Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under antiblockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.

Physical Review LettersJan 6, 202225 citations

Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

Matteo Marcuzzi, Jiří Minář, Daniel Barredo +6 more

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the many-body wave functions in Hilbert space.

arXiv:1607.06295Physical Review LettersFeb 10, 2017112 citations

Synthetic lattices, flat bands and localization in Rydberg quantum simulators

Maike Ostmann, Matteo Marcuzzi, Jiří Minář +1 more

The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism yields a Hilbert space structure in which the many-body states organize into synthetic lattices which feature in general one or several flat bands and may support immobile localized states. We focus our discussion on the case of a ladder geometry for which we analyze the influence of disorder generated by the uncertainty of the atomic positions. The localization properties of this system are characterized through two length scales (localization lengths) which are found to display anomalous scaling behavior at certain energies. Moreover, we discuss the experimental preparation of an immobile localized state, and analyze disorder-induced propagation effects.The most recent manifestation of cold Rydberg atom quantum simulators that employs tailored optical tweezer arrays enables the study of many-body dynamics under so-called facilitation conditions. We show how the facilitation mechanism yields a Hilbert space structure in which the many-body states organize into synthetic lattices which feature in general one or several flat bands and may support immobile localized states. We focus our discussion on the case of a ladder geometry for which we analyze the influence of disorder generated by the uncertainty of the atomic positions. The localization properties of this system are characterized through two length scales (localization lengths) which are found to display anomalous scaling behavior at certain energies. Moreover, we discuss the experimental preparation of an immobile localized state, and analyze disorder-induced propagation effects.

arXiv:1802.00379Quantum Science and TechnologyJan 9, 201916 citations

Random displacements in critical Rydberg atom arrays

Xingyu Li, Shuyan Zhou, Xue Chen +2 more

Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet, experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the expected behavior. Here, we study how such positional disorder influences the Ising criticality. Since disorder breaks the ${\mathbb{Z}}_{2}$ symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a pseudocriticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained ${\mathbb{Z}}_{2}$ -breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet, experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the expected behavior. Here, we study how such positional disorder influences the Ising criticality. Since disorder breaks the ${\mathbb{Z}}_{2}$ symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a pseudocriticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained ${\mathbb{Z}}_{2}$-breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.

arXiv:2508.05381Physical review. B./Physical review. BNov 21, 20253 citations

Lattice defects in Rydberg atom arrays

Hanteng Wang, Chengshu Li, Xingyu Li +2 more

Rydberg atom arrays have become a key platform for studying quantum many-body systems. In these setups, defects arise naturally due to various imperfections and can significantly modify the theoretical predictions compared to an ideal model. Here, we investigate the impact of geometric defects in the simplest situation---a one-dimensional Rydberg atom array, both at and away from its emergent Ising criticality. In the presence of defects, we demonstrate that relevant physical quantities can be extracted from one-point correlation functions. At the critical point, we show that different types of kinks yield distinct outcomes corresponding to their respective spatial-internal symmetries: site-centered kinks can effectively break the array at the kink position regardless of the kink angle, while bond-centered kinks lead to interesting intermediate-coupling fixed points. In the latter case, due to a special renormalization group flow trajectory, the whole system can appear ordered if the system is not large enough. Additionally, away from criticality, the bond-centered kink induces a localization-delocalization transition of the domain wall, characteristic of quantum wetting. These findings highlight the utility of kinks as experimental probes and stress the importance of controlling defects so that experimental observations remain faithful to the pristine model.Rydberg atom arrays have become a key platform for studying quantum many-body systems. In these setups, defects arise naturally due to various imperfections and can significantly modify the theoretical predictions compared to an ideal model. Here, we investigate the impact of geometric defects in the simplest situation---a one-dimensional Rydberg atom array, both at and away from its emergent Ising criticality. In the presence of defects, we demonstrate that relevant physical quantities can be extracted from one-point correlation functions. At the critical point, we show that different types of kinks yield distinct outcomes corresponding to their respective spatial-internal symmetries: site-centered kinks can effectively break the array at the kink position regardless of the kink angle, while bond-centered kinks lead to interesting intermediate-coupling fixed points. In the latter case, due to a special renormalization group flow trajectory, the whole system can appear ordered if the system is not large enough. Additionally, away from criticality, the bond-centered kink induces a localization-delocalization transition of the domain wall, characteristic of quantum wetting. These findings highlight the utility of kinks as experimental probes and stress the importance of controlling defects so that experimental observations remain faithful to the pristine model.

arXiv:2502.07886Physical review. B./Physical review. BOct 9, 20256 citations

Flat-Band (De)localization Emulated with a Superconducting Qubit Array

Ilan T. Rosen, Sarah E. Muschinske, Cora N. Barrett +10 more

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

arXiv:2410.07878Physical Review XJun 16, 202513 citations

{\mathbb{Z}}_{2}

symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a pseudocriticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained

{\mathbb{Z}}_{2}

-breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.