Control and Entanglement of Individual Rydberg Atoms near a Nanoscale Device

Coherent control of Rydberg atoms near dielectric surfaces is a major challenge due to the large sensitivity of Rydberg states to electric fields. We demonstrate coherent single-atom operations and two-qubit entanglement as close as 100  μm from a nanophotonic device. Using the individual atom control enabled by optical tweezers to study the spatial and temporal properties of the electric field from the surface, we employ dynamical decoupling techniques to characterize and cancel the electric-field noise with submicrosecond temporal resolution. We further use entanglement-assisted sensing to accurately map magnitude and direction of electric-field gradients on a micrometer scale. Our observations open a path for integration of Rydberg arrays with micro- and nanoscale devices for applications in quantum networking and quantum information science.

Enhancing detection of topological order by local error correction

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states-locally error-corrected decoration (LED)-by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.

Logical quantum processor based on reconfigurable atom arrays

Suppressing errors is the central challenge for useful quantum computing1, requiring quantum error correction (QEC)2-6 for large-scale processing. However, the overhead in the realization of error-corrected 'logical' qubits, in which information is encoded across many physical qubits for redundancy2-4, poses substantial challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Using logical-level control and a zoned architecture in reconfigurable neutral-atom arrays7, our system combines high two-qubit gate fidelities8, arbitrary connectivity7,9, as well as fully programmable single-qubit rotations and mid-circuit readout10-15. Operating this logical processor with various types of encoding, we demonstrate improvement of a two-qubit logic gate by scaling surface-code6 distance from d = 3 to d = 7, preparation of colour-code qubits with break-even fidelities5, fault-tolerant creation of logical Greenberger-Horne-Zeilinger (GHZ) states and feedforward entanglement teleportation, as well as operation of 40 colour-code qubits. Finally, using 3D [[8,3,2]] code blocks16,17, we realize computationally complex sampling circuits18 with up to 48 logical qubits entangled with hypercube connectivity19 with 228 logical two-qubit gates and 48 logical CCZ gates20. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical-qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling21,22. These results herald the advent of early error-corrected quantum computation and chart a path towards large-scale logical processors.

Robust Higher-Order Hamiltonian Engineering for Quantum Sensing with Strongly Interacting Systems

Dynamical decoupling techniques constitute an integral part of many quantum sensing platforms, often leading to orders-of-magnitude improvements in coherence time and sensitivity. Most ac sensing sequences involve a periodic echolike structure, in which the target signal is synchronized with the echo period. We show that for strongly interacting systems, this construction leads to a fundamental sensitivity limit associated with imperfect interaction decoupling. We present a simple physical picture demonstrating the origin of this limitation, and further formalize these considerations in terms of concise higher-order decoupling rules. We then show how these limitations can be surpassed by identifying a novel sequence building block, in which the signal period matches twice the echo period. Using these decoupling rules and the resulting sequence building block, we experimentally demonstrate significant improvements in dynamical decoupling timescales and magnetic field sensitivity, opening the door for new applications in quantum sensing and quantum many-body physics.

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15.

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ∼10^{9} two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble

Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from the system's intrinsic many-body dynamics and reveal the signatures of conservation laws within localized clusters of spins, which do not readily manifest using global probes. Our method provides an exquisite lens into the tunable nature of local thermalization dynamics and enables detailed studies of scrambling, thermalization, and hydrodynamics in strongly interacting quantum systems.

Quantum sensors for biomedical applications

Quantum sensors are finding their way from laboratories to the real world, as witnessed by the increasing number of start-ups in this field. The atomic length scale of quantum sensors and their coherence properties enable unprecedented spatial resolution and sensitivity. Biomedical applications could benefit from these quantum technologies, but it is often difficult to evaluate the potential impact of the techniques. This Review sheds light on these questions, presenting the status of quantum sensing applications and discussing their path towards commercialization. The focus is on two promising quantum sensing platforms: optically pumped atomic magnetometers, and nitrogen-vacancy centres in diamond. The broad spectrum of biomedical applications is highlighted by four case studies ranging from brain imaging to single-cell spectroscopy.

Dynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays

We theoretically analyze recent experiments [Semeghini et al., Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794] demonstrating the onset of a topological spin liquid using a programmable quantum simulator based on Rydberg atom arrays. In the experiment, robust signatures of topological order emerge in out-of-equilibrium states that are prepared using a quasiadiabatic state preparation protocol. We show theoretically that the state preparation protocol can be optimized to target the fixed point of the topological phase-the resonating valence bond state of hard dimers-in a time that scales linearly with the number of atoms. Moreover, we provide a two-parameter variational manifold of tensor network states that accurately describe the many-body dynamics of the preparation process. Using this approach we analyze the nature of the nonequilibrium state, establishing the emergence of topological order.

Efficient Source of Shaped Single Photons Based on an Integrated Diamond Nanophotonic System

An efficient, scalable source of shaped single photons that can be directly integrated with optical fiber networks and quantum memories is at the heart of many protocols in quantum information science. We demonstrate a deterministic source of arbitrarily temporally shaped single-photon pulses with high efficiency [detection efficiency=14.9%] and purity [g^{(2)}(0)=0.0168] and streams of up to 11 consecutively detected single photons using a silicon-vacancy center in a highly directional fiber-integrated diamond nanophotonic cavity. Combined with previously demonstrated spin-photon entangling gates, this system enables on-demand generation of streams of correlated photons such as cluster states and could be used as a resource for robust transmission and processing of quantum information.

Optical Entanglement of Distinguishable Quantum Emitters

Solid-state quantum emitters are promising candidates for the realization of quantum networks, owing to their long-lived spin memories, high-fidelity local operations, and optical connectivity for long-range entanglement. However, due to differences in local environment, solid-state emitters typically feature a range of distinct transition frequencies, which makes it challenging to create optically mediated entanglement between arbitrary emitter pairs. We propose and demonstrate an efficient method for entangling emitters with optical transitions separated by many linewidths. In our approach, electro-optic modulators enable a single photon to herald a parity measurement on a pair of spin qubits. We experimentally demonstrate the protocol using two silicon-vacancy centers in a diamond nanophotonic cavity, with optical transitions separated by 7.4 GHz. Working with distinguishable emitters allows for individual qubit addressing and readout, enabling parallel control and entanglement of both colocated and spatially separated emitters, a key step toward scaling up quantum information processing systems.

Quantum optimization of maximum independent set using Rydberg atom arrays

Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.

A quantum processor based on coherent transport of entangled atom arrays

The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is key for building scalable quantum information systems^1,2. In most state-of-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here we demonstrate a quantum processor with dynamic, non-local connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, between layers of single- and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation^3–5. We use this architecture to realize programmable generation of entangled graph states, such as cluster states and a seven-qubit Steane code state^6,7. Furthermore, we shuttle entangled ancilla arrays to realize a surface code state with thirteen data and six ancillary qubits⁸ and a toric code state on a torus with sixteen data and eight ancillary qubits⁹. Finally, we use this architecture to realize a hybrid analogue–digital evolution² and use it for measuring entanglement entropy in quantum simulations^10–12, experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars^13,14. Realizing a long-standing goal, these results provide a route towards scalable quantum processing and enable applications ranging from simulation to metrology.

A quantum processer is realized using arrays of neutral atoms that are transported in a parallel manner by optical tweezers during computations, and used for quantum error correction and simulations.

Resonantly enhanced polariton wave mixing and parametric instability in a Floquet medium

We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear systems of optical phonons. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell's equations and leads to such phenomena as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. which demonstrated light amplification in resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of the pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.

Probing topological spin liquids on a programmable quantum simulator

[Figure: see text].

Quantum Sampling Algorithms for Near-Term Devices

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples, including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices, as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)SCIEAS0036-807510.1126/science.abg2530] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

Entanglement transport and a nanophotonic interface for atoms in optical tweezers

The realization of an efficient quantum optical interface for multi-qubit systems is an outstanding challenge in science and engineering. Using two atoms in individually-controlled optical tweezers coupled to a nanofabricated photonic crystal cavity, we demonstrate entanglement generation, fast non-destructive readout, and full quantum control of atomic qubits. The entangled state is verified in free space after being transported away from the cavity by encoding the qubits into long-lived states and using dynamical decoupling. Our approach bridges quantum operations at an optical link and in free space by a coherent one-way transport, potentially enabling an integrated optical interface for atomic quantum processors.

Fast Preparation and Detection of a Rydberg Qubit Using Atomic Ensembles

We demonstrate a new approach for fast preparation, manipulation, and collective readout of an atomic Rydberg-state qubit. By making use of Rydberg blockade inside a small atomic ensemble, we prepare a single qubit within 3  μs with a success probability of F_{p}=0.93±0.02, rotate it, and read out its state in 6  μs with a single-shot fidelity of F_{d}=0.92±0.04. The ensemble-assisted detection is 10^{3} times faster than imaging of a single atom with the same optical resolution, and enables fast repeated nondestructive measurement. We observe qubit coherence times of 15  μs, much longer than the π rotation time of 90 ns. Potential applications ranging from faster quantum information processing in atom arrays to efficient implementation of quantum error correction are discussed.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Controlling Interactions between Quantum Emitters Using Atom Arrays

We investigate the potential for two-dimensional atom arrays to modify the radiation and interaction of individual quantum emitters. Specifically, we demonstrate that control over the emission linewidths, resonant frequency shifts, and local driving field enhancement in impurity atoms is possible due to strong dipole-dipole interactions within ordered, subwavelength atom array configurations. We demonstrate that these effects can be used to dramatically enhance coherent dipole-dipole interactions between distant impurity atoms within an atom array. Possible experimental realizations and potential applications are discussed.

Excitons in a reconstructed moiré potential in twisted WSe2/WSe2 homobilayers

Moiré superlattices in twisted van der Waals materials have recently emerged as a promising platform for engineering electronic and optical properties. A major obstacle to fully understanding these systems and harnessing their potential is the limited ability to correlate direct imaging of the moiré structure with optical and electronic properties. Here we develop a secondary electron microscope technique to directly image stacking domains in fully functional van der Waals heterostructure devices. After demonstrating the imaging of AB/BA and ABA/ABC domains in multilayer graphene, we employ this technique to investigate reconstructed moiré patterns in twisted WSe₂/WSe₂ bilayers and directly correlate the increasing moiré periodicity with the emergence of two distinct exciton species in photoluminescence measurements. These states can be tuned individually through electrostatic gating and feature different valley coherence properties. We attribute our observations to the formation of an array of two intralayer exciton species that reside in alternating locations in the superlattice, and open up new avenues to realize tunable exciton arrays in twisted van der Waals heterostructures, with applications in quantum optoelectronics and explorations of novel many-body systems.

Controlling quantum many-body dynamics in driven Rydberg atom arrays

The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.

Quantum phases of Rydberg atoms on a kagome lattice

We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.

Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe2/MoSe2 bilayers

Van der Waals heterostructures obtained via stacking and twisting have been used to create moiré superlattices¹, enabling new optical and electronic properties in solid-state systems. Moiré lattices in twisted bilayers of transition metal dichalcogenides (TMDs) result in exciton trapping^2-5, host Mott insulating and superconducting states⁶ and act as unique Hubbard systems^7-9 whose correlated electronic states can be detected and manipulated optically. Structurally, these twisted heterostructures feature atomic reconstruction and domain formation^10-14. However, due to the nanoscale size of moiré domains, the effects of atomic reconstruction on the electronic and excitonic properties have not been systematically investigated. Here we use near-0°-twist-angle MoSe₂/MoSe₂ bilayers with large rhombohedral AB/BA domains¹⁵ to directly probe the excitonic properties of individual domains with far-field optics. We show that this system features broken mirror/inversion symmetry, with the AB and BA domains supporting interlayer excitons with out-of-plane electric dipole moments in opposite directions. The dipole orientation of ground-state Γ-K interlayer excitons can be flipped with electric fields, while higher-energy K-K interlayer excitons undergo field-asymmetric hybridization with intralayer K-K excitons. Our study reveals the impact of crystal symmetry on TMD excitons and points to new avenues for realizing topologically non-trivial systems^16,17, exotic metasurfaces¹⁸, collective excitonic phases¹⁹ and quantum emitter arrays^20,21 via domain-pattern engineering.

Electrically Tunable Valley Dynamics in Twisted WSe_{2}/WSe_{2} Bilayers

The twist degree of freedom provides a powerful new tool for engineering the electrical and optical properties of van der Waals heterostructures. Here, we show that the twist angle can be used to control the spin-valley properties of transition metal dichalcogenide bilayers by changing the momentum alignment of the valleys in the two layers. Specifically, we observe that the interlayer excitons in twisted WSe_{2}/WSe_{2} bilayers exhibit a high (>60%) degree of circular polarization (DOCP) and long valley lifetimes (>40  ns) at zero electric and magnetic fields. The valley lifetime can be tuned by more than 3 orders of magnitude via electrostatic doping, enabling switching of the DOCP from ∼80% in the n-doped regime to <5% in the p-doped regime. These results open up new avenues for tunable chiral light-matter interactions, enabling novel device schemes that exploit the valley degree of freedom.

Single-Spin Magnetomechanics with Levitated Micromagnets

We demonstrate a new mechanical transduction platform for individual spin qubits. In our approach, single micromagnets are trapped using a type-II superconductor in proximity of spin qubits, enabling direct magnetic coupling between the two systems. Controlling the distance between the magnet and the superconductor during cooldown, we demonstrate three-dimensional trapping with quality factors around 1×10^{6} and kHz trapping frequencies. We further exploit the large magnetic moment to mass ratio of this mechanical oscillator to couple its motion to the spin degrees of freedom of an individual nitrogen vacancy center in diamond. Our approach provides a new path towards interfacing individual spin qubits with mechanical motion for testing quantum mechanics with mesoscopic objects, realization of quantum networks, and ultrasensitive metrology.

Optical Control of a Single Nuclear Spin in the Solid State

We demonstrate a novel method for coherent optical manipulation of individual nuclear spins in the solid state, mediated by the electronic states of a proximal quantum emitter. Specifically, using the nitrogen-vacancy (NV) color center in diamond, we demonstrate control of a proximal ^{14}N nuclear spin via an all-optical Raman technique. We evaluate the extent to which the intrinsic physical properties of the NV center limit the performance of coherent control, and we find that it is ultimately constrained by the relative rates of transverse hyperfine coupling and radiative decay in the NV center's excited state. Possible extensions and applications to other color centers are discussed.

Experimental demonstration of memory-enhanced quantum communication

The ability to communicate quantum information over long distances is of central importance in quantum science and engineering¹. Although some applications of quantum communication such as secure quantum key distribution^2,3 are already being successfully deployed^4-7, their range is currently limited by photon losses and cannot be extended using straightforward measure-and-repeat strategies without compromising unconditional security⁸. Alternatively, quantum repeaters⁹, which utilize intermediate quantum memory nodes and error correction techniques, can extend the range of quantum channels. However, their implementation remains an outstanding challenge^10-16, requiring a combination of efficient and high-fidelity quantum memories, gate operations, and measurements. Here we use a single solid-state spin memory integrated in a nanophotonic diamond resonator^17-19 to implement asynchronous photonic Bell-state measurements, which are a key component of quantum repeaters. In a proof-of-principle experiment, we demonstrate high-fidelity operation that effectively enables quantum communication at a rate that surpasses the ideal loss-equivalent direct-transmission method while operating at megahertz clock speeds. These results represent a crucial step towards practical quantum repeaters and large-scale quantum networks^20,21.

Generation and manipulation of Schrödinger cat states in Rydberg atom arrays

Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of "Schrödinger cat" states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.

Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays

We describe the zero-temperature phase diagram of a model of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena.

Topological Quantum Optics Using Atomlike Emitter Arrays Coupled to Photonic Crystals

We propose an experimentally feasible nanophotonic platform for exploring many-body physics in topological quantum optics. Our system is composed of a two-dimensional lattice of nonlinear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact through the guided modes of the photonic crystal, and a uniform magnetic field gives rise to large topological band gaps, robust edge states, and a nearly flat band with a nonzero Chern number. The presence of a topologically nontrivial nearly flat band paves the way for the realization of fractional quantum Hall states and fractional topological insulators in a topological quantum optical setting.

Strong Coupling of Two Individually Controlled Atoms via a Nanophotonic Cavity

We demonstrate photon-mediated interactions between two individually trapped atoms coupled to a nanophotonic cavity. Specifically, we observe collective enhancement when the atoms are resonant with the cavity and level repulsion when the cavity is coupled to the atoms in the dispersive regime. Our approach makes use of individual control over the internal states of the atoms and their position with respect to the cavity mode, as well as the light shifts to tune atomic transitions individually, allowing us to directly observe the anticrossing of the bright and dark two-atom states. These observations open the door for realizing quantum networks and studying quantum many-body physics based on atom arrays coupled to nanophotonic devices.

Controlling Excitons in an Atomically Thin Membrane with a Mirror

We demonstrate a new approach for dynamically manipulating the optical response of an atomically thin semiconductor, a monolayer of MoSe_{2}, by suspending it over a metallic mirror. First, we show that suspended van der Waals heterostructures incorporating a MoSe_{2} monolayer host spatially homogeneous, lifetime-broadened excitons. Then, we interface this nearly ideal excitonic system with a metallic mirror and demonstrate control over the exciton-photon coupling. Specifically, by electromechanically changing the distance between the heterostructure and the mirror, thereby changing the local photonic density of states in a controllable and reversible fashion, we show that both the absorption and emission properties of the excitons can be dynamically modulated. This electromechanical control over exciton dynamics in a mechanically flexible, atomically thin semiconductor opens up new avenues in cavity quantum optomechanics, nonlinear quantum optics, and topological photonics.

Integrating Neural Networks with a Quantum Simulator for State Reconstruction

We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.

Electrical control of interlayer exciton dynamics in atomically thin heterostructures

A van der Waals heterostructure built from atomically thin semiconducting transition metal dichalcogenides (TMDs) enables the formation of excitons from electrons and holes in distinct layers, producing interlayer excitons with large binding energy and a long lifetime. By employing heterostructures of monolayer TMDs, we realize optical and electrical generation of long-lived neutral and charged interlayer excitons. We demonstrate that neutral interlayer excitons can propagate across the entire sample and that their propagation can be controlled by excitation power and gate electrodes. We also use devices with ohmic contacts to facilitate the drift motion of charged interlayer excitons. The electrical generation and control of excitons provide a route for achieving quantum manipulation of bosonic composite particles with complete electrical tunability.

Quantum Network Nodes Based on Diamond Qubits with an Efficient Nanophotonic Interface

Quantum networks require functional nodes consisting of stationary registers with the capability of high-fidelity quantum processing and storage, which efficiently interface with photons propagating in an optical fiber. We report a significant step towards realization of such nodes using a diamond nanocavity with an embedded silicon-vacancy (SiV) color center and a proximal nuclear spin. Specifically, we show that efficient SiV-cavity coupling (with cooperativity C>30) provides a nearly deterministic interface between photons and the electron spin memory, featuring coherence times exceeding 1 ms. Employing coherent microwave control, we demonstrate heralded single photon storage in the long-lived spin memory as well as a universal control over a cavity-coupled two-qubit register consisting of a SiV and a proximal ^{13}C nuclear spin with nearly second-long coherence time, laying the groundwork for implementing quantum repeaters.

Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms

We report the implementation of universal two- and three-qubit entangling gates on neutral-atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states and are implemented in parallel on several clusters of atoms in a one-dimensional array of optical tweezers. Specifically, we realize the controlled-phase gate, enacted by a novel, fast protocol involving only global coupling of two qubits to Rydberg states. We benchmark this operation by preparing Bell states with fidelity F≥95.0(2)%, and extract gate fidelity ≥97.4(3)%, averaged across five atom pairs. In addition, we report a proof-of-principle implementation of the three-qubit Toffoli gate, in which two control atoms simultaneously constrain the behavior of one target atom. These experiments demonstrate key ingredients for high-fidelity quantum information processing in a scalable neutral-atom platform.

Optical Interferometry with Quantum Networks

We propose a method for optical interferometry in telescope arrays assisted by quantum networks. In our approach, the quantum state of incoming photons along with an arrival time index are stored in a binary qubit code at each receiver. Nonlocal retrieval of the quantum state via entanglement-assisted parity checks at the expected photon arrival rate allows for direct extraction of the phase difference, effectively circumventing transmission losses between nodes. Compared to prior proposals, our scheme (based on efficient quantum data compression) offers an exponential decrease in required entanglement bandwidth. Experimental implementation is then feasible with near-term technology, enabling optical imaging of astronomical objects akin to well-established radio interferometers and pushing resolution beyond what is practically achievable classically.

Large-scale uniform optical focus array generation with a phase spatial light modulator

In this Letter, to the best of our knowledge, we report a new method to generate uniform large-scale optical focus arrays (LOFAs). By identifying and removing undesired phase rotation in the iterative Fourier transform algorithm (IFTA), our approach rapidly produces computer-generated holograms of highly uniform LOFAs. The new algorithm also shows a faster compensation of system-induced LOFA intensity inhomogeneity than the conventional IFTA. After only three adaptive correction steps, we demonstrate LOFAs consisting of O(10³) optical foci with an intensity uniformity greater than 98%.

Electrically Tunable Exciton-Plasmon Coupling in a WSe2 Monolayer Embedded in a Plasmonic Crystal Cavity

We realize a new electroplasmonic switch based upon electrically tunable exciton-plasmon interactions. The device consists of a hexagonal boron nitride (hBN)-encapsulated tungsten diselenide (WSe₂) monolayer on top of a single-crystalline silver substrate. The ultrasmooth silver substrate serves a dual role as the medium to support surface plasmon polaritons (SPPs) and the bottom gate electrode to tune the WSe₂ exciton energy and brightness through electrostatic doping. To enhance the exciton-plasmon coupling, we implement a plasmonic crystal cavity on top of the hBN/WSe₂/hBN/Ag heterostructure with a quality factor reaching 550. The tight confinement of the SPPs in the plasmonic cavity enables strong coupling between excitons and SPPs when the WSe₂ exciton absorption is resonant with the cavity mode, leading to a vacuum Rabi splitting of up to 18 meV. This strong coupling can also be switched off with the application of a modest gate voltage that increases the doping density in the monolayer. This demonstration paves the way for new plasmonic modulators and a general device architecture to enhance light-matter interactions between SPPs and various embedded emitters.

Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasilocal deformation of the Rydberg-blockaded Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying nonintegrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates-quantum many-body scars. Furthermore, using these insights, we construct a toy model that hosts exact quantum many-body scars, providing an intuitive explanation of their origin. Our results offer specific routes to enhancing coherent many-body revivals and provide a step toward establishing the stability of quantum many-body scars in the thermodynamic limit.

Electron-phonon instability in graphene revealed by global and local noise probes

Understanding and controlling nonequilibrium electronic phenomena is an outstanding challenge in science and engineering. By electrically driving ultraclean graphene devices out of equilibrium, we observe an instability that is manifested as substantially enhanced current fluctuations and suppressed conductivity at microwave frequencies. Spatial mapping of the nonequilibrium current fluctuations using nanoscale magnetic field sensors reveals that the fluctuations grow exponentially along the direction of carrier flow. Our observations, including the dependence on density and temperature, are consistently explained by the emergence of an electron-phonon Cerenkov instability at supersonic drift velocities. These results offer the opportunity for tunable terahertz generation and active phononic devices based on two-dimensional materials.

Stepwise Ligand-induced Self-assembly for Facile Fabrication of Nanodiamond-Gold Nanoparticle Dimers via Noncovalent Biotin-Streptavidin Interactions

Nanodiamond-gold nanoparticle (ND-AuNP) dimers constitute a potent tool for controlled thermal heating of biological systems on the nanoscale, by combining a local light-induced heat source with a sensitive local thermometer. Unfortunately, previous solution-based strategies to build ND-AuNP conjugates resulted in large nanoclusters or a broad population of multimers with limited separation efficiency. Here, we describe a new strategy to synthesize discrete ND-AuNP dimers via the synthesis of biotin-labeled DNA-AuNPs through thiol chemistry and its immobilization onto the magnetic bead (MB) surface, followed by reacting with streptavidin-labeled NDs. The dimers can be easily released from MB via a strand displacement reaction and separated magnetically. Our method is facile, convenient, and scalable, ensuring high-throughput formation of very stable dimer structures. This ligand-induced self-assembly approach enables the preparation of a wide variety of dimers of designated sizes and compositions, thus opening up the possibility that they can be deployed in many biological actuation and sensing applications.

Probing Quantum Thermalization of a Disordered Dipolar Spin Ensemble with Discrete Time-Crystalline Order

We investigate thermalization dynamics of a driven dipolar many-body quantum system through the stability of discrete time crystalline order. Using periodic driving of electronic spin impurities in diamond, we realize different types of interactions between spins and demonstrate experimentally that the interplay of disorder, driving, and interactions leads to several qualitatively distinct regimes of thermalization. For short driving periods, the observed dynamics are well described by an effective Hamiltonian which sensitively depends on interaction details. For long driving periods, the system becomes susceptible to energy exchange with the driving field and eventually enters a universal thermalizing regime, where the dynamics can be described by interaction-induced dephasing of individual spins. Our analysis reveals important differences between thermalization of long-range Ising and other dipolar spin models.

Periodic Orbits, Entanglement, and Quantum Many-Body Scars in Constrained Models: Matrix Product State Approach

We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motion for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a theoretical framework for understanding quantum dynamics in a class of constrained spin models, which allow us to examine the recently suggested explanation of "quantum many-body scarring" [Nat. Phys. 14, 745 (2018)NPAHAX1745-247310.1038/s41567-018-0137-5], and establish a possible connection to the corresponding phenomenon in chaotic single-particle systems.

High-Fidelity Control and Entanglement of Rydberg-Atom Qubits

Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities associated with such Rydberg excitations. We report progress towards high-fidelity quantum control of Rydberg-atom qubits. Enabled by a reduction in laser phase noise, our approach yields a significant improvement in coherence properties of individual qubits. We further show that this high-fidelity control extends to the multi-particle case by preparing a two-atom entangled state with a fidelity exceeding 0.97(3), and extending its lifetime with a two-atom dynamical decoupling protocol. These advances open up new prospects for scalable quantum simulation and quantum computation with neutral atoms.

Quantum Nonlinear Optics in Atomically Thin Materials

We show that a nonlinear optical response associated with a resonant, atomically thin material can be dramatically enhanced by placing it in front of a partially reflecting mirror, rendering otherwise weakly nonlinear systems suitable for experiments and applications involving quantum nonlinear optics. Our approach exploits the nonlinear response of long-lived polariton resonances that arise at particular distances between the material and the mirror. The scheme is entirely based on free-space optics, eliminating the need for cavities or complex nanophotonic structures. We analyze a specific implementation based on exciton-polariton resonances in two-dimensional semiconductors and discuss the role of imperfections and loss.

High-resolution magnetic resonance spectroscopy using a solid-state spin sensor

Quantum systems that consist of solid-state electronic spins can be sensitive detectors of nuclear magnetic resonance (NMR) signals, particularly from very small samples. For example, nitrogen-vacancy centres in diamond have been used to record NMR signals from nanometre-scale samples, with sensitivity sufficient to detect the magnetic field produced by a single protein. However, the best reported spectral resolution for NMR of molecules using nitrogen-vacancy centres is about 100 hertz. This is insufficient to resolve the key spectral identifiers of molecular structure that are critical to NMR applications in chemistry, structural biology and materials research, such as scalar couplings (which require a resolution of less than ten hertz) and small chemical shifts (which require a resolution of around one part per million of the nuclear Larmor frequency). Conventional, inductively detected NMR can provide the necessary high spectral resolution, but its limited sensitivity typically requires millimetre-scale samples, precluding applications that involve smaller samples, such as picolitre-volume chemical analysis or correlated optical and NMR microscopy. Here we demonstrate a measurement technique that uses a solid-state spin sensor (a magnetometer) consisting of an ensemble of nitrogen-vacancy centres in combination with a narrowband synchronized readout protocol to obtain NMR spectral resolution of about one hertz. We use this technique to observe NMR scalar couplings in a micrometre-scale sample volume of approximately ten picolitres. We also use the ensemble of nitrogen-vacancy centres to apply NMR to thermally polarized nuclear spins and resolve chemical-shift spectra from small molecules. Our technique enables analytical NMR spectroscopy at the scale of single cells.

Critical Thermalization of a Disordered Dipolar Spin System in Diamond

Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law decay with disorder-dependent exponents; this behavior is modified at late times owing to many-body interactions. These observations are quantitatively explained by a resonance counting theory that incorporates the effects of both disorder and interactions.