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Laser excitation pulses that lead to perfect adiabatic state transfer in anensemble of three-level ladder atoms lead to highly entangled states of manyatoms if their highest excited state is subject to Rydberg blockade. Solutionof the Schr\"odinger equation shows that it is increasingly difficult to ensurethe adiabatic evolution as the number of atoms increases. A diminishing energygap, significant variations in collective observables, and increased workfluctuations link the critical slowing down of the adiabatic evolution with aquantum phase transition-like behavior of the system.

Critical slowing down of multi-atom entanglement by Rydberg blockade