Rydberg Atom Chains, Disorder and the Scaling of Quantum Simulation.

The precise control of individual atoms represents a significant advance in the pursuit of quantum simulation, offering a pathway to model complex physical systems. Researchers are now investigating how imperfections in the trapping of these atoms influence the emergence of collective quantum behaviour. Jose Soto-Garcia and Natalia Chepiga, both from the Kavli Institute of Nanoscience at Delft University of Technology, address this challenge in their paper, “Ising versus infinite randomness criticality in arrays of Rydberg atoms trapped with non-perfect tweezers”. Their work examines the impact of positional disorder, inherent in the use of optical tweezers to arrange atoms, on phase transitions within chains of highly excited Rydberg atoms, a system increasingly employed to emulate low-dimensional physics. The study utilises Kibble-Zurek dynamics, a method for observing the formation of topological defects during a rapid phase transition, to characterise the nature of these transitions and establish limits on the scalability of Rydberg-based quantum simulators.

Rydberg atom arrays represent a flexible platform for simulating low-dimensional physics, utilising the precise control afforded by optical tweezer technology. These systems exploit a competition between repulsive van der Waals interactions and laser detuning, inducing highly excited Rydberg states. A Rydberg state occurs when an electron is excited to a very high energy level, causing the atom to become large and strongly interacting. This allows for the observation of diverse phases and phase transitions, including crystalline arrangements and more exotic states. Recent experiments on one-dimensional Rydberg atom chains advance understanding of crystalline phase transitions, alongside predictions of chiral transitions and a ‘floating phase’, a state of matter characterised by a lack of long-range order.

Practical limitations inherent in optical tweezer implementation, specifically finite tweezer width, introduce deviations in interatomic distances and disorder in interaction strengths. Optical tweezers use highly focused laser beams to trap and manipulate individual atoms. The finite size of these beams means atoms cannot be positioned with perfect precision. This disorder significantly impacts the nature of phase transitions, with the random transverse-field Ising chain serving as an example of infinite randomness criticality. Infinite randomness criticality describes a scenario where disorder is so strong that it fundamentally alters the nature of the phase transition, leading to behaviours not seen in clean systems. Researchers demonstrate how disorder alters the transition to the period-2 phase, employing Kibble-Zurek dynamics to characterise the transition. Kibble-Zurek dynamics describes how systems evolve during a rapid change in parameters, predicting the formation of defects and topological structures.

Findings demonstrate the emergence of infinite randomness criticality for strong disorder and large system sizes, indicating the system lacks a well-defined order parameter. An order parameter is a quantity that characterises the degree of order in a system; its absence signifies a lack of long-range order. Conversely, smaller system sizes and weaker disorder exhibit a crossover to a conventional Ising transition, characterised by long-range order, highlighting a crucial technical constraint on the scalability of Rydberg-based quantum simulators.

Scientists utilise optical tweezers to trap and manipulate atoms, arranging them in specific geometries and tuning their interactions with laser light. This allows them to create artificial quantum systems that mimic the behaviour of materials and phenomena found in nature, enabling the study of complex quantum effects including magnetism, superconductivity, and topological phases of matter.

The inherent disorder in current Rydberg atom array experiments stems from the finite size of the optical tweezers, which limits the precision of atomic spacing and interaction strength. Scientists are actively exploring techniques to minimise disorder, such as using more advanced optical tweezers and developing new methods for atom placement.

Researchers utilise high-performance computing resources, including the DelftBlue HPC cluster and the Dutch national e-infrastructure SURF, to perform the complex numerical simulations required to model these quantum systems. These simulations allow them to explore a wide range of parameters and system sizes, providing insights that would be difficult or impossible to obtain through experiments alone.

The study demonstrates that the Ising transition in Rydberg atom arrays is highly sensitive to disorder, with even small amounts significantly altering the critical behaviour. The research successfully bridges the gap between theoretical predictions and experimental observations, providing a comprehensive understanding of the effects of disorder on the Ising transition. The findings not only advance knowledge of critical phenomena in disordered systems but also provide valuable guidance for the development of more robust and scalable quantum simulators.

Researchers meticulously characterise the level of disorder in their experiments, employing advanced imaging techniques and statistical analysis. This allows them to quantify the variations in atomic spacing and interaction strength, providing a baseline for theoretical modelling and simulation.

The research team plans to extend their studies to explore the effects of different types of disorder and investigate the potential for mitigating its effects. They are also interested in exploring the use of Rydberg atom arrays for studying other complex quantum phenomena, such as many-body localisation and topological phases of matter.

The findings have important implications for the development of quantum technologies, particularly those based on Rydberg atom arrays. Understanding the effects of disorder is crucial for building reliable and scalable quantum simulators, enabling the study of complex quantum phenomena and the development of new quantum algorithms.