Ising versus infinite randomness criticality in arrays of Rydberg atoms trapped with non-perfect tweezers

Chains of Rydberg atoms have emerged as an amazing platform for simulating quantum physics in low dimensions. This remarkable success is due to the versatility of lattice geometries achieved by trapping neutral atoms with optical tweezers. On a given lattice, the competition between the repulsive van der Waals potential and the detuning of the laser frequency brings the atoms to highly excited Rydberg states, leading to a variety of exotic phases and quantum phase transitions. Experiments on the simplest one-dimensional array of Rydberg atoms have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. In addition to standard conformal transitions, numerical simulations have predicted two exotic chiral transitions and a floating phase, raising the question of their experimental realization. However, in reality, optical tweezers have a finite width, which results in small deviations in interatomic distances and disorder in interaction strength. However, disorder can affect the nature of transitions. Infinite randomness criticality in the random transverse-field Ising chain is perhaps the most prominent examples. In this paper, we demonstrate how the disorder typical for Rydberg experiments alters the Ising transition to the period-2 phase. Following the experimental protocol closely, we probe the nature of quantum criticality with Kibble-Zurek dynamics. While we clearly observe infinite randomness for strong disorder and large system sizes, we also report a crossover into a clean Ising transition, which is visible for small system sizes and weak disorder. Our results clearly demonstrate an additional technical constraint on the scalability of Rydberg-based quantum simulators.