We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition ${{}^{1}S}_0-{}^3{P}_0$ with an accuracy of a few hertz. Combined with one of the recently reported isotope-shift measurements of ${\mathrm{Yb}}^{+}$ on two optical transitions, the result allows us to construct the King plots—a set of scaled isotope shifts data on two different optical transitions plotted in two-dimensional plane. When only the leading-order terms of isotope shifts are taken into account, a King plot should exhibit a linear relation as a result of elimination of the leading nuclear-size dependence. Extremely large nonlinearity unexplainable by a quadratic field shift is revealed, which was proposed previously as a source of the observed nonlinearity of the King plot. We further construct the generalized King plot with three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the standard model. Our analysis of the generalized King plot shows a deviation from linearity at the $3\sigma$ level, indicating that there exist at least two higher-order contributions in the measured isotope shifts. Under reasonable assumptions, we obtain the upper bound of the product of the couplings for a new boson, mediating a force between electrons and neutrons—$|y_e{y}_n|/(\hslash c)<1\times {10}^{-10}$ for the mass less than 1 keV—with the 95% confidence level, providing an important step toward probing new physics via isotope-shift spectroscopy.

Neutral atom arrays are a rapidly developing platform for quantum science. Recently, alkaline earth atoms (AEAs) have attracted interest because their unique level structure provides several opportunities for improved performance. In this work, we present the first demonstration of a universal set of quantum gate operations on a nuclear spin qubit in an AEA, using ${}^{171}\mathrm{Yb}$. We implement narrow-line cooling and imaging using a newly discovered magic trapping wavelength at $\lambda =486.78\mathrm{nm}$. We also demonstrate nuclear spin initialization, readout, and single-qubit gates and observe long coherence times [$T_1\approx 20\mathrm{s}$ and $T_2^{*}=1.24(5)\mathrm{s}$] and a single-qubit operation fidelity ${\mathcal{F}}_{1Q}=0.99959(6)$. We also demonstrate two-qubit entangling gates using the Rydberg blockade, as well as coherent control of these gate operations using light shifts on the ${\mathrm{Yb}}^{+}$ ion core transition at 369 nm. These results are a significant step toward highly coherent quantum gates in AEA tweezer arrays.

We report on the realization of a fast, scalable, and high-fidelity qubit architecture, based on ${}^{171}\mathrm{Yb}$ atoms in an optical tweezer array. We demonstrate several attractive properties of this atom for its use as a building block of a quantum information processing platform. Its nuclear spin of $1/2$ serves as a long-lived and coherent two-level system, while its rich, alkaline-earth-like electronic structure allows for low-entropy preparation, fast qubit control, and high-fidelity readout. We present a near-deterministic loading protocol, which allows us to fill a $10\times 10$ tweezer array with 92.73(8)% efficiency and a single tweezer with 96.0(1.4)% efficiency. In the future, this loading protocol will enable efficient and uniform loading of target arrays with high probability, an essential step in quantum simulation and information applications. Employing a robust optical approach, we perform submicrosecond qubit rotations and characterize their fidelity through randomized benchmarking, yielding $5.2(5)\times {10}^{-3}$ error per Clifford gate. For quantum memory applications, we measure the coherence of our qubits with $T_2^{*}=3.7(4)\mathrm{s}$ and $T_2=7.9(4)\mathrm{s}$, many orders of magnitude longer than our qubit rotation pulses. We measure spin depolarization times on the order of tens of seconds and find that this can be increased to the 100 s scale through the application of a several-gauss magnetic field. Finally, we use 3D Raman-sideband cooling to bring the atoms near their motional ground state, which will be central to future implementations of two-qubit gates that benefit from low motional entropy.

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around $g_s/2\pi =40\mathrm{MHz}$. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around $2J/2\pi =20\mathrm{MHz}$. In addition, photon-number states are resolved from the shift $2{\chi }_s/2\pi =-13\mathrm{MHz}$ that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.

We investigate a model system for the rotational dynamics of inertial many-particle clustering, in which submillimeter objects are acoustically levitated in air. Driven by scattered sound, levitated grains self-assemble into a monolayer of particles, forming mesoscopic granular rafts with both an acoustic binding energy and a bending rigidity. Detuning the acoustic trap can give rise to stochastic forces and torques that impart angular momentum to levitated objects. As the angular momentum of a quasi-two-dimensional granular raft is increased, the raft deforms from a disk to an ellipse, eventually pinching off into multiple separate rafts, in a mechanism that resembles the breakup of a liquid drop. We extract the raft effective surface tension and elastic modulus and show that nonpairwise acoustic forces give rise to effective elastic moduli that scale with the raft size. We also show that the raft size controls the microstructural basis of plastic deformation, resulting in a transition from fracture to ductile failure.

We observe the emission of bunches of $k\ge 1$ photons by a circuit made of a microwave resonator in series with a voltage-biased tunable Josephson junction. The bunches are emitted at specific values $V_k$ of the bias voltage, for which each Cooper pair tunneling across the junction creates exactly $k$ photons in the resonator. The latter is a microfabricated spiral coil which resonates and leaks photons at 4.4 GHz in a measurement line. Its characteristic impedance of $1.97\mathrm{k}\mathrm{\Omega }$ is high enough to reach a strong junction-resonator coupling and a bright emission of the $k$-photon bunches. We show that a rotating-wave approximation treatment of the system accounts quantitatively for the observed radiation intensity, from $k=1$ to 6, and over 3 orders of magnitude when varying the Josephson energy $E_J$. We also measure the second-order correlation function of the radiated microwave to determine its Fano factor $F_k$, which in the low $E_J$ limit confirms with $F_k\simeq k$ the emission of $k$-photon bunches. At larger $E_J$, a more complex behavior is observed in quantitative agreement with numerical simulations.

We investigate the collective decay dynamics of atoms with a generic multilevel structure (angular momenta $F\leftrightarrow F^{\prime }$) coupled to two light modes of different polarization inside a cavity. In contrast to two-level atoms, we find that multilevel atoms can harbor eigenstates that are perfectly dark to cavity decay even within the subspace of permutationally symmetric states (collective Dicke manifold). The dark states arise from destructive interference between different internal transitions and are shown to be entangled. Remarkably, the superradiant decay of multilevel atoms can end up stuck in one of these dark states, where a macroscopic fraction of the atoms remains excited. This opens the door to the preparation of entangled dark states of matter through collective dissipation that are useful for quantum sensing and quantum simulation. Our predictions should be readily observable in current optical cavity experiments with alkaline-earth atoms or Raman-dressed transitions.

Cladding layers of waveguides prevent interchannel interference yet are unfavorable for the integration of photonic circuits. Here, we report the realization of ultracompact waveguide arrays, bends, and circuits with essentially zero interchannel separation. This supercompactness is achieved via arrays of waveguides with shifted spatial dispersions, where each waveguide functions as both the transmission channel and an effective “cladding layer” of its neighboring waveguides, and has been experimentally realized in low-loss all-dielectric photonic crystals. We show that the zero-spacing transmission array possesses the remarkable features of negligible crosstalk, high-efficiency sharp bending, and ultracompact photonic routing where the light can traverse the entire physical space. This finding opens a new avenue for extreme space utilization efficiency in waveguide physics and integrated photonics.

A thorough understanding of molecular scattering in the ultralow temperature regime is crucial for realizing long coherence times and enabling tunable interactions in molecular gases, systems which offer many opportunities in quantum simulation, quantum information, and precision measurement. Of particular importance is the nature of the long-lived intermediate complexes which may be formed in ultracold molecular collisions, as such complexes can dramatically affect the stability of molecular gases, even when exothermic reaction channels are not present. Here, we investigate collisional loss in an ultracold mixture of ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules and ${}^{87}\mathrm{Rb}$ atoms, where chemical reactions between the two species are energetically forbidden. Through direct detection of the ${{\mathrm{KRb}}_2}^{*}$ intermediate complexes formed from atom-molecule collisions, we show that a 1064 nm laser source used for optical trapping of the sample can efficiently deplete the complex population via photoexcitation, an effect which can explain the strong two-body loss observed in the mixture. By monitoring the time evolution of the ${{\mathrm{KRb}}_2}^{*}$ population after a sudden reduction in the 1064 nm laser intensity, we measure the lifetime of the complex [0.39(6) ms], as well as the photoexcitation rate for 1064 nm light [$0.50(3)\mu {\mathrm{s}}^{-1}(\mathrm{kW}/{\mathrm{cm}}^2{)}^{-1}$]. The observed lifetime, which is $\sim {10}^5$ times longer than recent estimates based on the Rice-Ramsperger-Kassel-Marcus statistical theory, calls for new theoretical insight to explain its origin.

Quantum processing architectures that include multiple qubit modalities offer compelling strategies for high-fidelity operations and readout, quantum error correction, and a path for scaling to large system sizes. Such hybrid architectures have been realized for leading platforms, including superconducting circuits and trapped ions. Recently, a new approach for constructing large, coherent quantum processors has emerged based on arrays of individually trapped neutral atoms. However, these demonstrations have been limited to arrays of a single atomic element where the identical nature of the atoms makes crosstalk-free control and nondemolition readout of a large number of atomic qubits challenging. Here we introduce a dual-element atom array with individual control of single rubidium and cesium atoms. We demonstrate their independent placement in arrays with up to 512 trapping sites and observe negligible crosstalk between the two elements. Furthermore, by continuously reloading one atomic element while maintaining an array of the other, we demonstrate a new continuous operation mode for atom arrays without any off-time. Our results enable avenues for auxiliary-qubit-assisted quantum protocols such as quantum nondemolition measurements and quantum error correction, as well as continuously operating quantum processors and sensors.

A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there. Despite the central role played by Anderson localization in the modern understanding of condensed matter, this “quantum boomerang” effect, an essential feature of the localized state, was only recently theoretically predicted. We report the experimental observation of the quantum boomerang effect. Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries. Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears. Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics. These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

Coherent feedback stabilizes a system toward a target state without the need of a measurement, thus avoiding the quantum backaction inherent to measurements. Here, we employ optical coherent feedback to remotely cool a nanomechanical membrane using atomic spins as a controller. Direct manipulation of the atoms allows us to tune from strong coupling to an overdamped regime. Making use of the full coherent control offered by our system, we perform spin-membrane state swaps combined with stroboscopic spin pumping to cool the membrane in a room-temperature environment to $T=216\mathrm{mK}$ (${\overline{n}}_m=2.3\times {10}^3\mathrm{phonons}$) in $200\mu \mathrm{s}$. We furthermore observe and study the effects of delayed feedback on the cooling performance. Starting from a cryogenically precooled membrane, this method would enable cooling of the mechanical oscillator close to its quantum mechanical ground state and the preparation of nonclassical states.

Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, midcircuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the $[[7,1,3]]$ color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of $1.7(2)\times {10}^{-3}$, compared to the average physical SPAM error $2.4(4)\times {10}^{-3}$ of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a $\overline{T}|+{⟩}_L$ magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.

Continued timing observations of the double pulsar PSR J0737–3039A/B, which consists of two active radio pulsars (A and B) that orbit each other with a period of 2.45 h in a mildly eccentric ($e=0.088$) binary system, have led to large improvements in the measurement of relativistic effects in this system. With a 16-yr data span, the results enable precision tests of theories of gravity for strongly self-gravitating bodies and also reveal new relativistic effects that have been expected but are now observed for the first time. These include effects of light propagation in strong gravitational fields which are currently not testable by any other method. In particular, we observe the effects of retardation and aberrational light bending that allow determination of the spin direction of the pulsar. In total, we detect seven post-Keplerian parameters in this system, more than for any other known binary pulsar. For some of these effects, the measurement precision is now so high that for the first time we have to take higher-order contributions into account. These include the contribution of the A pulsar’s effective mass loss (due to spin-down) to the observed orbital period decay, a relativistic deformation of the orbit, and the effects of the equation of state of superdense matter on the observed post-Keplerian parameters via relativistic spin-orbit coupling. We discuss the implications of our findings, including those for the moment of inertia of neutron stars, and present the currently most precise test of general relativity’s quadrupolar description of gravitational waves, validating the prediction of general relativity at a level of $1.3\times {10}^{-4}$ with 95% confidence. We demonstrate the utility of the double pulsar for tests of alternative theories of gravity by focusing on two specific examples and also discuss some implications of the observations for studies of the interstellar medium and models for the formation of the double pulsar system. Finally, we provide context to other types of related experiments and prospects for the future.

We discuss quantum variational optimization of Ramsey interferometry with ensembles of $N$ entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean squared error of the estimated phase for a given prior distribution; i.e., we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions. While in the present work variationally optimized circuits are found with classical simulations, optimization can also be performed “on” the (physical) quantum sensor, also in regimes not accessible to classical computations and in the presence of imperfections.

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlet-triplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

Under physiological conditions, ballistic long-range transfer of electronic excitations in molecular aggregates is generally expected to be suppressed by noise and dissipative processes. Hence, quantum phenomena are not considered to be relevant for the design of efficient and controllable energy transfer over significant length scales and timescales. Contrary to this conventional wisdom, here we show that the robust quantum properties of small configurations of repeating clusters of molecules can be used to tune energy-transfer mechanisms that take place on much larger scales. With the support of an exactly solvable model, we demonstrate that coherent exciton delocalization and dark states within unit cells can be used to harness dissipative phenomena of varying nature (thermalization, fluorescence, nonradiative decay, and weak intersite correlations) to support classical propagation over macroscopic distances. In particular, we argue that coherent delocalization of electronic excitations over just a few pigments can drastically alter the relevant dissipation pathways that influence the energy-transfer mechanism and thus serve as a molecular control tool for large-scale properties of molecular materials. Building on these principles, we use extensive numerical simulations to demonstrate that they can explain currently not-understood measurements of micron-scale exciton diffusion in nanofabricated arrays of bacterial photosynthetic complexes. Based on these results, we provide quantum design guidelines at the molecular scale to optimize both energy-transfer speed and range over macroscopic distances in artificial light-harvesting architectures.

Multiple aspects of an economy can be regulated, tampered with, or left to chance. Economic actors can exploit these degrees of freedom, at a cost, to bend the flow of wealth in their favor. If intervention becomes widespread, microeconomic strategies of different actors can build into emergent macroeconomic effects. How viable is a “rigged” economy? How do growing economic complexity and wealth affect it? We study rigged economies with a toy model. In it, economic degrees of freedom progress from minority to coordination games as intervention increases. Growing economic complexity spontaneously defuses cartels. But excessive complexity leads to large-fluctuations regimes, threatening the system’s stability. Simulations suggest that wealth must grow faster than linearly with economic complexity to avoid this regime and keep economies viable in the long run. We discuss a real-case scenario of multiple economic actors coordinated to result in an emergent upset of the stock market.

Suppressing noise in physical systems is of fundamental importance. As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level. However in the noisy, intermediate-scale quantum (NISQ) era, the complexity and scale required to adopt even the smallest QEC is prohibitive: a single logical qubit needs to be encoded into many thousands of physical qubits. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms) one can indeed achieve an effective exponential suppression. We take $n$ independently prepared circuit outputs to create a state whose symmetries prevent errors from contributing bias to the expected value. The approach is very well suited for current and near-term quantum devices as it is modular in the main computation and requires only a shallow circuit that bridges the $n$ copies immediately prior to measurement. Using no more than four circuit copies, we confirm error suppression below ${10}^{-6}$ for circuits consisting of several hundred noisy gates (2-qubit gate error 0.5%) in numerical simulations validating our approach.

Molecular matter-wave interferometry enables novel strategies for manipulating the internal mechanical motion of complex molecules. Here, we show how chiral molecules can be prepared in a quantum superposition of two enantiomers by far-field matter-wave diffraction and how the resulting tunneling dynamics can be observed. We determine the impact of rovibrational phase averaging and propose a setup for sensing enantiomer-dependent forces, parity-violating weak interactions, and environment-induced superselection of handedness, as suggested to resolve Hund’s paradox. Using ab initio tunneling calculations, we identify [4]-helicene derivatives as promising candidates to implement the proposal with state-of-the-art techniques. This work opens the door for quantum sensing with chiral molecules.