Critical slowing down of multi-atom entanglement by Rydberg blockade

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.