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.

Antiferromagnetic Bosonic t-J Models and Their Quantum Simulation in Tweezer Arrays

The combination of optical tweezer arrays with strong interactions-via dipole exchange of molecules and Van der Waals interactions of Rydberg atoms-has opened the door for the exploration of a wide variety of quantum spin models. A next significant step will be the combination of such settings with mobile dopants. This will enable one to simulate the physics believed to underlie many strongly correlated quantum materials. Here, we propose an experimental scheme to realize bosonic t-J models via encoding the local Hilbert space in a set of three internal atomic or molecular states. By engineering antiferromagnetic (AFM) couplings between spins, competition between charge motion and magnetic order similar to that in high-T_{c} cuprates can be realized. Since the ground states of the 2D bosonic AFM t-J model we propose to realize have not been studied extensively before, we start by analyzing the case of two dopants-the simplest instance in which their bosonic statistics plays a role-and compare our results to the fermionic case. We perform large-scale density matrix renormalization group calculations on six-legged cylinders, and find a strong tendency for bosonic holes to form stripes. This demonstrates that bosonic, AFM t-J models may contain similar physics as the collective phases in strongly correlated electrons.

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX-YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan-Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin-spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Quantum simulation of the bosonic Kitaev chain

Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Nonlinear topological symmetry protection in a dissipative system

We investigate experimentally and theoretically a system ruled by an intricate interplay between topology, nonlinearity, and spontaneous symmetry breaking. The experiment is based on a two-mode coherently-driven optical resonator where photons interact through the Kerr nonlinearity. In presence of a phase defect, the modal structure acquires a synthetic Möbius topology enabling the realization of spontaneous symmetry breaking in inherently bias-free conditions without fine tuning of parameters. Rigorous statistical tests confirm the robustness of the underlying symmetry protection, which manifests itself by a periodic alternation of the modes reminiscent of period-doubling. This dynamic also confers long term stability to various localized structures including domain walls, solitons, and breathers. Our findings are supported by an effective Hamiltonian model and have relevance to other systems of interacting bosons and to the Floquet engineering of quantum matter. They could also be beneficial to the implementation of coherent Ising machines.

Quantum Phases from Competing Van der Waals and Dipole-Dipole Interactions of Rydberg Atoms

Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the Van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.

Floquet-tailored Rydberg interactions

The Rydberg blockade is a key ingredient for entangling atoms in arrays. However, it requires atoms to be spaced well within the blockade radius, which limits the range of local quantum gates. Here we break this constraint using Floquet frequency modulation, with which we demonstrate Rydberg-blockade entanglement beyond the traditional blockade radius and show how the enlarged entanglement range improves qubit connectivity in a neutral atom array. Further, we find that the coherence of entangled states can be extended under Floquet frequency modulation. Finally, we realize Rydberg anti-blockade states for two sodium Rydberg atoms within the blockade radius. Such Rydberg anti-blockade states for atoms at close range enables the robust preparation of strongly-interacting, long-lived Rydberg states, yet their steady-state population cannot be achieved with only the conventional static drive. Our work transforms between the paradigmatic regimes of Rydberg blockade versus anti-blockade and paves the way for realizing more connected, coherent, and tunable neutral atom quantum processors with a single approach.

Exact New Mobility Edges between Critical and Localized States

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This Letter may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.

Shadow Tomography from Emergent State Designs in Analog Quantum Simulators

We introduce a method that allows one to infer many properties of a quantum state-including nonlinear functions such as Rényi entropies-using only global control over the constituent degrees of freedom. In this protocol, the state of interest is first entangled with a set of ancillas under a fixed global unitary, before projective measurements are made. We show that when the unitary is sufficiently entangling, a universal relationship between the statistics of the measurement outcomes and properties of the state emerges, which can be connected to the recently discovered phenomeonon of emergent quantum state designs in chaotic systems. Thanks to this relationship, arbitrary observables can be reconstructed using the same number of experimental repetitions that would be required in classical shadow tomography [Huang et al., Nat. Phys. 16, 1050 (2020)NPAHAX1745-247310.1038/s41567-020-0932-7]. Unlike previous approaches to shadow tomography, our protocol can be implemented using only global Hamiltonian evolution, as opposed to qubit-selective logic gates, which makes it particularly well suited to analog quantum simulators, including ultracold atoms in optical lattices and arrays of Rydberg atoms.

Picosecond-Scale Ultrafast Many-Body Dynamics in an Ultracold Rydberg-Excited Atomic Mott Insulator

We report the observation and control of ultrafast many-body dynamics of electrons in ultracold Rydberg-excited atoms, spatially ordered in a three-dimensional Mott insulator (MI) with unity filling in an optical lattice. By mapping out the time-domain Ramsey interferometry in the picosecond timescale, we can deduce entanglement growth indicating the emergence of many-body correlations via dipolar forces. We analyze our observations with different theoretical approaches and find that the semiclassical model breaks down, thus indicating that quantum fluctuations play a decisive role in the observed dynamics. Combining picosecond Rydberg excitation with MI lattice thus provides a platform for simulating nonequilibrium dynamics of strongly correlated systems in synthetic ultracold atomic crystals, such as in a metal-like quantum gas regime.

Embedding Semiclassical Periodic Orbits into Chaotic Many-Body Hamiltonians

Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a family of nonintegrable many-body Hamiltonians, whose dynamics is otherwise chaotic. Our construction is based on time-dependent variational principle that projects quantum dynamics onto a manifold of low-entangled states, and it complements earlier approaches for embedding nonthermal eigenstates, known as quantum many-body scars, into thermalizing spectra. By designing terms that suppress "leakage" of the dynamics outside the variational manifold, we engineer families of Floquet models that host exact scarred dynamics, as we illustrate using a driven Affleck-Kennedy-Lieb-Tasaki model and a recent experimental realization of scars in a dimerized superconducting qubit chain.

Entanglement in the quantum phases of an unfrustrated Rydberg atom array

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.

Observation of a Topological Edge State Stabilized by Dissipation

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated.

Landau-Forbidden Quantum Criticality in Rydberg Quantum Simulators

The Landau-Ginzburg-Wilson theory of phase transitions precludes a continuous transition between two phases that spontaneously break distinct symmetries. However, quantum mechanical effects can intertwine the symmetries, giving rise to an exotic phenomenon called deconfined quantum criticality (DQC). In this Letter, we study the ground state phase diagram of a one-dimensional array of individually trapped neutral atoms interacting strongly via Rydberg states, and demonstrate through extensive numerical simulations that it hosts a variety of symmetry-breaking phases and their transitions including DQC. We show how an enlarged, emergent continuous symmetry arises at the DQCs, which can be experimentally observed in the joint distribution of two distinct order parameters, obtained within measurement snapshots in the standard computational basis. Our findings highlight quantum simulators of Rydberg atoms not only as promising platforms to experimentally realize such exotic phenomena, but also as unique ones allowing access to physical properties not obtainable in traditional experiments.

Anomalous Diffusion in the Long-Range Haken-Strobl-Reineker Model

We analyze the propagation of excitons in a d-dimensional lattice with power-law hopping ∝1/r^{α} in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing (quantum Zeno) regime the dynamics is described by a classical master equation for an exclusion process with long jumps. In this limit, we analytically compute the spatial distribution, whose shape changes at a critical value of the decay exponent α_{cr}=(d+2)/2. The exciton always diffuses anomalously: a superdiffusive motion is associated to a Lévy stable distribution with long-range algebraic tails for α≤α_{cr}, while for α>α_{cr} the distribution corresponds to a surprising mixed Gaussian profile with long-range algebraic tails, leading to the coexistence of short-range diffusion and long-range Lévy flights. In the many-exciton case, we demonstrate that, starting from a domain-wall exciton profile, algebraic tails appear in the distributions for any α, which affects thermalization: the longer the hopping range, the faster equilibrium is reached. Our results are directly relevant to experiments with cold trapped ions, Rydberg atoms, and supramolecular dye aggregates. They provide a way to realize an exclusion process with long jumps experimentally.

Bichromatic Imaging of Single Molecules in an Optical Tweezer Array

We report on a novel bichromatic fluorescent imaging scheme for background-free detection of single CaF molecules trapped in an optical tweezer array. By collecting fluorescence on one optical transition while using another for laser cooling, we achieve an imaging fidelity of 97.7(2)% and a nondestructive detection fidelity of 95.5(6)%. Notably, these fidelities are achieved with a modest photon budget, suggesting that the method could be extended to more complex laser-coolable molecules with less favorable optical cycling properties. We also report on a framework and new methods to characterize various loss mechanisms that occur generally during fluorescent detection of trapped molecules, including two-photon decay and admixtures of higher excited states that are induced by the trapping light. In particular, we develop a novel method to dispersively measure transition matrix elements between electronically excited states. The method could also be used to measure arbitrarily small Franck-Condon factors between electronically excited states, which could significantly aid in ongoing efforts to laser cool complex polyatomic molecules.

Quantization and its breakdown in a Hubbard-Thouless pump

Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems1. For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue-the Thouless pump2-4. However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms5-9, the study of topological matter under variations in interparticle interactions has proven challenging10. Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump's robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter10, including edge effects11 and interaction-induced topological phases12-15.

Spatially Tunable Spin Interactions in Neutral Atom Arrays

Analog quantum simulations with Rydberg atoms in optical tweezers routinely address strongly correlated many-body problems due to the hardware-efficient implementation of the Hamiltonian. Yet, their generality is limited, and flexible Hamiltonian-design techniques are needed to widen the scope of these simulators. Here we report on the realization of spatially tunable interactions for XYZ models implemented by two-color near-resonant coupling to Rydberg pair states. Our results demonstrate the unique opportunities of Rydberg dressing for Hamiltonian design in analog quantum simulators.

Emergent Glassy Behavior in a Kagome Rydberg Atom Array

We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.

Dark-State Enhanced Loading of an Optical Tweezer Array

Neutral atoms and molecules trapped in optical tweezers have become a prevalent resource for quantum simulation, computation, and metrology. However, the maximum achievable system sizes of such arrays are often limited by the stochastic nature of loading into optical tweezers, with a typical loading probability of only 50%. Here we present a species-agnostic method for dark-state enhanced loading (DSEL) based on real-time feedback, long-lived shelving states, and iterated array reloading. We demonstrate this technique with a 95-tweezer array of ^{88}Sr atoms, achieving a maximum loading probability of 84.02(4)% and a maximum array size of 91 atoms in one dimension. Our protocol is complementary to, and compatible with, existing schemes for enhanced loading based on direct control over light-assisted collisions, and we predict it can enable close-to-unity filling for arrays of atoms or molecules.

Scalable Multilayer Architecture of Assembled Single-Atom Qubit Arrays in a Three-Dimensional Talbot Tweezer Lattice

We report on the realization of a novel platform for the creation of large-scale 3D multilayer configurations of planar arrays of individual neutral-atom qubits: a microlens-generated Talbot tweezer lattice that extends 2D tweezer arrays to the third dimension at no additional costs. We demonstrate the trapping and imaging of rubidium atoms in integer and fractional Talbot planes and the assembly of defect-free atom arrays in different layers. The Talbot self-imaging effect for microlens arrays constitutes a structurally robust and wavelength-universal method for the realization of 3D atom arrays with beneficial scaling properties. With more than 750 qubit sites per 2D layer, these scaling properties imply that 10 000 qubit sites are already accessible in 3D in our current implementation. The trap topology and functionality are configurable in the micrometer regime. We use this to generate interleaved lattices with dynamic position control and parallelized sublattice addressing of spin states for immediate application in quantum science and technology.

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.

Rydberg Macrodimers: Diatomic Molecules on the Micrometer Scale

Controlling molecular binding at the level of single atoms is one of the holy grails of quantum chemistry. Rydberg macrodimers─bound states between highly excited Rydberg atoms─provide a novel perspective in this direction. Resulting from binding potentials formed by the strong, long-range interactions of Rydberg states, Rydberg macrodimers feature bond lengths in the micrometer regime, exceeding those of conventional molecules by orders of magnitude. Using single-atom control in quantum gas microscopes, the unique properties of these exotic states can be studied with unprecedented control, including the response to magnetic fields or the polarization of light in their photoassociation. The high accuracy achieved in spectroscopic studies of macrodimers makes them an ideal testbed to benchmark Rydberg interactions, with direct relevance to quantum computing and information protocols where these are employed. This review provides a historic overview and summarizes the recent findings in the field of Rydberg macrodimers. Furthermore, it presents new data on interactions between macrodimers, leading to a phenomenon analogous to Rydberg blockade at the level of molecules, opening the path toward studying many-body systems of ultralong-range Rydberg molecules.

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties^1-11. These include a large set of internal states with long coherence times^12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids¹⁸, quantum spin liquids¹⁹, fractional Chern insulators²⁰ and quantum magnets^21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy²³ to measure the site-resolved dynamics of quantum correlations of polar ²³Na⁸⁷Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model^21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses^26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation^29,30 and metrology³¹.

Emergent Z_{2} Gauge Theories and Topological Excitations in Rydberg Atom Arrays

Strongly interacting arrays of Rydberg atoms provide versatile platforms for exploring exotic many-body phases and dynamics of correlated quantum systems. Motivated by recent experimental advances, we show that the combination of Rydberg interactions and appropriate lattice geometries naturally leads to emergent Z_{2} gauge theories endowed with matter fields. Based on this mapping, we describe how Rydberg platforms could realize two distinct classes of topological Z_{2} quantum spin liquids, which differ in their patterns of translational symmetry fractionalization. We also discuss the natures of the fractionalized excitations of these Z_{2} spin liquid states using both fermionic and bosonic parton theories and illustrate their rich interplay with proximate solid phases.

Preparing random states and benchmarking with many-body quantum chaos

Producing quantum states at random has become increasingly important in modern quantum science, with applications being both theoretical and practical. In particular, ensembles of such randomly distributed, but pure, quantum states underlie our understanding of complexity in quantum circuits¹ and black holes², and have been used for benchmarking quantum devices^3,4 in tests of quantum advantage^5,6. However, creating random ensembles has necessitated a high degree of spatio-temporal control^7-12 placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization¹³. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 10⁴ experimental samples. This method has broad applicability, as we demonstrate for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analogue and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics¹⁴ and enables applications of this concept in a much wider context^{4,5,9,10,15-20}.

Observing the quantum topology of light

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

Demonstration of a Quantum Gate Using Electromagnetically Induced Transparency

We demonstrate a native CNOT gate between two individually addressed neutral atoms based on electromagnetically induced transparency. This protocol utilizes the strong long-range interactions of Rydberg states to enable conditional state transfer on the target qubit when operated in the blockade regime. An advantage of this scheme is it enables implementation of multiqubit CNOT^{k} gates using a pulse sequence independent of qubit number, providing a simple gate for efficient implementation of digital quantum algorithms and stabilizer measurements for quantum error correction. We achieve a loss corrected gate fidelity of F_{CNOT}^{cor}=0.82(6), and prepare an entangled Bell state with F_{Bell}^{cor}=0.66(5), limited at present by laser power. We present a number of technical improvements to advance this to a level required for fault-tolerant scaling.

Edge State, Localization Length, and Critical Exponent from Survival Probability in Topological Waveguides

Edge states in topological phase transitions have been observed in various platforms. To date, verification of the edge states and the associated topological invariant are mostly studied, and yet a quantitative measurement of topological phase transitions is still lacking. Here, we show the direct measurement of edge states and their localization lengths from survival probability. We employ photonic waveguide arrays to demonstrate the topological phase transitions based on the Su-Schrieffer-Heeger model. By measuring the survival probability at the lattice boundary, we show that in the long-time limit, the survival probability is P=(1-e^{-2/ξ_{loc}})^{2}, where ξ_{loc} is the localization length. This length derived from the survival probability is compared with the distance from the transition point, yielding a critical exponent of ν=0.94±0.04 at the phase boundary. Our experiment provides an alternative route to characterizing topological phase transitions and extracting their key physical quantities.

New trends in quantum integrability: recent experiments with ultracold atoms

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.

Multipartite Entangled States in Dipolar Quantum Simulators

The scalable production of multipartite entangled states in ensembles of qubits is a crucial function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the U(1) symmetric Hamiltonians for qubits with dipolar interactions-a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the nonequilibrium dynamics generated by this Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely, the simplest interacting collective-spin model with U(1) symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states-spin-squeezed states, Schrödinger's cat states, and multicomponent superpositions of coherent spin states. Investigating systems with up to N=144 qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely, scalable spin squeezing at an evolution time O(N^{1/3}) and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times O(N). Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.

Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer

Chiral edge states are highly sought after as paradigmatic topological states relevant to both quantum information processing and dissipationless electron transport. Using superconducting transmon-based quantum computers, we demonstrate chiral topological propagation that is induced by suitably designed interactions, instead of flux or spin-orbit coupling. Also different from conventional 2D realizations, our effective Chern lattice is implemented on a much smaller equivalent 1D spin chain, with sequences of entangling gates encapsulating the required time-reversal breaking. By taking advantage of the quantum nature of the platform, we circumvented difficulties from the limited qubit number and gate fidelity in present-day noisy intermediate-scale quantum era quantum computers, paving the way for the quantum simulation of more sophisticated topological states on very rapidly developing quantum hardware.

Two-Dimensional Programmable Tweezer Arrays of Fermions

We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

Tuning Long-Range Fermion-Mediated Interactions in Cold-Atom Quantum Simulators

Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Fermionic atoms in ultracold atomic mixtures can act as mediators, giving rise to long-range Ruderman-Kittel-Kasuya-Yosida-type interactions characterized by the dimensionality and density of the fermionic gas. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow one to further control the range and shape of the mediated interactions, extending the existing quantum simulation toolbox. In particular, we include an additional optical lattice for the fermionic mediator, as well as anisotropic traps to change its dimensionality in a continuous manner. This allows us to interpolate between power-law and exponential decays, introducing an effective cutoff for the interaction range, as well as to tune the relative interaction strengths at different distances. Finally, we show how our approach allows one to investigate frustrated regimes that were not previously accessible, where symmetry-protected topological phases as well as chiral spin liquids emerge.

Experimental Realization of Reconfigurable Photonic Lattices in Coherent Rydberg Atomic Vapors

We experimentally demonstrated the formation of a one-dimensional electromagnetically induced optical lattice in coherently prepared three-level 85Rb Rydberg atomic vapors with electromagnetically induced transparency (EIT). The one-dimensional photonic lattice was optically induced by a coupling field with a spatially periodical intensity distribution deriving from the interference of two strong Gaussian beams from the same laser source (~480 nm). Under the Rydberg-EIT condition, the incident weak probe beam can feel a tunable spatially modulated susceptibility, which is verified by the controllable discrete diffraction pattern observed at the output plane of the vapor cell. This investigation not only opens the door for experimentally introducing the strong interaction between Rydberg atoms to govern the beam dynamics in photonic lattices based on atomic coherence but also provides an easily accessible periodic environment for exploring Rydberg-atom physics and related applications.

One decade of quantum optimal control in the chopped random basis

The chopped random basis (CRAB) ansatz for quantum optimal control has been proven to be a versatile tool to enable quantum technology applications such as quantum computing, quantum simulation, quantum sensing, and quantum communication. Its capability to encompass experimental constraints-while maintaining an access to the usually trap-free control landscape-and to switch from open-loop to closed-loop optimization (including with remote access-or RedCRAB) is contributing to the development of quantum technology on many different physical platforms. In this review article we present the development, the theoretical basis and the toolbox for this optimization algorithm, as well as an overview of the broad range of different theoretical and experimental applications that exploit this powerful technique.

Realizing the symmetry-protected Haldane phase in Fermi-Hubbard ladders

Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain^1,2. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter^3,4. More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement^5–7. Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi–Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.

A ladder-like arrangement of an ultracold gas of lithium atoms trapped in an optical lattice enables the observation of a symmetry-protected topological phase.

Engineering topological states in atom-based semiconductor quantum dots

The realization of controllable fermionic quantum systems via quantum simulation is instrumental for exploring many of the most intriguing effects in condensed-matter physics^1–3. Semiconductor quantum dots are particularly promising for quantum simulation as they can be engineered to achieve strong quantum correlations. However, although simulation of the Fermi–Hubbard model⁴ and Nagaoka ferromagnetism⁵ have been reported before, the simplest one-dimensional model of strongly correlated topological matter, the many-body Su–Schrieffer–Heeger (SSH) model^6–11, has so far remained elusive—mostly owing to the challenge of precisely engineering long-range interactions between electrons to reproduce the chosen Hamiltonian. Here we show that for precision-placed atoms in silicon with strong Coulomb confinement, we can engineer a minimum of six all-epitaxial in-plane gates to tune the energy levels across a linear array of ten quantum dots to realize both the trivial and the topological phases of the many-body SSH model. The strong on-site energies (about 25 millielectronvolts) and the ability to engineer gates with subnanometre precision in a unique staggered design allow us to tune the ratio between intercell and intracell electron transport to observe clear signatures of a topological phase with two conductance peaks at quarter-filling, compared with the ten conductance peaks of the trivial phase. The demonstration of the SSH model in a fermionic system isomorphic to qubits showcases our highly controllable quantum system and its usefulness for future simulations of strongly interacting electrons.

Precision-engineered devices consisting of a linear array of ten quantum dots are used to realize both the trivial and topological phases of the many-body Su–Schrieffer–Heeger model.

Anti-drude metal of bosons

In the absence of frustration, interacting bosons in their ground state in one or two dimensions exist either in the superfluid or insulating phases. Superfluidity corresponds to frictionless flow of the matter field, and in optical conductivity is revealed through a distinct δ-functional peak at zero frequency with the amplitude known as the Drude weight. This characteristic low-frequency feature is instead absent in insulating phases, defined by zero static optical conductivity. Here we demonstrate that bosonic particles in disordered one dimensional chains can also exist in a conducting, non-superfluid, phase when their hopping is of the dipolar type, often viewed as short-ranged in one dimension. This phase is characterized by finite static optical conductivity, followed by a broad anti-Drude peak at finite frequencies. Off-diagonal correlations are also unconventional: they feature an integrable algebraic decay for arbitrarily large values of disorder. These results do not fit the description of any known quantum phase, and strongly suggest the existence of an unusual conducting state of bosonic matter in the ground state.

Interacting bosons in one or two dimensions are expected to be in either a superfluid or an insulating ground state. Here, the authors show numerically that an experimentally relevant 1D model of disordered bosons with dipolar couplings supports an unusual metallic phase that does not fit into existing descriptions.

Long-range order and quantum criticality in antiferromagnetic chains with long-range staggered interactions

We study quantum phase transitions in Heisenberg antiferromagnetic chains with a staggered power-law decaying long-range interactions. Employing the density-matrix renormalization group (DMRG) algorithm and the fidelity susceptibility as the criticality measure, we establish more accurate values of quantum critical points than the results obtained from the spin-wave approximation, quantum Monte Carlo, and DMRG in literatures. The deviation is especially evident for strong long-range interactions. We extend isotropic long-range interactions to the anisotropic cases and find that kaleidoscope of quantum phases emerge from the interplay of anisotropy of the long-range exchange interaction and symmetry breaking. We demonstrate nonfrustrating long-range interactions induce the true long-range order in Heisenberg antiferromagnetic chains with a continuous symmetry breaking, lifting the restrictions imposed by the Mermin-Wagner theorem.

Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model-dependent multifractal scaling of the wave functions at any nonzero measurement rate. The subleading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant nonzero in the error-correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.

Realizing Distance-Selective Interactions in a Rydberg-Dressed Atom Array

Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.

Observation of Core-Excited Dipole-Bound States

Polar molecules can bind an electron in a diffuse orbital due to the charge-dipole interaction. Electronic excited states of polar molecules can also bind an electron to form core-excited dipole-bound states (DBSs), analogous to core-excited Rydberg states. However, core-excited DBSs have not been observed because of the complicated electronic structure of molecular systems. Here, we report the observation of a core-excited DBS in the pyrazolide anion as a result of the favorable electronic structure of the neutral pyrazolyl core, which has a low-lying excited state (òB₁) only 266 cm^-1 above its ground state (X̃²A₂). The binding energy of the DBS associated with the ground state is measured to be 221 cm^-1, while that of the core-excited DBS is 276 cm^-1, which is still a bound state relative to the detachment threshold. Vibrational Feshbach resonances are observed for both DBSs, and their autodetachment behaviors are studied by resonant photoelectron imaging.

Defect-Free Arbitrary-Geometry Assembly of Mixed-Species Atom Arrays

Optically trapped mixed-species single atom arrays with arbitrary geometry are an attractive and promising platform for various applications, because tunable quantum systems with multiple components provide extra degrees of freedom for experimental control. Here, we report the first demonstration of two-dimensional 6×4 dual-species atom assembly of ^{85}Rb (^{87}Rb) atoms with a filling fraction of 0.88 (0.89). This mixed-species atomic synthesis is achieved via rearranging initially randomly distributed atoms by a sorting algorithm (heuristic heteronuclear algorithm) which is designed for bottom-up atom assembly with both user-defined geometries and two-species atom number ratios. Our fully tunable hybrid-atom systems with scalable advantages are a good starting point for high-fidelity quantum logic, many-body quantum simulation, and single molecule array formation.

Realizing topological edge states with Rydberg-atom synthetic dimensions

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold ⁸⁴Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.

Synthetic dimensions, states of a system engineered to act as if they were a reconfigurable extra spatial dimension, have been demonstrated with different systems previously. Here the authors create a synthetic dimension using Rydberg atoms and configure it to support topological edge states.

Kink Dynamics and Quantum Simulation of Supersymmetric Lattice Hamiltonians

We propose a quantum simulation of a supersymmetric lattice model using atoms trapped in a 1D configuration and interacting through a Rydberg dressed potential. The elementary excitations in the model are kinks or (in a sector with one extra particle) their superpartners-the skinks. The two are connected by supersymmetry and display identical quantum dynamics. We provide an analytical description of the kink (skink) quench dynamics and propose a protocol to prepare and detect these excitations in the quantum simulator. We make a detailed analysis, based on numerical simulation, of the Rydberg atom simulator and show that it accurately tracks the dynamics of the supersymmetric model.

Topological Quantum Critical Points in the Extended Bose-Hubbard Model

The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results show that the topological critical points separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. The long-range order persists also at the topological critical points and explains the presence of localized edge states protected by a finite charge gap. Finally, we introduce a superresolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

Trapping Alkaline Earth Rydberg Atoms Optical Tweezer Arrays

Neutral atom qubits with Rydberg-mediated interactions are a leading platform for developing large-scale coherent quantum systems. In the majority of experiments to date, the Rydberg states are not trapped by the same potential that confines ground state atoms, resulting in atom loss and constraints on the achievable interaction time. In this Letter, we demonstrate that the Rydberg states of an alkaline earth atom, ytterbium, can be stably trapped by the same red-detuned optical tweezer that also confines the ground state, by leveraging the polarizability of the Yb^{+} ion core. Using the previously unobserved ^{3}S_{1} series, we demonstrate trapped Rydberg atom lifetimes exceeding 100  μs, and observe no evidence of auto- or photoionization from the trap light for these states. We measure a coherence time of T_{2}=59  μs between two Rydberg levels, exceeding the 28  μs lifetime of untrapped Rydberg atoms under the same conditions. These results are promising for extending the interaction time of Rydberg atom arrays for quantum simulation and computing, and are vital to capitalize on the extended Rydberg lifetimes in circular states or cryogenic environments.

Symmetry-Protected Topological Phases in a Rydberg Glass

Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.