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.

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.

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.

In-plane and out-of-plane diffraction of H2 from Ru(001).

H(2) diffraction from the Ru(001) surface has been measured for incident energies E(i) = 78-150 meV and incident angles Θ(i) = 22.1-64.1°. In-plane and out-of-plane angular distributions were measured for incidence along [110] and [100] directions. Out-of-plane diffraction channels were found to be predominant for the explored experimental conditions regardless of the incidence direction. An analysis of diffraction intensities reveals that diffraction out of the scattering plane is enhanced for high incidence angles. Diffractive transitions with wavevector change in the surface plane and transversal to the incidence direction ΔK(⊥) were observed to be favored among the out-of-plane diffractive transitions. These features could be reproduced by model calculations of diffraction intensities performed using a three-dimensional soft potential. This suggests that a kinematic effect is responsible for the large out-of-plane intensities observed in experiment, more than any other features of the six-dimensional H(2)-surface interaction potential.

Experimental and theoretical study of rotationally inelastic diffraction of D2 from NiAl(110).

We present a detailed experimental and theoretical study of elastic and rotationally inelastic diffraction of D(2) from NiAl(110) in the energy range 85-150 meV. The experiments were performed using a high-resolution, fixed angle geometry apparatus. Quantum and classical dynamical calculations were performed by using a six-dimensional potential energy surface constructed upon interpolation of a set of DFT (density functional theory) data. We show that, although elastic diffraction peak intensities are accurately described by theory in the whole range of incidence energies and angles explored, significant discrepancies are obtained for RID peaks, especially for those involving rotational initial states with j(i) > 0. Possible reasons for this discrepancy are discussed.

High-resolution elastic and rotationally inelastic diffraction of D2 from NiAl(110).

High-resolution angular distributions of D(2) scattered from NiAl(110) have been measured at incident energies between 20 and 150 meV. The measurements were performed along the [110] azimuth using a high sensitivity time-of-flight apparatus, which allows the recording of diffraction channels not previously studied, including out-of-plane rotationally inelastic diffraction peaks. The attenuation of both elastic and rotationally inelastic diffraction intensities with surface temperature was found to follow a Debye-Waller model. The time-of-flight data analysis allowed us to assign unequivocally the different transition probabilities to each final state. In this way, 0→2, 2→0, and 1→3 transition probabilities were observed, covering relative intensities over two orders of magnitude. In the energy range investigated, the 0→2 transition was found to be a factor of 2-3 larger than the 2→0 one, which lies a factor of 10 above the 1→3 transition probability.

Reactive and nonreactive scattering of H2 from a metal surface is electronically adiabatic.

The Born-Oppenheimer approximation of uncoupled electronic and nuclear motion is a standard tool of the computational chemist. However, its validity for molecule-metal surface reactions, which are important to heterogeneous catalysis, has been questioned because of the possibility of electron-hole pair excitations. We have performed experiments and calculations on the scattering of molecular hydrogen from a catalytically relevant metal surface, obtaining absolute probabilities for changes in the molecule's velocity parallel to the representative Pt(111) surface. The comparison for in-plane and out-of-plane scattering and results for dissociative chemisorption in the same system show that for hydrogen-metal systems, reaction and diffractive scattering can be accurately described using the Born-Oppenheimer approximation.