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arXiv:2201.03189 · Nature Communications

Entanglement in the quantum phases of an unfrustrated Rydberg atom array

Matthew J. O’Rourke, Garnet Kin‐Lic Chan

Published Sep 5, 2023• 14 citations
arXivHTMLPDF

Abstract

Recent experimental advances have stimulated interest in the use of large, two-dimensional arrays of Rydberg atoms as a platform for quantum information processing and to study exotic many-body quantum states. However, the native long-range interactions between the atoms complicate experimental analysis and precise theoretical understanding of these systems. Here we use new tensor network algorithms capable of including all long-range interactions to study the ground state phase diagram of Rydberg atoms in a geometrically unfrustrated square lattice array. We find a greatly altered phase diagram from earlier numerical and experimental studies, revealed by studying the phases on the bulk lattice and their analogs in experiment-sized finite arrays. We further describe a previously unknown region with a nematic phase stabilized by short-range entanglement and an order from disorder mechanism. Broadly our results yield a conceptual guide for future experiments, while our techniques provide a blueprint for converging numerical studies in other lattices.

DOI
10.1038/s41467-023-41166-0

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Recent experimental advances have stimulated interest in the use of large, two-dimensional arrays of Rydberg atoms as a platform for quantum information processing and to study exotic many-body quantum states. However, the native long-range interactions between the atoms complicate experimental analysis and precise theoretical understanding of these systems. Here we use new tensor network algorithms capable of including all long-range interactions to study the ground state phase diagram of Rydberg atoms in a geometrically unfrustrated square lattice array. We find a greatly altered phase diagram from earlier numerical and experimental studies, revealed by studying the phases on the bulk lattice and their analogs in experiment-sized finite arrays. We further describe a previously unknown region with a nematic phase stabilized by short-range entanglement and an order from disorder mechanism. Broadly our results yield a conceptual guide for future experiments, while our techniques provide a blueprint for converging numerical studies in other lattices.
Rydberg atom arrays have recently emerged to be a promising platform for the exploration of exotic quantum phases of matter and quantum phenomena. In this work, we map out the ground-state phase diagram of Rydberg atoms on a honeycomb lattice as a function of the Rydberg blockade radius and the laser detuning by performing large-scale finite-size density matrix renormalization group simulations. Apart from a featureless disordered phase, we find five other intricate long-range density-wave-ordered phases within a relatively wide parameter space. The properties of these quantum phases are analyzed by calculating their Rydberg excitation profiles and static structure factors. In addition, a continuous quantum phase transition belonging to the (2+1)-dimensional Ising universality class is explored by a standard finite-size scaling analysis. Our work implies some different physics, such as the possible nontrivial quantum phase transitions and a highly degenerate string ordered phase, that a honeycomb geometry could bring to the Rydberg system and serves as a numerical guide for possible real experiments.
We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.
Rydberg atom arrays have emerged as a powerful platform for experimental research and a challenging subject for theoretical investigation in quantum science. In this study, we investigate the finite-temperature properties of two-dimensional square-lattice Rydberg atom arrays using the projected entangled pair states (PEPS) method. By analyzing the thermal behavior of systems in the checkerboard and striated phases, we extract critical exponents and identify phase transition characteristics. Our results confirm that the checkerboard phase transition belongs to the 2D Ising universality class, while the striated phase exhibits critical exponents that deviate from known universality classes, possibly due to finite-size effects. These findings provide theoretical insights into the thermal stability of quantum phases in Rydberg atom arrays and offer valuable guidance for future experimental efforts.
Rydberg atom arrays (RAA) have been advocated as a promising avenue for the quantum simulation of different exotic quantum states. Numerical predictions for the ground state properties of this experimental platform can, however, be challenging in two-dimensional setups. In particular, faithfully treating long-range interactions is often crucial for distinguishing the fate of competing phases, but it usually comes at considerable cost. Projected entangled-pair states (PEPS), optimized via a sampling-based approach, have been shown to deal with such terms on the same ground as shorter-range ones. In this work, we employ these tools to investigate debated physical questions in different frustrated geometries of RAA, from the emergence of spin-glass physics on the Kagomé lattice to topological order beyond the PXP model on the Ruby lattice. By that, we contribute to establishing PEPS as well-suited tools for creating digital twins of RAA experiments.
Arrays of ultracold neutral atoms, also known as Rydberg atom arrays, are rapidly developing into a powerful and versatile platform for quantum simulation. However, theoretical predictions about the bulk quantum phases of matter present in these systems have often diverged from experimental realizations on finite-sized arrays due to the strong effects of the boundaries. Here we propose a general, experimentally straightforward strategy to mitigate the effects of the boundaries and thus enable finite-sized arrays to stabilize bulk-like quantum order. Our scheme makes use of the properties of the ubiquitous disordered phase in Rydberg systems, driving the boundaries into an unbiased set of configurations that depend on the bulk physics. We numerically demonstrate the efficacy of this protocol in one- and two-dimensional systems on both ordered and critical phases.
The neutral atoms coupled to a highly excited Rydberg state on a two-dimensional triangular lattice are investigated by employing the density matrix renormalization group technique in the matrix product state form. The full ground-state phase diagram as a function of blockade radius and the detuning of the exciting laser is determined by the behavior of entanglement entropy. We find several quantum phases including stripe-ordered and symmetry-breaking density-wave-ordered phases featured with regular excitation patterns of different excitation densities ρ = 1/3, 1/4, and 1/7. In addition, a ρ = 2/3 ordered phase and an interesting "order-by-disorder" phase, which has been prepared experimentally, are also observed in this work. Our work provides an exploration of the possible quantum phases that can occur in a triangularly arrayed Rydberg system, and thus could be a faithful theoretical guide for further experimental research.