Spin models are the prime example of simplified manybody Hamiltonians used to model complex, real-world strongly correlated materials 1 . However, despite their simplified character, their dynamics often cannot be simulated exactly on classical computers as soon as the number of particles exceeds a few tens. For this reason, the quantum simulation 2 of spin Hamiltonians using the tools of atomic and molecular physics has become very active over the last years, using ultracold atoms 3 or molecules 4 in optical lattices, or trapped ions 5 . All of these approaches have their own assets, but also limitations. Here, we report on a novel platform for the study of spin systems, using individual atoms trapped in two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100% with exact knowledge of the initial configuration. When excited to Rydberg D-states, the atoms undergo strong interactions whose anisotropic character opens exciting prospects for simulating exotic matter 6 . We illustrate the versatility of our system by studying the dynamics of an Ising-like spin-1/2 system in a transverse field with up to thirty spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects we find an excellent agreement with ab-initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D-states has a measurable influence 7,8 . Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.Rydberg atoms have recently attracted a lot of interest for quantum information processing 9 and quantum simulation 10 . In this work, we use a system of individual Rydberg atoms to realize highly-tunable artificial quantum Ising magnets. By shining on the atoms lasers that are resonant with the transition between the ground state |g and a chosen Rydberg state |r , we implement the Ising-like Hamiltonianwhich acts on the pseudo-spin states |↓ i and |↑ i corresponding to states |g and |r of atom i, respectively. Here, Ω is the Rabi frequency of the laser coupling, the σ i α (α = x, y, z) are the Pauli matrices acting on atom i, and n i = (1 + σ i z )/2 is the number of Rydberg excitations (0 or 1) on site i. FIG. 1|: Experimental platform. a: An array of microtraps is created by imprinting an appropriate phase on a dipole-trap beam. Siteresolved fluorescence of the atoms, at 780 nm, is imaged on a camera using a dichroic mirror (DM). Rydberg excitation beams at 795 and 475 nm are shone onto the atoms. The inset shows the measured light intensity for an array of Nt = 19 traps. b: Sketch of an experimental sequence. During loading, the camera images are analyzed continuously to extract the number of loaded traps. As soon as a triggering criterion is met, the loading is stopped and an image of the initial configuration is acquired. After Rydberg excitation, a final image is ...

Large arrays of individually controlled atoms trapped in optical tweezers are a very promising platform for quantum engineering applications. However, to date, only disordered arrays have been demonstrated, due to the non-deterministic loading of the traps. Here, we demonstrate the preparation of fully loaded, two-dimensional arrays of up to ∼ 50 microtraps each containing a single atom, and arranged in arbitrary geometries. Starting from initially larger, half-filled matrices of randomly loaded traps, we obtain user-defined target arrays at unit filling. This is achieved with a real-time control system and a moving optical tweezers that performs a sequence of rapid atom moves depending on the initial distribution of the atoms in the arrays. These results open exciting prospects for quantum engineering with neutral atoms in tunable geometries.The last decade has seen tremendous progress over the control of individual quantum objects [1, 2]. Many experimental platforms, from trapped ions [3] to superconducting qubits [4], are actively explored. The current challenge is now to extend these results towards large assemblies of such objects, while keeping the same degree of control, in view of applications in quantum information processing [5], quantum metrology [6], or quantum simulation [7]. Neutral atoms offer some advantages over other systems for these tasks. Besides being well isolated from the environment and having tunable interactions, systems of cold atoms hold the promise of being scalable to hundreds of individually controlled qubits. Control of the atomic positions at the single-particle level can been achieved with optical potentials. In a 'top-down' approach using optical lattices and quantum gas microscopes, hundreds of traps can now be created and addressed individually [8]. By making use of the superfluid to Mott-insulator transition, single atom filling fractions exceeding 90% are achieved [9], albeit at the expense of relatively long experimental duty cycles and constraints in the lattice geometries.Single atoms can also be trapped in 2d arrays of microscopic optical tweezers with single-site resolution using holographic methods [10][11][12]. This bottom-up approach offers faster preparation and a higher degree of tunability of the underlying geometry. However, achieving unit filling of the arrays is hampered by the stochastic nature of the loading and has remained so far elusive. Although proof-of-principle demonstrations of quantum gates [13] and quantum simulations [14] using this latter platform have been reported [15], this non-deterministic loading poses a serious limitation for applications where large-scale ordered arrays are required. To solve this problem, several approaches have been considered, exploiting the Rydberg blockade mechanism [16], or using tailored light-assisted collisions [17]. To date, despite those efforts, loading efficiencies of around 90% at best for a single atom in a single tweezers could be achieved [18,19], making the probabilities to fully load large arrays still...

A great challenge in current quantum science and technology research is to realize artificial systems of a large number of individually controlled quantum bits for applications in quantum computing and quantum simulation. Many experimental platforms are being explored, including solid-state systems, such as superconducting circuits or quantum dots, and atomic, molecular and optical systems, such as photons, trapped ions or neutral atoms. The latter offer inherently identical qubits that are well decoupled from the environment and could provide synthetic structures scalable to hundreds of qubits or more. Quantum-gas microscopes allow the realization of two-dimensional regular lattices of hundreds of atoms, and large, fully loaded arrays of about 50 microtraps (or 'optical tweezers') with individual control are already available in one and two dimensions. Ultimately, however, accessing the third dimension while keeping single-atom control will be required, both for scaling to large numbers and for extending the range of models amenable to quantum simulation. Here we report the assembly of defect-free, arbitrarily shaped three-dimensional arrays, containing up to 72 single atoms. We use holographic methods and fast, programmable moving tweezers to arrange-atom by atom and plane by plane-initially disordered arrays into target structures of almost any geometry. These results present the prospect of quantum simulation with tens of qubits arbitrarily arranged in space and show that realizing systems of hundreds of individually controlled qubits is within reach using current technology.

The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.

We explore the dynamics of artificial one-and two-dimensional Ising-like quantum antiferromagnets with different lattice geometries by using a Rydberg quantum simulator of up to 36 spins in which we dynamically tune the parameters of the Hamiltonian. We observe a region in parameter space with antiferromagnetic (AF) ordering, albeit with only finite-range correlations. We study systematically the influence of the ramp speeds on the correlations and their growth in time. We observe a delay in their build-up associated to the finite speed of propagation of correlations in a system with short-range interactions. We obtain a good agreement between experimental data and numerical simulations taking into account experimental imperfections measured at the single particle level. Finally, we develop an analytical model, based on a short-time expansion of the evolution operator, which captures the observed spatial structure of the correlations, and their build-up in time.

We study experimentally various physical limitations and technical imperfections that lead to damping and finite contrast of optically-driven Rabi oscillations between ground and Rydberg states of a single atom. Finite contrast is due to preparation and detection errors and we show how to model and measure them accurately. Part of these errors originates from the finite lifetime of Rydberg states and we observe its n 3 -scaling with the principal quantum number n. To explain the damping of Rabi oscillations, we use simple numerical models, taking into account independently measured experimental imperfections, and show that the observed damping actually results from the accumulation of several small effects, each at the level of a few percents. We discuss prospects for improving the coherence of ground-Rydberg Rabi oscillations in view of applications in quantum simulation and quantum information processing with arrays of single Rydberg atoms.

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 manybody wave functions in Hilbert space. DOI: 10.1103/PhysRevLett.118.063606 Introduction.-Rydberg gases provide a versatile platform for studies of quantum few-body and many-body phenomena with applications ranging from quantum information processing [1] to simulations of complex condensed matter systems. The experimental degree of control has reached a stage which enables efficient entanglement creation [2] and implementation of quantum Ising models [3,4]. This opens pathways towards probing magnetic structures [5][6][7][8] as well as the exploration of open many-body quantum systems [9][10][11][12][13][14][15].Of particular interest is the so-called facilitation mechanism (or antiblockade), where the excitation of an atom to a Rydberg state is strongly enhanced in the vicinity of an already excited atom [16,17]. This effect is of broad relevance and exploited in the design of quantum gates [18,19], as well as in protocols for dissipative quantum state preparation [6]. In the many-body context it effectuates an aggregation mechanism, where an initial Rydberg excitation seed triggers a dynamical growth of excitation clusters [18,[20][21][22][23] and it enables the implementation of kinetic constraints [12,24,25] thereby connecting to the physics of glass-forming substances [26][27][28].Here we perform a theoretical and experimental study of the facilitated dynamics of Rydberg excitations in a onedimensional array of optical tweezers. In a first experiment conducted with only two of them, we establish that the uncertainty of the atomic positions introduces disorder

We experimentally realize a Peierls phase in the hopping amplitude of excitations carried by Rydberg atoms, and observe the resulting characteristic chiral motion in a minimal setup of three sites. Our demonstration relies on the intrinsic spin-orbit coupling of the dipolar exchange interaction combined with time-reversal symmetry breaking by a homogeneous external magnetic field. Remarkably, the phase of the hopping amplitude between two sites strongly depends on the occupancy of the third site, thus leading to a correlated hopping associated with a density-dependent Peierls phase. We experimentally observe this density-dependent hopping and show that the excitations behave as anyonic particles with a nontrivial phase under exchange. Finally, we confirm the dependence of the Peierls phase on the geometrical arrangement of the Rydberg atoms.