Approaching the Heisenberg Limit without Single-Particle Detection

Confined Meson Excitations in Rydberg-Atom Arrays Coupled to a Cavity Field

Confinement is a pivotal phenomenon in numerous models of high-energy and statistical physics. In this study, we investigate the emergence of confined meson excitations within a one-dimensional system, comprising Rydberg-dressed atoms trapped and coupled to a cavity field. This system can be effectively represented by an Ising-Dicke Hamiltonian model. The observed ground-state phase diagram reveals a first-order transition from a ferromagnetic-subradiant phase to a paramagnetic-superradiant phase. Notably, a quench near the transition point within the ferromagnetic-subradiant phase induces meson oscillations in the spins and leads to the creation of squeezed-vacuum light states. We suggest a method for the photonic characterization of these confined excitations, utilizing homodyne detection and single-site imaging techniques to observe the localized particles. The methodologies and results detailed in this Letter are feasible for implementation on existing cavity-QED platforms, employing Rydberg-atom arrays in deep optical lattices or optical tweezers.

Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules

Polar molecules confined in an optical lattice are a versatile platform to explore spin-motion dynamics based on strong, long-range dipolar interactions1,2. The precise tunability3 of Ising and spin-exchange interactions with both microwave and d.c. electric fields makes the molecular system particularly suitable for engineering complex many-body dynamics4-6. Here we used Floquet engineering7 to realize new quantum many-body systems of polar molecules. Using a spin encoded in the two lowest rotational states of ultracold 40K87Rb molecules, we mutually validated XXZ spin models tuned by a Floquet microwave pulse sequence against those tuned by a d.c. electric field through observations of Ramsey contrast dynamics. This validation sets the stage for the realization of Hamiltonians inaccessible with static fields. In particular, we observed two-axis twisting8 mean-field dynamics, generated by a Floquet-engineered XYZ model using itinerant molecules in two-dimensional layers. In the future, Floquet-engineered Hamiltonians could generate entangled states for molecule-based precision measurement9 or could take advantage of the rich molecular structure for quantum simulation of multi-level systems10,11.

Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics

Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.

Resilience of quantum spin fluctuations against Dzyaloshinskii-Moriya interaction

In low-dimensional systems, the lack of structural inversion symmetry combined with the spin-orbit coupling gives rise to an anisotropic antisymmetric superexchange known as the Dzyaloshinskii-Moriya interaction (DMI). Various features have been reported due to the presence of DMIs in quantum systems. We here study the one-dimensional spin-1/2 transverse field XY chains with a DMI at zero temperature. Our focus is on the quantum fluctuations of the spins measured by the spin squeezing and the entanglement entropy. We find that these fluctuations are resistant to the effect of the DMI in the system. This resistance will fail as soon as the system is placed in the chiral phase where its state behaves as a squeezed state, suggesting the merit of the chiral phase to be used for quantum metrology. Remarkably, we prove that the central charge vanishes on the critical lines between gapless chiral and ferromagnetic/paramagnetic phases where there is no critical scaling versus the system size for the spin squeezing parameter. Our phenomenal results provide a further understanding of the effects of the DMIs in the many-body quantum systems which may be testable in experiments.

Exploiting Nonclassical Motion of a Trapped Ion Crystal for Quantum-Enhanced Metrology of Global and Differential Spin Rotations

We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.

Entangled unique coherent line in the ground-state phase diagram of the spin-1/2 XX chain model with three-spin interaction

Entangled spin coherent states are a type of quantum states that involve two or more spin systems that are correlated in a nonclassical way. These states can improve metrology and information processing, as they can surpass the standard quantum limit, which is the ultimate bound for precision measurements using coherent states. However, finding entangled coherent states in physical systems is challenging because they require precise control and manipulation of the interactions between the modes. In this work we show that entangled unique coherent states can be found in the ground state of the spin-1/2 XX chain model with three-spin interaction, which is an exactly solvable model in quantum magnetism. We use the spin squeezing parameter, the l_{1}-norm of coherence, and the entanglement entropy as tools to detect and characterize these unique coherent states. We find that these unique coherent states exist in a gapless spin liquid phase, where they form a line that separates two regions with different degrees of squeezing. We call this line the entangled unique coherent line, as it corresponds to the almost maximum entanglement between two halves of the system. We also study the critical scaling of the spin squeezing parameter and the entanglement entropy versus the system size.

Combining Critical and Quantum Metrology

Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically, this increases the quantum Fisher information with respect to changes in system parameters and thus improves the optimally possible measurement precision limited by the Cramér-Rao bound. Hence critical metrology involves encoding information about the unknown parameter in changes of the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is encoded in the relative phases that excited system states accumulate during their time evolution. Here we introduce an approach combining these two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We show that the quantum Fisher information in this case exhibits an additional interference term originating from the interplay between eigenstate and relative phase changes. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach that nearly attains the maximum precision permissible under the Cramér-Rao bound. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.

Heisenberg-limited spin squeezing in a hybrid system with silicon-vacancy centers

In this paper, we investigate the spin squeezing in a hybrid quantum system consisting of a Silicon-Vacancy (SiV) center ensemble coupled to a diamond acoustic waveguide via the strain interaction. Two sets of non-overlapping driving fields, each contains two time-dependent microwave fields, are applied to this hybrid system. By modulating these fields, the one-axis twist (OAT) interaction and two-axis two-spin (TATS) interaction can be independently realized. In the latter case the squeezing parameter scales to spin number as ξ R2∼1.61N -0.64 with the consideration of dissipation, which is very close to the Heisenberg limit. Furthermore, this hybrid system allows for the study of spin squeezing generated by the simultaneous presence of OAT and TATS interactions, which reveals sensitivity to the parity of the number of spins Ntot, whether it is even or odd. Our scheme enriches the approach for generating Heisenberg-limited spin squeezing in spin-phonon hybrid systems and offers the possibility for future applications in quantum information processing.

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.

Quantum-enhanced sensing on optical transitions through finite-range interactions

The control over quantum states in atomic systems has led to the most precise optical atomic clocks so far1-3. Their sensitivity is bounded at present by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can-nevertheless-be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real-world sensors is extremely challenging. Here we illustrate a pathway for harnessing large-scale entanglement in an optical transition using 1D chains of up to 51 ions with interactions that decay as a power-law function of the ion separation. We show that our sensor can emulate many features of the one-axis-twisting (OAT) model, an iconic, fully connected model known to generate scalable squeezing4 and Greenberger-Horne-Zeilinger-like states5-8. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of the structure factor, that is, spin-wave excitations (SWE), at finite momenta, the generation of spin squeezing comparable with OAT (a Wineland parameter9,10 of -3.9 ± 0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of multi-headed cat states in the Q-distribution. We demonstrate the metrological utility of the states in a Ramsey-type interferometer, in which we reduce the measurement uncertainty by -3.2 ± 0.5 dB below the standard quantum limit for N = 51 ions.

Detection of Entangled States Supported by Reinforcement Learning

Discrimination of entangled states is an important element of quantum-enhanced metrology. This typically requires low-noise detection technology. Such a challenge can be circumvented by introducing nonlinear readout process. Traditionally, this is realized by reversing the very dynamics that generates the entangled state, which requires a full control over the system evolution. In this Letter, we present nonlinear readout of highly entangled states by employing reinforcement learning to manipulate the spin-mixing dynamics in a spin-1 atomic condensate. The reinforcement learning found results in driving the system toward an unstable fixed point, whereby the (to be sensed) phase perturbation is amplified by the subsequent spin-mixing dynamics. Working with a condensate of 10 900 ^{87}Rb atoms, we achieve a metrological gain of 6.97_{-1.38}^{+1.30}  dB beyond the classical precision limit. Our work will open up new possibilities in unlocking the full potential of entanglement caused quantum enhancement in experiments.

Squeezed Superradiance Enables Robust Entanglement-Enhanced Metrology Even with Highly Imperfect Readout

Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.

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.

Improving metrology with quantum scrambling

Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.

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.

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.

Squeezing and Overcoming the Heisenberg Scaling with Spin-Orbit Coupled Quantum Gases

We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can be facilitated via squeezed center-of-mass excitations of the atomic motion using 1D spin-orbit coupled fermions or strongly interacting bosons (Tonks-Girardeau gas). Based on predictions derived from analytic calculations of the corresponding quantum Fisher information, we then introduce a protocol which overcomes the Heisenberg scaling (and limit) with the help of a tailored excited and entangled many-body state of a noninteracting Bose-Einstein condensate. We identify corresponding optimal measurements and argue that even finite temperature as a source of decoherence is, in principle, rather favorable for the obtainable precision scaling.

Quantum-enabled millimetre wave to optical transduction using neutral atoms

Early experiments with transiting circular Rydberg atoms in a superconducting resonator laid the foundations of modern cavity and circuit quantum electrodynamics1, and helped explore the defining features of quantum mechanics such as entanglement. Whereas ultracold atoms and superconducting circuits have since taken rather independent paths in the exploration of new physics, taking advantage of their complementary strengths in an integrated system enables access to fundamentally new parameter regimes and device capabilities2,3. Here we report on such a system, coupling an ensemble of cold 85Rb atoms simultaneously to an, as far as we are aware, first-of-its-kind optically accessible, three-dimensional superconducting resonator4 and a vibration-suppressed optical cavity in a cryogenic (5 K) environment. To demonstrate the capabilities of this platform, and with an eye towards quantum networking5, we leverage the strong coupling between Rydberg atoms and the superconducting resonator to implement a quantum-enabled millimetre wave (mmwave) photon to optical photon transducer6. We measured an internal conversion efficiency of 58(11)%, a conversion bandwidth of 360(20) kHz and added thermal noise of 0.6 photons, in agreement with a parameter-free theory. Extensions of this technique will allow near-unity efficiency transduction in both the mmwave and microwave regimes. More broadly, our results open a new field of hybrid mmwave/optical quantum science, with prospects for operation deep in the strong coupling regime for efficient generation of metrologically or computationally useful entangled states7 and quantum simulation/computation with strong non-local interactions8.

Tunable itinerant spin dynamics with polar molecules

Strongly interacting spins underlie many intriguing phenomena and applications^1-4 ranging from magnetism to quantum information processing. Interacting spins combined with motion show exotic spin transport phenomena, such as superfluidity arising from pairing of spins induced by spin attraction^5,6. To understand these complex phenomena, an interacting spin system with high controllability is desired. Quantum spin dynamics have been studied on different platforms with varying capabilities^7-13. Here we demonstrate tunable itinerant spin dynamics enabled by dipolar interactions using a gas of potassium-rubidium molecules confined to two-dimensional planes, where a spin-1/2 system is encoded into the molecular rotational levels. The dipolar interaction gives rise to a shift of the rotational transition frequency and a collision-limited Ramsey contrast decay that emerges from the coupled spin and motion. Both the Ising and spin-exchange interactions are precisely tuned by varying the strength and orientation of an electric field, as well as the internal molecular state. This full tunability enables both static and dynamical control of the spin Hamiltonian, allowing reversal of the coherent spin dynamics. Our work establishes an interacting spin platform that allows for exploration of many-body spin dynamics and spin-motion physics using the strong, tunable dipolar interaction.

Quantum metrology with imperfect measurements

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections-with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

High finesse bow-tie cavity for strong atom-photon coupling in Rydberg arrays

We report a high-finesse bow-tie cavity designed for atomic physics experiments with Rydberg atom arrays. The cavity has a finesse of 51,000 and a waist of 7.1 μm at the cesium D2 line (852 nm). With these parameters, the cavity is expected to induce strong coupling between a single atom and a single photon, corresponding to a cooperativity per traveling mode of 35 at the cavity waist. To trap and image atoms, the cavity setup utilizes two in-vacuum aspheric lenses with a numerical aperture (NA) of 0.35 and is capable of housing NA = 0.5 microscope objectives. In addition, the large atom-mirror distance (≳1.5 cm) provides good optical access and minimizes stray electric fields at the position of the atoms. This cavity setup can operate in tandem with a Rydberg array platform, creating a fully connected system for quantum simulation and computation.

Optimal metrology with programmable quantum sensors

Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. Here we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a programmable quantum sensor operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped-ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45 ± 0.01, outperforming conventional spin-squeezing with a factor of 1.87 ± 0.03. Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59 ± 0.06 compared with traditional methods not using entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to 'self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be used without previous knowledge of the device or its noise environment.

Quantum Enhanced Cavity QED Interferometer with Partially Delocalized Atoms in Lattices

We propose a quantum enhanced interferometric protocol for gravimetry and force sensing using cold atoms in an optical lattice supported by a standing-wave cavity. By loading the atoms in partially delocalized Wannier-Stark states, it is possible to cancel the undesirable inhomogeneities arising from the mismatch between the lattice and cavity fields and to generate spin squeezed states via a uniform one-axis twisting model. The quantum enhanced sensitivity of the states is combined with the subsequent application of a compound pulse sequence that allows us to separate atoms by several lattice sites. This, together with the capability to load small atomic clouds in the lattice at micrometric distances from a surface, make our setup ideal for sensing short-range forces. We show that for arrays of 10^{4} atoms, our protocol can reduce the required averaging time by a factor of 10 compared to unentangled lattice-based interferometers after accounting for primary sources of decoherence.

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.

Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals

Fully controllable ultracold atomic systems are creating opportunities for quantum sensing, yet demonstrating a quantum advantage in useful applications by harnessing entanglement remains a challenging task. Here, we realize a many-body quantum-enhanced sensor to detect displacements and electric fields using a crystal of ~150 trapped ions. The center-of-mass vibrational mode of the crystal serves as a high-Q mechanical oscillator, and the collective electronic spin serves as the measurement device. By entangling the oscillator and collective spin and controlling the coherent dynamics via a many-body echo, a displacement is mapped into a spin rotation while avoiding quantum back-action and thermal noise. We achieve a sensitivity to displacements of 8.8 ± 0.4 decibels below the standard quantum limit and a sensitivity for measuring electric fields of 240 ± 10 nanovolts per meter in 1 second. Feasible improvements should enable the use of trapped ions in searches for dark matter.

Dynamical Generation of Spin Squeezing in Ultracold Dipolar Molecules

We study a bulk fermionic dipolar molecular gas in the quantum degenerate regime confined in a two-dimensional geometry. Using two rotational states of the molecules, we encode a spin 1/2 degree of freedom. To describe the many-body spin dynamics of the molecules, we derive a long-range interacting XXZ model valid in the regime where motional degrees of freedom are frozen. Because of the spatially extended nature of the harmonic oscillator modes, the interactions in the spin model are very long ranged, and the system behaves close to the collective limit, resulting in robust dynamics and generation of entanglement in the form of spin squeezing even at finite temperature and in the presence of dephasing and chemical reactions. We discuss how the internal state structure can be exploited to realize time reversal and enhanced metrological sensing protocols.

Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol

We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.

Protecting Spin Coherence in a Tunable Heisenberg Model

Using an ensemble of atoms in an optical cavity, we engineer a family of nonlocal Heisenberg Hamiltonians with continuously tunable anisotropy of the spin-spin couplings. We thus gain access to a rich phase diagram, including a paramagnetic-to-ferromagnetic Ising phase transition that manifests as a diverging magnetic susceptibility at the critical point. The susceptibility displays a symmetry between Ising interactions and XY (spin-exchange) interactions of the opposite sign, which is indicative of the spatially extended atomic system behaving as a single collective spin. Images of the magnetization dynamics show that spin-exchange interactions protect the coherence of the collective spin, even against inhomogeneous fields that completely dephase the noninteracting and Ising systems. Our results underscore prospects for harnessing spin-exchange interactions to enhance the robustness of spin squeezing protocols.

Protocol for Precise Field Sensing in the Optical Domain with Cold Atoms in a Cavity

In the context of quantum metrology, optical cavity-QED platforms have primarily been focused on the generation of entangled atomic spin states useful for next-generation frequency and time standards. Here, we report a complementary application: the use of optical cavities to generate nonclassical states of light for electric field sensing below the standard quantum limit. We show that cooperative atom-light interactions in the strong collective coupling regime can be used to engineer generalized atom-light cat states which enable quantum enhanced sensing of small displacements of the cavity field even in the presence of photon loss. We demonstrate that metrological gains of 10-20 dB below the standard quantum limit are within reach for current cavity-QED systems operating with long-lived alkaline-earth atoms.

Machine-Designed Sensor to Make Optimal Use of Entanglement-Generating Dynamics for Quantum Sensing

We use machine optimization to develop a quantum sensing scheme that achieves significantly better sensitivity than traditional schemes with the same quantum resources. Utilizing one-axis twisting dynamics to generate quantum entanglement, we find that, rather than dividing the temporal resources into separate "state-preparation" and "interrogation" stages, a complicated machine-designed sequence of rotations allows for the generation of metrologically useful entanglement while the parameter is interrogated. This provides much higher sensitivities for a given total time compared to states generated via traditional one-axis twisting schemes. This approach could be applied to other methods of generating quantum-enhanced states, allowing for atomic clocks, magnetometers, and inertial sensors with increased sensitivities.

Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas

We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.

Observation of a transition between dynamical phases in a quantum degenerate Fermi gas

A proposed paradigm for out-of-equilibrium quantum systems is that an analog of quantum phase transitions exists between parameter regimes of qualitatively distinct time-dependent behavior. Here, we present evidence of such a transition between dynamical phases in a cold-atom quantum simulator of the collective Heisenberg model. Our simulator encodes spin in the hyperfine states of ultracold fermionic potassium. Atoms are pinned in a network of single-particle modes, whose spatial extent emulates the long-range interactions of traditional quantum magnets. We find that below a critical interaction strength, magnetization of an initially polarized fermionic gas decays quickly, while above the transition point, the magnetization becomes long-lived because of an energy gap that protects against dephasing by the inhomogeneous axial field. Our quantum simulation reveals a nonequilibrium transition predicted to exist but not yet directly observed in quenched s-wave superconductors.

Squeezing out higher precision

Well-timed kicks to an ion's momentum enable better position measurements

Near-Unitary Spin Squeezing in ^{171}Yb

Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in ^{171}Yb, an optical lattice clock atom. The collective nuclear spin of ∼10^{3} atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical-clock transition of ^{171}Yb.

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.

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.

Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification

Homodyne measurement is a corner-stone method of quantum optics that measures the quadratures of light—the quantum optical analog of the canonical position and momentum. Standard homodyne, however, suffers from a severe bandwidth limitation: while the bandwidth of optical states can span many THz, standard homodyne is inherently limited to the electronically accessible MHz-to-GHz range, leaving a dramatic gap between relevant optical phenomena and the measurement capability. We demonstrate a fully parallel optical homodyne measurement across an arbitrary optical bandwidth, effectively lifting this bandwidth limitation completely. Using optical parametric amplification, which amplifies one quadrature while attenuating the other, we measure quadrature squeezing of 1.7 dB simultaneously across 55 THz, using the pump as the only local oscillator. As opposed to standard homodyne, our measurement is robust to detection inefficiency, and was obtained with >50% detection loss. Broadband parametric homodyne opens a wide window for parallel processing of quantum information.

Standard homodyne detection is intrinsically limited by the electronic bandwidth of the photo-detectors. Here, the authors exploit parametric amplification to demonstrate sub-shot-noise optical quadrature measurement across a bandwidth of 55 THz.

Optimal and secure measurement protocols for quantum sensor networks

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.

Optimal and Robust Quantum Metrology Using Interaction-Based Readouts

Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cramér-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.

Quasicontinuous-Variable Quantum Computation with Collective Spins in Multipath Interferometers

Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the resonators in multipath interferometers one can realize coupling between different samples, and that polynomial Hamiltonians can be constructed by repeated spin rotations and twisting induced by dispersive interaction of the atoms with light. Application can be expected in the efficient simulation of quantum systems.

Pumped-Up SU(1,1) Interferometry

Although SU(1,1) interferometry achieves Heisenberg-limited sensitivities, it suffers from one major drawback: Only those particles outcoupled from the pump mode contribute to the phase measurement. Since the number of particles outcoupled to these "side modes" is typically small, this limits the interferometer's absolute sensitivity. We propose an alternative "pumped-up" approach where all the input particles participate in the phase measurement and show how this can be implemented in spinor Bose-Einstein condensates and hybrid atom-light systems-both of which have experimentally realized SU(1,1) interferometry. We demonstrate that pumped-up schemes are capable of surpassing the shot-noise limit with respect to the total number of input particles and are never worse than conventional SU(1,1) interferometry. Finally, we show that pumped-up schemes continue to excel-both absolutely and in comparison to conventional SU(1,1) interferometry-in the presence of particle losses, poor particle-resolution detection, and noise on the relative phase difference between the two side modes. Pumped-up SU(1,1) interferometry therefore pushes the advantages of conventional SU(1,1) interferometry into the regime of high absolute sensitivity, which is a necessary condition for useful quantum-enhanced devices.

Quantum-Enhanced Sensing Based on Time Reversal of Nonlinear Dynamics

We experimentally demonstrate a nonlinear detection scheme exploiting time-reversal dynamics that disentangles continuous variable entangled states for feasible readout. Spin-exchange dynamics of Bose-Einstein condensates is used as the nonlinear mechanism which not only generates entangled states but can also be time reversed by controlled phase imprinting. For demonstration of a quantum-enhanced measurement we construct an active atom SU(1,1) interferometer, where entangled state preparation and nonlinear readout both consist of parametric amplification. This scheme is capable of exhausting the quantum resource by detecting solely mean atom numbers. Controlled nonlinear transformations widen the spectrum of useful entangled states for applied quantum technologies.

Detecting Large Quantum Fisher Information with Finite Measurement Precision

We propose an experimentally accessible scheme to determine the lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the measurement statistics of a state before and after a small unitary rotation. We argue that, in general, the limited resolution of collective observables prevents the detection of large QFI. This can be overcome by performing an additional operation prior to the measurement. We illustrate the power of this protocol for present-day spin-squeezing experiments, where the same operation used for the preparation of the initial spin-squeezed state improves also the measurement precision and hence the lower bound on the QFI by 2 orders of magnitude. We also establish a connection to the Leggett-Garg inequalities. We show how to simulate a variant of the inequalities with our protocol and demonstrate that large QFI is necessary for their violation with coarse-grained detectors.