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Summary form only given. Second harmonic generation in the simple travelling plane wave configuration is often taken in textbooks as the simplest example of a nonlinear interaction. When one starts only from a nonzero field at the fundamental frequency, classical nonlinear optics predicts a monotonous energy transfer from the fundamental to the second harmonic mode, and a perfect doubling efficiency when the interaction length tends to infinity. The usual linearized approach of quantum optics predicts in the same configuration and for an infinite interaction length a perfect intensity squeezing for the fundamental wave and a 50% intensity squeezing on the second harmonic wave. We show that this is no longer true when one uses more accurate approaches of the full quantum problem. If one takes into account the commutation relations at the lowest order in the propagation equations, one finds a periodic solution for the mean fields: the fundamental wave thus undergoes a spectacular full revival for very long interaction lengths, that is triggered by the quantum fluctuations responsible of spontaneous down-conversion.