  It is a straightforward result of electromagnetism that dipole oscillators
radiate more strongly when they are synchronized, and that if there are $N$
dipoles, the overall emitted intensity scales with $N^2$. In atomic physics,
such an enhanced radiative property appears when coherence among two-level
identical atoms is established, and is well-known as "superradiance"
\cite{Dicke:1954aa}. In superfluorescence (SF), atomic coherence develops via a
self-organisation process stemming from the common radiated field, starting
from a incoherently prepared population inversion \cite{Bonifacio:1975aa}.
First demonstrated in a gas \cite{Skribanowitz:1973} and later in condensed
matter systems \cite{Florian:1984}, its potential is currently being
investigated in the fields of ultranarrow linewidth 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,Angerer:2018aa}.
  A barely developed aspect in superradiance is related to the properties of
the dipole array that generates 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 represents 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 a
decay rate that is enhanced by more than 1-million times compared to that of
independently emitting atoms. We thoroughly resolve the dynamics by directly
measuring the intensity of the emitted radiation as a function of time.
