Twin matter waves for interferometry beyond the classical limit

Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing

Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction-enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.

Spin- and Momentum-Correlated Atom Pairs Mediated by Photon Exchange and Seeded by Vacuum Fluctuations

Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this Letter, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single channel or two discernible channels. The scheme is independent of collisional interactions, fast, and tunable. We observe a collectively enhanced production of pairs and probe interspin correlations in momentum space. We characterize the emergent pair statistics and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.

Squeezing Multilevel Atoms in Dark States via Cavity Superradiance

We describe a method to create and store scalable and long-lived entangled spin-squeezed states within a manifold of many-body cavity dark states using collective emission of light from multilevel atoms inside an optical cavity. We show that the system can be tuned to generate squeezing in a dark state where it will be immune to superradiance. We also show more generically that squeezing can be generated using a combination of superradiance and coherent driving in a bright state, and subsequently be transferred via single-particle rotations to a dark state where squeezing can be stored. Our findings, readily testable in current optical cavity experiments with alkaline-earth-like atoms, can open a path for dissipative generation and storage of metrologically useful states in optical transitions.

Tomography of a Number-Resolving Detector by Reconstruction of an Atomic Many-Body Quantum State

The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.

Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms

We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.

Phase estimation of definite photon number states by using quantum circuits

We propose a method to map the conventional optical interferometry setup into quantum circuits. The unknown phase shift inside a Mach-Zehnder interferometer in the presence of photon loss is estimated by simulating the quantum circuits. For this aim, we use the Bayesian approach in which the likelihood functions are needed, and they are obtained by simulating the appropriate quantum circuits. The precision of four different definite photon-number states of light, which all possess six photons, is compared. The measurement scheme that we have considered is counting the number of photons detected after the final beam splitter of the interferometer, and photon loss is modeled by using fictitious beam splitters in the arms of the interferometer. Our results indicate that three of the four definite photon-number states considered can have better precision than the standard interferometry limit whenever the photon loss rate is in a specific range. In addition, the Fisher information for the four definite photon-number states in the setup is also estimated to check the optimality of the chosen measurement scheme.

Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles

We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.

Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models

We study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity

We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.

Measuring Correlations from the Collective Spin Fluctuations of a Large Ensemble of Lattice-Trapped Dipolar Spin-3 Atoms

We perform collective spin measurements to study the buildup of two-body correlations between ≈10^{4} spin s=3 chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with analytical short- and long-time expansions and numerical simulations. Our Letter shows that measuring fluctuations of spin populations for s>1/2 spins provides new ways to characterize correlations in quantum many-body systems.

Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits

Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28}  dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.

Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below ℏ

We present a magnetic sensor with energy resolution per bandwidth [Formula: see text] We show how a 87Rb single-domain spinor Bose-Einstein condensate, detected by nondestructive Faraday rotation probing, achieves single-shot low-frequency magnetic sensitivity of 72(8) fT measuring a volume [Formula: see text] for 3.5 s, and thus, [Formula: see text] We measure experimentally the condensate volume, spin coherence time, and readout noise and use phase space methods, backed by three-dimensional mean-field simulations, to compute the spin noise. Contributions to the spin noise include one-body and three-body losses and shearing of the projection noise distribution, due to competition of ferromagnetic contact interactions and quadratic Zeeman shifts. Nonetheless, the fully coherent nature of the single-domain, ultracold two-body interactions allows the system to escape the coherence vs. density trade-off that imposes an energy resolution limit on traditional spin precession sensors. We predict that other Bose-condensed alkalis, especially the antiferromagnetic 23Na, can further improve the energy resolution of this method.

Reduction-based strategy for optimal control of Bose-Einstein condensates

Applications of Bose-Einstein condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to the time-dependent Gross-Pitaevskii equation (GPE) model of BEC in multiple space dimensions, results in a large computational problem. We propose a control method based on first reducing the problem, using a Galerkin expansion, from a partial differential equation to a low-dimensional Hamiltonian ordinary differential equation system. We then apply a two-stage hybrid control strategy. At the first stage, we approximate the control using a second Galerkin-like method known as the chopped random basis to derive a finite-dimensional nonlinear programing problem, which we solve with a differential evolution algorithm. This search method then yields a candidate local minimum which we further refine using a variant of gradient descent. This hybrid strategy allows us to greatly reduce excitations both in the reduced model and the full GPE system.

Interaction Control and Bright Solitons in Coherently Coupled Bose-Einstein Condensates

We demonstrate fast control of the interatomic interactions in a Bose-Einstein condensate by coherently coupling two atomic states with intra- and interstate scattering lengths of opposite signs. We measure the elastic and inelastic scattering properties of the system and find good agreement with a theoretical model describing the interactions between dressed states. In the attractive regime, we observe the formation of bright solitons formed by dressed-state atoms. Finally, we study the response of the system to an interaction quench from repulsive to attractive values, and observe how the resulting modulational instability develops into a bright soliton train.

Delta-Kick Squeezing

We explore the possibility to overcome the standard quantum limit (SQL) in a free-fall atom interferometer using a Bose-Einstein condensate (BEC) in either of the two relevant cases of Bragg or Raman scattering light pulses. The generation of entanglement in the BEC is dramatically enhanced by amplifying the atom-atom interactions via the rapid action of an external trap, focusing the matter waves to significantly increase the atomic densities during a preparation stage-a technique we refer to as delta-kick squeezing (DKS). The action of a second DKS operation at the end of the interferometry sequence allows one to implement a nonlinear readout scheme, making the sub-SQL sensitivity highly robust against imperfect atom counting detection. We predict more than 30 dB of sensitivity gain beyond the SQL for the variance, assuming realistic parameters and 10^{6}  atoms.

Scaling Laws for the Sensitivity Enhancement of Non-Gaussian Spin States

We identify the large-N scaling of the metrological quantum gain offered by over-squeezed spin states that are accessible by one-axis twisting, as a function of the preparation time. We further determine how the scaling is modified by relevant decoherence processes and predict a discontinuous change of the quantum gain at a critical preparation time that depends on the noise. Our analytical results provide recipes for optimal and feasible implementations of quantum enhancements with non-Gaussian spin states in existing experiments, well beyond the reach of spin squeezing.

Momentum Entanglement for Atom Interferometry

Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise is large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8)  dB. Entanglement-enhanced atom interferometers promise unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.

Emission of Spin-Correlated Matter-Wave Jets from Spinor Bose-Einstein Condensates

We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of ^{7}Li atoms. Directional atomic beams with |F=1,m_{F}=1⟩ and |F=1,m_{F}=-1⟩ spin states are generated from |F=1,m_{F}=0⟩ state condensates or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states (|F=1,m_{F}=±1⟩) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter- and intraspin-momentum correlation peaks display a high-contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level. Our Letter paves the way to generating macroscopic quantum entanglement with the spin and motional degree of freedom with massive particles. It has a wide range of applications from quantum information science to the fundamental studies of quantum entanglement.

Interferometric Order Parameter for Excited-State Quantum Phase Transitions in Bose-Einstein Condensates

Excited-state quantum phase transitions extend the notion of quantum phase transitions beyond the ground state. They are characterized by closing energy gaps amid the spectrum. Identifying order parameters for excited-state quantum phase transitions poses, however, a major challenge. We introduce a topological order parameter that distinguishes excited-state phases in a large class of mean-field models and can be accessed by interferometry in current experiments with spinor Bose-Einstein condensates. Our work opens a way for the experimental characterization of excited-state quantum phases in atomic many-body systems.

From Many-Body Oscillations to Thermalization in an Isolated Spinor Gas

The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin-1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the nonlinearity of the spectrum leads to irreversibility, characterized by a universal behavior. When the integrability of the Hamiltonian is broken, a chaotic dynamics emerges and leads to thermalization, in agreement with the eigenstate thermalization hypothesis paradigm.

Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning

An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20  dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.

Observation of Universal Quench Dynamics and Townes Soliton Formation from Modulational Instability in Two-Dimensional Bose Gases

We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.

Geometric Pathway to Scalable Quantum Sensing

Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large N spin entangled states is challenging in the presence of decoherence. We present a quantum control strategy using highly nonlinear geometric phase gates which can be used for generic state or unitary synthesis on the Dicke subspace with O(N) or O(N^{2}) gates, respectively. The method uses a dispersive coupling of the spins to a common bosonic mode and does not require addressability, special detunings, or interactions between the spins. By using amplitude amplification our control sequence for preparing states ideal for metrology can be significantly simplified to O(N^{5/4}) geometric phase gates with action angles O(1/N) that are more robust to mode decay. The geometrically closed path of the control operations ensures the gates are insensitive to the initial state of the mode and the sequence has built-in dynamical decoupling providing resilience to dephasing errors.

High-Precision Quantum-Enhanced Gravimetry with a Bose-Einstein Condensate

We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between 10^{4} and 10^{6} in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.

Quantum hybrid optomechanical inertial sensing

We discuss the design of quantum hybrid inertial sensor that combines an optomechanical inertial sensor with the retroreflector of a cold atom interferometer. This sensor fusion approach provides absolute and high-accuracy measurements with cold atom interferometers, while utilizing the optomechanical inertial sensor at frequencies above the repetition rate of the atom interferometer. This improves the overall measurement bandwidth as well as the robustness and field deployment capabilities of these systems. We evaluate which parameters yield an optimal acceleration sensitivity, from which we anticipate a noise floor at nano-g levels from DC to 1 kHz.

Multiparameter squeezing for optimal quantum enhancements in sensor networks

Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.

Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level

Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.

Activating Hidden Metrological Usefulness

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian for which a given quantum state performs the best compared to separable states. We obtain analytically the optimal Hamiltonian for some quantum states with a high symmetry. We show that all bipartite entangled pure states outperform separable states in metrology. Some potential applications of the results are also suggested.

Nematic-Orbit Coupling and Nematic Density Waves in Spin-1 Condensates

We propose the creation of artificial nematic-orbit coupling in spin-1 Bose-Einstein condensates, in analogy with spin-orbit coupling. Using a suitably designed microwave chip, the quadratic Zeeman shift, normally uniform in space, can be made to be spatiotemporally varying, leading to a coupling between spatial and nematic degrees of freedom. A phase diagram is explored where three quantum phases with the nematic order emerge: easy axis, easy plane with single-well structure, and easy plane with double-well structure in momentum space. By including spin-dependent and spin-independent interactions, we also obtain the low energy excitation spectra in these three phases. Last, we show that the nematic-orbit coupling leads to a periodic nematic density modulation in relation to the period λ_{T} of the cosinusoidal quadratic Zeeman term. Our results point to the rich possibilities for manipulation of tensorial degrees of freedom in ultracold gases without requiring Raman lasers, and therefore, obviating light-scattering induced heating.

Quantum Interferometer Combining Squeezing and Parametric Amplification

High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24  dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.

Quantum Autoencoders to Denoise Quantum Data

Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders-neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.

Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors

Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.

Heralded Generation of Macroscopic Superposition States in a Spinor Bose-Einstein Condensate

Macroscopic superposition states enable fundamental tests of quantum mechanics and hold a huge potential in metrology, sensing, and other quantum technologies. We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a spin-1 Bose-Einstein condensate. Measuring the number of particles in one mode prepares with large probability highly entangled macroscopic superposition states in the two remaining modes. The macroscopic superposition states are heralded by the measurement outcome. Our protocol is robust under realistic conditions in current experiments, including finite adiabaticity, particle loss, and measurement uncertainty.

Helicity-Changing Brillouin Light Scattering by Magnons in a Ferromagnetic Crystal

Brillouin light scattering in ferromagnetic materials usually involves one magnon and two photons and their total angular momentum is conserved. Here, we experimentally demonstrate the presence of a helicity-changing two-magnon Brillouin light scattering in a ferromagnetic crystal, which can be viewed as a four-wave mixing process involving two magnons and two photons. Moreover, we observe an unconventional helicity-changing one-magnon Brillouin light scattering, which apparently infringes the conservation law of the angular momentum. We show that the crystal angular momentum intervenes to compensate the missing angular momentum in the latter scattering process.

Efficient Generation of Many-Body Entangled States by Multilevel Oscillations

We generate high-fidelity massively entangled states in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC) by utilizing multilevel oscillations. Combining the multilevel oscillations with additional adiabatic drives, we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting, from microgauss to milligauss, for a ^{23}Na spinor BEC. The achieved high fidelities over 96% show that two kinds of massively entangled states, the many-body singlet state and the twin-Fock state, are almost perfectly generated. The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of atom number fluctuations and stray magnetic fields, illustrating the robustness of our protocol under real experimental conditions. The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science.

Many-Body Entanglement in Short-Range Interacting Fermi Gases for Metrology

We explore many-body entanglement in spinful Fermi gases with short-range interactions, for metrology purposes. We characterize the emerging quantum phases via density-matrix renormalization group simulations and quantify their entanglement content for metrological usability via quantum Fisher information (QFI). Our study establishes a method, promoting QFI to be an order parameter. Short-range interactions reveal to build up metrologically promising entanglement in the XY-ferromagnetic and cluster ordering, the cluster physics being unexplored so far.

Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions

The quantum noise of the vacuum limits the achievable sensitivity of quantum sensors. In non-classical measurement schemes the noise can be reduced to overcome this limitation. However, schemes based on squeezed or Schrödinger cat states require alignment of the relative phase between the measured interaction and the non-classical quantum state. Here we present two measurement schemes on a trapped ion prepared in a motional Fock state for displacement and frequency metrology that are insensitive to this phase. The achieved statistical uncertainty is below the standard quantum limit set by quantum vacuum fluctuations, enabling applications in spectroscopy and mass measurements.

Quantum metrology allows surpassing the standard quantum limit, but methods relying on squeezing require to know the orientation of the squeezed quadrature with respect to the signal. Here, instead, the authors propose a phase-insensitive Fock-state-based protocol, and demonstrate it using trapped ions.

Supersolid-Based Gravimeter in a Ring Cavity

We propose a novel type of composite light-matter interferometer based on a supersolidlike phase of a driven Bose-Einstein condensate coupled to a pair of degenerate counterpropagating electromagnetic modes of an optical ring cavity. The supersolidlike condensate under the influence of the gravity drags the cavity optical potential with itself, thereby changing the relative phase of the two cavity electromagnetic fields. Monitoring the phase evolution of the cavity output fields thus allows for a nondestructive measurement of the gravitational acceleration. We show that the sensitivity of the proposed gravimeter exhibits Heisenberg-like scaling with respect to the atom number. As the relative phase of the cavity fields is insensitive to photon losses, the gravimeter is robust against these deleterious effects. For state-of-the-art experimental parameters, the relative sensitivity Δg/g of such a gravimeter could be of the order of 10^{-10}-10^{-8} for a condensate of a half a million atoms and interrogation time of the order of a few seconds.

Enhanced Magnetic Sensitivity with Non-Gaussian Quantum Fluctuations

The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In Gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-Gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of nonclassical states of the electronic spin J=8 of dysprosium atoms, created using light-induced nonlinear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-Gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.

Thermally robust spin correlations between two 85Rb atoms in an optical microtrap

The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped ⁸⁵Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for ⁸⁵Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation.

Spin-changing atomic collisions are important for thermally robust entanglement generation with applications in quantum information. Here the authors demonstrate record high spin state correlations and long spin relaxation times in the collision of two Rb atoms at relatively warm temperatures.

Rapid Production of Many-Body Entanglement in Spin-1 Atoms via Cavity Output Photon Counting

We propose a simple and efficient method for generating metrologically useful quantum entanglement in an ensemble of spin-1 atoms that interacts with a high-finesse optical cavity mode. It requires straightforward preparation of N atoms in the m_{F}=0 sublevel, tailoring of the atom-field interaction to give an effective Tavis-Cummings model for the collective spin-1 ensemble, and a photon counting measurement on the cavity output field. The photon number provides a projective measurement of the collective spin length S, which, for the chosen initial state, is heavily weighted around values S≃sqrt[N], for which the corresponding spin states are strongly entangled and exhibit Heisenberg scaling of the metrological sensitivity with N, as quantified by the quantum Fisher information.

Metrological Nonlinear Squeezing Parameter

The well-known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally feasible recipes for a high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and nonclassicality witnesses for complex quantum states.

Correlations in high-harmonic generation of matter-wave jets revealed by pattern recognition

Correlations in interacting many-body systems are key to the study of quantum matter. The complexity of the correlations typically grows quickly as the system evolves and thus presents a challenge for experimental characterization and intuitive understanding. In a strongly driven Bose-Einstein condensate, we observe the high-harmonic generation of matter-wave jets with complex correlations as a result of bosonic stimulation. Based on a pattern recognition scheme, we identify a pattern of correlations that reveals the underlying secondary scattering processes and higher-order correlations. We show that pattern recognition offers a versatile strategy to visualize and analyze the quantum dynamics of a many-body system.

Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms

We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of 500  μm are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the m_{f}=0 Zeeman state, we observe correlated pair creation in the m_{f}=±1 states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.

Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom

Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. Here, we use dysprosium atoms-the most magnetic element in its ground state-to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J = 8. We drive coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states-close to the Heisenberg limit 2J = 16-and an intrinsic fragility to environmental noise.

Multipartite Entanglement at Finite Temperature

The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the universal phase diagram of the quantum Fisher information at a quantum phase transition. Different regions in the diagram are identified by characteristic scaling laws of the quantum Fisher information with respect to temperature. This feature has immediate consequences on the thermal robustness of quantum coherence and multipartite entanglement. We support the theoretical predictions with the analysis of paradigmatic spin systems showing symmetry-breaking quantum phase transitions and free-fermion models characterized by topological phases. In particular we show that topological systems are characterized by the survival of large multipartite entanglement, reaching the Heisenberg limit at finite temperature.

Characterization of Topological States via Dual Multipartite Entanglement

We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the spin operators defined in the dual lattice. We investigate an extended Kitaev chain with a Z symmetry identified equivalently by winding numbers and paired Majorana zero modes at each end. The topological phases with high winding numbers are detected by the scaling coefficient of the quantum Fisher information density with respect to generators in different dual lattices. Containing richer properties and more complex structures than bipartite entanglement, the dual multipartite entanglement of the topological state has promising applications in robust quantum computation and quantum metrology, and can be generalized to identify topological order in the Kitaev honeycomb model.

Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms

Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.

Entanglement between two spatially separated atomic modes

Modern quantum technologies in the fields of quantum computing, quantum simulation, and quantum metrology require the creation and control of large ensembles of entangled particles. In ultracold ensembles of neutral atoms, nonclassical states have been generated with mutual entanglement among thousands of particles. The entanglement generation relies on the fundamental particle-exchange symmetry in ensembles of identical particles, which lacks the standard notion of entanglement between clearly definable subsystems. Here, we present the generation of entanglement between two spatially separated clouds by splitting an ensemble of ultracold identical particles prepared in a twin Fock state. Because the clouds can be addressed individually, our experiments open a path to exploit the available entangled states of indistinguishable particles for quantum information applications.