Nonlocal entanglement between pair-correlated particles is a highly counter-intuitive aspect of quantum mechanics, where measurement on one particle can instantly affect the other, regardless of distance. While the rigorous Bell's inequality framework has enabled the demonstration of such entanglement in photons and atomic internal states, no experiment has yet involved motional states of massive particles. Here we report the experimental observation of Bell correlations in motional states of momentum-entangled ultracold helium atoms. Momentum-entangled pairs are first generated via s-wave collisions. Using a Rarity-Tapster interferometer and a Bell-test framework, we observe atom-atom correlations required for violation of a Bell inequality. This result shows the potential of ultracold atoms for fundamental tests of quantum mechanics and opens new avenues to studying gravitational effects in quantum states.

We investigate the generation of quantum states for precision metrology in noisy two-level systems. These states are obtained by optimizing a variational quantum circuit to maximize the quantum Fisher information (QFI) of the output state for a given decoherence rate and interaction Hamiltonian. The circuit architecture, inspired by twist-and-turn schemes, features a sequence of n entangling layers, each consisting of entangling gates followed by a global rotation. We observe notable improvements in the QFI as the circuit layer depth increases, even for appreciable noise rates, demonstrating that our entangle-rotate architecture expands the accessible state space under realistic noise conditions. Our approach thus provides a general and efficient framework for generating quantum-enhanced sensing states. Our analysis extends to systems of power-law interactions spanning from all-to-all to nearest-neighbor interactions. We also analyze the capabilities of our circuit to prepare states for system sizes greater than 8 qubits.

Scaling trapped-ion quantum sensors from single ions to large ensembles is a key challenge for next-generation precision measurements. At the same time, many ion species of interest for optical clocks and tests of fundamental physics lack closed cycling transitions required for direct laser cooling and state detection. Collective quantum logic spectroscopy addresses both limitations by coupling an ensemble of sensor, or spectroscopy, ions to one or more logic ions that provide sympathetic cooling and state readout. Here, we establish the fundamental performance limits and operating regimes of this protocol, identifying how the interaction strength, interrogation time, and logic-ensemble size govern sensitivity, dynamic range, and robustness to experimental imperfections. We show that quantum-limited sensitivity can be retained even with a single logic ion, while increasing the number of logic ions substantially improves readout efficiency and robustness. Beyond precision metrology, the same collective interface enables many-body measurements relevant to quantum information processing, including parity measurements and stabilizer-like syndrome extraction. Our results establish collective quantum logic spectroscopy as a scalable framework for optical clocks, quantum-enhanced sensing, and trapped-ion quantum information processing.

We propose a unifying framework for non-equilibrium relaxation dynamics in ensembles of positionally disordered interacting quantum spins based on the statistical properties, such as mean and variance, of the underlying disorder distribution. Our framework is validated through extensive exact numerical calculations and we use it to disentangle and understand the importance of dimensionality and interaction range for the observation of glassy (i.e., sub-exponential) decay dynamics. Leveraging the deterministic control of qubit positioning enabled by modern tweezer array architectures, we also introduce a method (“J-mapping”) that can be used to emulate the relaxation dynamics of a disordered system with arbitrary dimensionality and interaction range in bespoke one-dimensional arrays. Our approach paves the way towards tunable relaxation dynamics that can be explored in quantum simulators based on arrays of neutral atoms and molecules.

Quantum many-body systems driven far from equilibrium can exhibit chaos, entanglement, and non-classical correlations, yet directly observing these phenomena in large, closed quantum systems remains challenging. Here we realize the Dicke model – a fundamental description of light-matter interactions – in a two-dimensional crystal of approximately 100 trapped ions. The ions' internal state is optically coupled to the center of mass vibrational mode via an optical spin-dependent force, enabling unitary many-body dynamics beyond the mean-field and few-body limits. In the integrable regime, where the phonons can be adiabatically eliminated, we observe a dynamical phase transition between ferromagnetic to paramagnetic spin phases. In contrast, when the spins and phonons are strongly coupled, we observe clear signatures of non-integrable chaotic dynamics, including erratic phase-space trajectories and the exponential growth of excitations and entanglement quantified by the one-body Rényi entropy. By quenching from an unstable fixed point in the near-integrable regime, quantum noise can generate correlated spin-phonon excitations. Our numerical calculations, in clear agreement with experiment, reveal the generation of two-mode spin-phonon squeezing, 2.6 dB below the standard quantum limit (4.6 dB relative to the initial thermal state), followed by generalized vacuum Rabi collapses and revivals. Our results establish large ion crystals as scalable analog quantum simulators of non-equilibrium light-matter dynamics and provide a controlled platform for experimental studies of information scrambling and entanglement in closed many-body systems.

Using a strontium cavity-QED apparatus, we first explore dynamical phases of BCS superconductors and perform time-resolved spectral gap spectroscopy. We also observe the continuous dissipation-induced superradiant transition in the cooperative resonance fluorescence (CRF) model.

Many-body quantum chaos has immense potential as a tool to accelerate the preparation of entangled states and overcome challenges due to decoherence and technical noise. Here, we study how chaos in the paradigmatic Dicke model, which describes the uniform coupling of an ensemble of qubits to a common bosonic mode, can enable the rapid generation of non-Gaussian entangled spin-boson states without fine-tuning of system parameters or initial conditions. However, the complexity of these states means that unlocking their utility for quantum-enhanced sensing with standard protocols would require the measurement of complex or typically inaccessible observables. To address this challenge, we develop a sensing scheme based on interaction-based readout that enables us to implement near-optimal quantum-enhanced metrology of global spin rotations or bosonic displacements using only spin measurements. We show that our approach is robust to technical noise and imperfections and thus opens new opportunities to exploit complex entangled states generated by chaotic dynamics in current quantum science platforms such as trapped-ion and cavity-QED experiments.

We use an ensemble of laser-cooled strontium atoms in a high-finesse cavity to cleanly emulate the technique of rf spectroscopy employed in studies of BEC-BCS physics in fermionic superfluids of degenerate cold gases. Here, we leverage the multilevel internal structure of the atoms to study the physics of Cooper pair breaking in this system. In doing so, we observe and distinguish the properties of two distinct many-body gaps, the BCS pairing gap and the spectral gap, using nondestructive readout techniques. The latter is found to depend on the populations of the internal atomic states, reflecting the chemical potential dependence predicted in fermionic superfluids. This work opens the path for more fully exploiting the rich internal structure of atoms in cavity QED emulators to study both analogous systems and also more exotic states yet to be realized.

We investigate optimized quantum state preparation for quantum metrology applications in noisy environments. Using the QFI-Opt package, we simulate a low-depth variational quantum circuit (VQC) composed of a sequence of global rotations and entangling operations applied to a chain of qubits that are subject to dephasing noise. The parameters controlling the VQC are numerically optimized to maximize the quantum Fisher information, which characterizes the ultimate metrological sensitivity of a quantum state with respect to a global rotation. We find that regardless of the details of the entangling operation implemented in the VQC, the optimal quantum states can be broadly classified into a trio of qualitative regimes–cat-like, squeezed-like, and product states–associated with different dephasing rates. Our findings are relevant for designing optimal state-preparation strategies for next-generation quantum sensors exploiting entanglement, such as time and frequency standards and magnetometers, aimed at achieving state-of-the-art performance in the presence of noise and decoherence.

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.

We propose protocols for the creation of useful entangled states in a system of spins collectively coupled to a bosonic mode, directly applicable to trapped-ion and cavity QED setups. The protocols use coherent manipulations of the resonant spin-boson interactions naturally arising in these systems to prepare spin squeezed states exponentially fast in time. The resonance condition harnesses the full spin-boson coupling and thus avoids the slower timescales when operating in the off-resonance regime. We demonstrate the robustness of the protocols by analyzing the effects of natural sources of decoherence in these systems and show their advantage compared to more standard slower approaches where entanglement is generated with off-resonant spin-boson interactions.

Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the eigendecomposition of a matrix. We explored several automatic differentiation frameworks for these tasks, finding that no framework natively supports our application requirements. We therefore demonstrate a need for broader support of complex-valued, differentiable numerical integration in scientific computing libraries.

We propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via internal states of the atoms and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model, as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of non-equilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.

Optical tweezer arrays of neutral atoms provide a versatile platform for quantum simulation due to the range of interactions and Hamiltonians that can be realized and explored. We propose to simulate a two-component Bose-Hubbard model with power-law hopping using arrays of multilevel Rydberg atoms featuring resonant dipolar interactions. The diversity of states that can be used to encode the local Hilbert space of the BoseHubbard model enables control of the relative hopping rate of each component and even the realization of spinflip hopping. We use numerical simulations to show how multilevel Rydberg atoms provide an opportunity to explore the diverse nonequilibrium quench dynamics of the model. For example, we demonstrate a separation of the relaxation time scales of effective spin and charge degrees of freedom, and observe regimes of slow relaxation when the effective hopping rates of the two components are vastly different due to dynamical constraints arising from hardcore boson interactions. We discuss prospects for studying these effects in state-of-the-art Rydberg tweezer arrays.

We theoretically investigate the out-of-equilibrium dynamics of irregular one- and two-dimensional arrays of Rydberg dipoles featuring spatially anisotropic interactions. Starting from a collectively polarized initial state, we map out the dynamical phase diagram and identify a crossover between regimes of regular and anomalously slow relaxation of the initial collective order that strongly depends on both the degree of interaction disorder and anisotropy. In addition, we find that the regime of slow relaxation is characterized by a subballistic propagation of correlations that remained confined to short distances even at long times. To explain our findings we develop an analytic model based on decoupled clusters of interacting dipoles that goes beyond prior theoretical works and enables us to identify multiple relaxation timescales. Our findings can be relevant for a wide variety of quantum science platforms naturally featuring disordered dipolar interactions, including polar molecules, frozen Rydberg gases, and nitrogen-vacancy centers.

We experimentally demonstrate that well-designed driven lattices are versatile tools to simultaneously tune multiple key parameters (namely spin-dependent interactions, spinor phase, and Zeeman energy) for manipulating phase diagrams of spinor gases with negligible heating and atom losses. This opens a new avenue for studying dynamical phase transitions in engineered Hamiltonians. The driven lattice creates additional separatrices in phase space at driving-frequency-determined locations, with progressively narrower separatrices at higher Zeeman energies due to modulation-induced higher harmonics. The vastly expanded range of magnetic fields at which significant spin dynamics occur and improved sensitivities at higher harmonics represent a step towards quantum sensing with ultracold gases.

The generation of very narrow linewidth light sources is of great importance in modern science. One such source is the superradiant laser, which relies on collectively interacting ultra long lived dipoles driven by incoherent light. Here we discuss a different way of generating spectrally pure light by coherently driving such dipoles inside an optical QED cavity. The light exiting the cavity carries information about the detuning between the driving light and the atomic transition, but is also affected by the noise originating from all the decoherence processes that act on the combined atom-cavity system. We calculate these effects to obtain fundamental limits for frequency estimation and stabilization across a range of values of input light intensities and atom-light interaction strengths, estimate these limits in state-of-the-art cavity experiments with alkaline-earth atoms and identify favorable operating conditions. We find that the achievable linewidths are comparable to those of the superradiant laser.

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.

We present an experimental realization of dynamic self-trapping and non-exponential tunneling in a multi-state system consisting of ultracold sodium spinor gases confined in moving optical lattices. Taking advantage of the fact that the tunneling process in the sodium spinor system is resolvable over a broader dynamic energy scale than previously observed in rubidium scalar gases, we demonstrate that the tunneling dynamics in the multi-state system strongly depends on an interaction induced nonlinearity and is influenced by the spin degree of freedom under certain conditions. We develop a rigorous multi-state tunneling model to describe the observed dynamics. Combined with our recent observation of spatially-manipulated spin dynamics, these results open up prospects for alternative multi-state ramps and state transfer protocols.

The isolation and control of disparate degrees of freedom underpins quantum simulators. We advance the programmability of cold atom quantum simulators with a realization of the dynamic coupling of spatial and spin degrees of freedom. We experimentally demonstrate that violent spatial evolutions tune long-lived coherent spin dynamics and develop a model of quantum spin mixing incorporating the spatial evolution via time-dependent spin-spin interactions. Our results may open new paths towards the simulation of quantum spin models with tunable interactions via tailored spatial dynamics.