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.
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