  We report the analysis of paired photon pulses arising from two cascading
transitions in continuously pumped Erbium-doped YLiF$_4$ 1% and 0.01% crystals
at 1.6 K. The dependence of the pulse peak intensity on the squared number of
involved Erbium ions, between 10$^{11}$ and 10$^{13}$, definitely identifies
the cooperative nature of the two pulsed emissions, that are generated by the
subsequent, spontaneous formation of coherent states. The observed fluctuations
of the time interval between the paired pulses and, most importantly, its
correlation with the second pulse duration, demonstrate that the Erbium ions
coherence is indeed seeded by vacuum fluctuations.
