Enhancing a Many-Body Dipolar Rydberg Tweezer Array with Arbitrary Local Controls.

We implement and characterize a protocol that enables arbitrary local controls in a dipolar atom array, where the degree of freedom is encoded in a pair of Rydberg states. Our approach relies on a combination of local addressing beams and global microwave fields. Using this method, we directly prepare two different types of three-atom entangled states, including a W state and a state exhibiting finite chirality. We verify the nature of the underlying entanglement by performing quantum state tomography. Finally, leveraging our ability to measure multibasis, multibody observables, we explore the adiabatic preparation of low-energy states in a frustrated geometry consisting of a pair of triangular plaquettes. By using local addressing to tune the symmetry of the initial state, we demonstrate the ability to prepare correlated states distinguished only by correlations of their chirality (a fundamentally six-body observable). Our protocol is generic, allowing for rotations on arbitrary sub-groups of atoms within the array at arbitrary times during the experiment; this extends the scope of capabilities for quantum simulations of the dipolar XY model.

Non-Gaussian Correlations in the Steady State of Driven-Dissipative Clouds of Two-Level Atoms.

We report experimental measurements of the second-order coherence function g^{(2)}(τ) of the light emitted by a laser-driven dense ensemble of ^{87}Rb atoms. We observe a clear departure from the Siegert relation valid for Gaussian chaotic light. Measuring intensity and first-order coherence, we conclude that the violation is not due to the emergence of a coherent field. This indicates that the light obeys non-Gaussian statistics, stemming from non-Gaussian correlations in the atomic medium. More specifically, the steady state of this driven-dissipative many-body system sustains high-order correlations in the absence of first-order coherence. These findings call for new theoretical and experimental explorations to uncover their origin, and they open new perspectives for the realization of non-Gaussian states of light.

Trapping and Imaging Single Dysprosium Atoms in Optical Tweezer Arrays.

We report the preparation and observation of single atoms of dysprosium in arrays of optical tweezers with a wavelength of 532 nm, imaged on the intercombination line at 626 nm. We use the anisotropic light shift specific to lanthanides and in particular a large difference in tensor and vector polarizabilities between the ground and excited states to tune the differential light shift and produce tweezers in near-magic or magic polarization. This allows us to find a regime where single atoms can be trapped and imaged. Using the tweezer array toolbox to manipulate lanthanides will open new research directions for quantum physics studies by taking advantage of their rich spectrum, large spin, and magnetic dipole moment.

Scalable spin squeezing in a dipolar Rydberg atom array.

The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems to enhance the precision of measurements beyond the standard quantum limit1,2. To do so, one can reshape the quantum projection noise-a strategy known as squeezing3,4. In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model4) between the constituents to generate the structured entanglement characteristic of spin squeezing5. Here we explore the prediction, motivated by recent theoretical work6-10, that short-range interactions-and in particular, the two-dimensional dipolar XY model-can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to N = 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 ± 0.3 dB (before correcting for detection errors, or roughly -5 ± 0.3 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by roughly 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.

Continuous symmetry breaking in a two-dimensional Rydberg array.

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions1-3. The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase4,5. Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry6-9.

From superradiance to subradiance: exploring the many-body Dicke ladder.

We report a time-resolved study of collective emission in dense ensembles of two-level atoms. We compare, on the same sample, the buildup of superradiance and subradiance from the ensemble when driven by a strong laser. This allows us to measure the dynamics of the population of superradiant and subradiant states as a function of time. In particular, we demonstrate the buildup in time of subradiant states through superradiant dynamics. This illustrates the dynamics of the many-body density matrix of superradiant ensembles of two-level atoms when departing from the ideal conditions of Dicke superradiance, in which symmetry forbids the population of subradiant states.

Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms.

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail1. Many platforms are being developed towards this goal, in particular based on trapped ions2-4, superconducting circuits5-7, neutral atoms8-11 or molecules12,13. All of these platforms face two key challenges: scaling up the ensemble size while retaining high-quality control over the parameters, and validating the outputs for these large systems. Here we use programmable arrays of individual atoms trapped in optical tweezers, with interactions controlled by laser excitation to Rydberg states11, to implement an iconic many-body problem-the antiferromagnetic two-dimensional transverse-field Ising model. We push this platform to a regime with up to 196 atoms manipulated with high fidelity and probe the antiferromagnetic order by dynamically tuning the parameters of the Hamiltonian. We illustrate the versatility of our platform by exploring various system sizes on two qualitatively different geometries-square and triangular arrays. We obtain good agreement with numerical calculations up to a computationally feasible size (approximately 100 particles). This work demonstrates that our platform can be readily used to address open questions in many-body physics.

Collective Shift in Resonant Light Scattering by a One-Dimensional Atomic Chain.

We experimentally study resonant light scattering by a one-dimensional randomly filled chain of cold two-level atoms. By a local measurement of the light scattered along the chain, we observe constructive interferences in light-induced dipole-dipole interactions between the atoms. They lead to a shift of the collective resonance despite the average interatomic distance being larger than the wavelength of the light. This result demonstrates that strong collective effects can be enhanced by structuring the geometrical arrangement of the ensemble. We also explore the high intensity regime where atoms cannot be described classically. We compare our measurement to a mean-field, nonlinear coupled-dipole model accounting for the saturation of the response of a single atom.

Many-Body Signatures of Collective Decay in Atomic Chains.

Fully inverted atoms placed at exactly the same location synchronize as they deexcite, and light is emitted in a burst (known as "Dicke's superradiance"). We investigate the role of finite interatomic separation on correlated decay in mesoscopic chains and provide an understanding in terms of collective jump operators. We show that the superradiant burst survives at small distances, despite Hamiltonian dipole-dipole interactions. However, for larger separations, competition between different jump operators leads to dephasing, suppressing superradiance. Collective effects are still significant for arrays with lattice constants of the order of a wavelength, and lead to a photon emission rate that decays nonexponentially in time. We calculate the two-photon correlation function and demonstrate that emission is correlated and directional, as well as sensitive to small changes in the interatomic distance. These features can be measured in current experimental setups, and are robust to realistic imperfections.

Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms.

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.

Synthetic three-dimensional atomic structures assembled atom by atom.

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 circuits1 or quantum dots2, and atomic, molecular and optical systems, such as photons, trapped ions or neutral atoms3-7. The latter offer inherently identical qubits that are well decoupled from the environment and could provide synthetic structures scalable to hundreds of qubits or more8. Quantum-gas microscopes9 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 one10 and two11 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.

Accurate Mapping of Multilevel Rydberg Atoms on Interacting Spin-1/2 Particles for the Quantum Simulation of Ising Models.

We study a system of atoms that are laser driven to nD_{3/2} Rydberg states and assess how accurately they can be mapped onto spin-1/2 particles for the quantum simulation of anisotropic Ising magnets. Using nonperturbative calculations of the pair potentials between two atoms in the presence of electric and magnetic fields, we emphasize the importance of a careful selection of experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1/2 Ising models in systems with up to 49 spins, for which numerical simulations become intractable.

Optical Control of the Resonant Dipole-Dipole Interaction between Rydberg Atoms.

We report on the local control of the transition frequency of a spin 1/2 encoded in two Rydberg levels of an individual atom by applying a state-selective light shift using an addressing beam. With this tool, we first study the spectrum of an elementary system of two spins, tuning it from a nonresonant to a resonant regime, where "bright" (super-radiant) and "dark" (subradiant) states emerge. We observe the collective enhancement of the microwave coupling to the bright state. We then show that after preparing an initial single spin excitation and letting it hop due to the spin-exchange interaction, we can freeze the dynamics at will with the addressing laser, while preserving the coherence of the system. In the context of quantum simulation, this scheme opens exciting prospects for engineering inhomogeneous XY spin Hamiltonians or preparing spin-imbalanced initial states.

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

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.

An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays.

Large arrays of individually controlled atoms trapped in optical tweezers are a very promising platform for quantum engineering applications. However, deterministic loading of the traps is experimentally challenging. 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, which together enable 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 two-dimensional geometries.

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 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 on the dynamics, we find 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. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

Coherent excitation transfer in a spin chain of three Rydberg atoms.

We study coherent excitation hopping in a spin chain realized using highly excited individually addressable Rydberg atoms. The dynamics are fully described in terms of an XY spin Hamiltonian with a long range resonant dipole-dipole coupling that scales as the inverse third power of the lattice spacing, C(3)/R(3). The experimental data demonstrate the importance of next neighbor interactions which are manifest as revivals in the excitation dynamics. The results suggest that arrays of Rydberg atoms are ideally suited to large scale, high-fidelity quantum simulation of spin dynamics.