  Laser excitation pulses that lead to perfect adiabatic state transfer in an
ensemble of three-level ladder atoms lead to highly entangled states of many
atoms if their highest excited state is subject to Rydberg blockade. Solution
of the Schr\"odinger equation shows that it is increasingly difficult to ensure
the adiabatic evolution as the number of atoms increases. A diminishing energy
gap, significant variations in collective observables, and increased work
fluctuations link the critical slowing down of the adiabatic evolution with a
quantum phase transition-like behavior of the system.
