2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97607Using the methods of quantum trajectories we study numerically the phenomenon of quantum synchronization in a quantum dissipative system with periodic driving. Our results show that at small values of Planck constant $\hbar$ the classical devil's staircase remains robust with respect to quantum fluctuations while at large $\hbar$ values synchronization plateaus are destroyed. Quantum synchronization in our model has close similarities with Shapiro steps in Josephson junctions and it can be also realized in experiments with cold atoms.5 pages, 5 figs, 1 fig added, research at http://www.quantware.ups-tlse.frOther Condensed MatterDisordered Systems and Neural Networkstext