $4\times10^{12}$ atoms. Even though rapidly evolving in time, it holds the numbers for becoming a flexible test-bed in quantum optics. Self-driven atom dynamics, without the mediation of cavity QED nor quantum dots or quantum well structures, is observed in a cryogenically cooled rare-earth doped material. We present clear evidence of more than 1-million times enhanced decay rate compared to that of independently emitting atoms, and thoroughly resolve the dynamics by directly measuring the intensity of the emitted radiation as a function of time.