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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 limit 1,2 . To do so, one can reshape the quantum projection noise-a strategy known as squeezing 3,4 . In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model 4 ) between the constituents to generate the structured entanglement characteristic of spin squeezing 5 . Here we explore the prediction, motivated by recent theoretical work 6-10 , 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., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions 1-3 . 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 phase 4,5 . 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 symmetry 6-9 ., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Quantum simulation using synthetic systems is a promising route to solve outstanding quantum many-body problems in regimes where other approaches, including numerical ones, fail 1 . Many platforms are being developed towards this goal, in particular based on trapped ions 2-4 , superconducting circuits 5-7 , neutral atoms 8-11 or molecules 12,13 . 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 states 11 , 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.

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 1 or quantum dots 2 , and atomic, molecular and optical systems, such as photons, trapped ions or neutral atoms 3-7 . The latter offer inherently identical qubits that are well decoupled from the environment and could provide synthetic structures scalable to hundreds of qubits or more 8 . Quantum-gas microscopes 9 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 10 and two 11 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.

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.

Symmetry-breaking interactions have a crucial role in many areas of physics, ranging from classical ferrofluids to superfluid (3)He and d-wave superconductivity. For superfluid quantum gases, a variety of new physical phenomena arising from the symmetry-breaking interaction between electric or magnetic dipoles are expected. Novel quantum phases in optical lattices, such as chequerboard or supersolid phases, are predicted for dipolar bosons. Dipolar interactions can also enrich considerably the physics of quantum gases with internal degrees of freedom. Arrays of dipolar particles could be used for efficient quantum information processing. Here we report the realization of a chromium Bose-Einstein condensate with strong dipolar interactions. By using a Feshbach resonance, we reduce the usual isotropic contact interaction, such that the anisotropic magnetic dipole-dipole interaction between 52Cr atoms becomes comparable in strength. This induces a change of the aspect ratio of the atom cloud; for strong dipolar interactions, the inversion of ellipticity during expansion (the usual 'smoking gun' evidence for a Bose-Einstein condensate) can be suppressed. These effects are accounted for by taking into account the dipolar interaction in the superfluid hydrodynamic equations governing the dynamics of the gas, in the same way as classical ferrofluids can be described by including dipolar terms in the classical hydrodynamic equations. Our results are a first step in the exploration of the unique properties of quantum ferrofluids.