Optical cavities are a foundational technology for controlling light-matter interactions. While interfacing a single cavity to either an atom or ensemble has become a standard tool, the advent of single-atom control in large atomic arrays has spurred interest in a new frontier of “many-cavity QED,” featuring many independent resonators capable of separately addressing individual quantum emitters. In this fast-evolving landscape, the cavity array microscope was recently introduced—employing free space intracavity optics to engineer a two-dimensional array of tightly spaced cavity ${\mathrm{TEM}}_{00}$ modes with wavelength-scale waists, ideally suited for interfacing with atom arrays. Here, we realize the next generation of this architecture, achieving hundreds of degenerate cavity modes with improved, uniform finesse, and explore the technical features of the system which will enable further scalability. In particular, we study imperfections, including optical aberrations, field of view constraints, array nondegeneracies, and losses from optical elements. We identify the sensitivity to these various factors and exposit the control knobs and techniques necessary to align and operate the system in a stable manner. Ultimately, we lay out a pathway toward operation with tens of thousands of independent cavities while maintaining compatibility with existing atom arrays, paving the way to myriad applications including highly parallelized remote entanglement generation, fast and nondestructive midcircuit readout, and the implementation of hybrid atom-photon Hamiltonians.

Topology can imbue lattice systems with special properties, notably, the presence of robust eigenstates living at their boundary. Through dimensional reduction, the robust bulk band topology of, e.g., the integer quantum Hall system can be mapped onto similarly robust charge-pumping dynamics of a topological pump living in one lower dimension. Recent studies have uncovered a rich influence of interactions on the dynamics of topological pumps in nonlinear systems, including the robust pumping of self-bound solitons. These striking observations in classical nonlinear photonics have raised a number of questions, chiefly if and how this phenomenology persists in strongly correlated quantum systems and in the few-body limit. Here, using few- and many-atom arrays, we explore how dipolar interactions impact the dynamics of topological population pumping along a Rydberg synthetic dimension. In the few-body limit, we find that dipolar interactions lead to self-bound states that are efficiently pumped along the synthetic dimension, described by an emergent pair-state topological pump. We find that this interaction-assisted pumping persists in many-atom arrays, with a sharpened dependence on the dipolar interaction strength that stems from the enhanced spatial connectivity. These Rydberg-based studies on interaction-assisted topological pumping help connect observations from classical nonlinear photonics to the few-body quantum limit and pave the way for studies of new strongly correlated topological phenomena.

Preparation of quantum thermal states of many-body systems is a key computational challenge for quantum processors, with applications in physics, chemistry, and classical optimization. We provide a simple and efficient algorithm for thermal state preparation, combining engineered bath resetting and modulated system-bath coupling to derive a quantum channel approximately satisfying quantum detailed balance relations. We show that the fixed point $\widehat{\sigma }$ of the channel approximates the Gibbs state as $\parallel \widehat{\sigma }-{\widehat{\sigma }}_{\beta }\parallel \sim {\theta }^2$, where $\theta$ is the system-bath coupling and ${\widehat{\sigma }}_{\beta }\propto e^{-\beta {\widehat{H}}_S}$. We provide extensive numerics, for the example of the 2D quantum Ising model, confirming that the protocol successfully prepares the thermal state throughout the finite-temperature phase diagram, including near the quantum phase transition. Simulations for free-fermion systems provide further evidence for the accuracy of the protocol for large system sizes in the weak-coupling limit. Our algorithm provides a path to efficient quantum simulation of quantum-correlated states at finite temperature with current and near-term quantum processors.

Divalent atoms have emerged as powerful alternatives to alkalis in ultracold atom platforms, offering unique advantages arising from their two-electron structure. Among these species, ytterbium (Yb) is especially promising, yet its anionic properties and its Rydberg spectrum remain comparatively unexplored. In this work, we perform a comprehensive experimental and theoretical investigation of ultralong-range Rydberg molecules (ULRMs) of ${}^{174}\mathrm{Yb}$ in $6sns{{}^{1}S}_0$ Rydberg states across nearly two decades in principal quantum number $n$ and 3 orders of magnitude in molecular binding energy. Using the Coulomb Green’s function formalism, we compute Born-Oppenheimer molecular potentials describing the Rydberg atom in the presence of a ground-state perturber and achieve quantitative agreement with high-resolution molecular spectra. This enables the extraction of low-energy electron-Yb scattering phase shifts, including the zero-energy $s$-wave scattering length and the positions of two spin-orbit split $p$-wave shape resonances. Our results provide strong evidence that the ${\mathrm{Yb}}^{-}$ anion exists only as a metastable resonance. We additionally show the sensitivity of ULRM spectra to the atomic quantum defects, using this to determine the quantum defect of the $6s23f{{}^{1}F}_3$ state. Together, these findings establish Yb ULRMs as a powerful probe of electron-Yb interactions and lay essential groundwork for future Rydberg experiments with divalent atoms.

Analog quantum simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous uncertainty bounds is essential for elevating such devices from qualitative demonstrations to quantitative scientific tools. Here we introduce a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties. The approach combines Hamiltonian and Lindbladian Learning—a statistically rigorous inference of the coherent and dissipative generators governing the dynamics—with the propagation of their uncertainties into the simulated observables, yielding confidence bounds directly derived from experimental data. We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions. We analyze error bounds on two levels. First, we learn an open-system model from experimental data collected in an initial time window of quench dynamics, simulate the corresponding master equation, and quantitatively verify consistency between theoretical predictions and measured dynamics at long times. Second, we discuss short-time error bounds directly from experimental measurements alone, without relying on classical simulation—crucial for entering regimes of quantum advantage. In both cases, the learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. By integrating statistical learning, open-system modeling, and precise experimental control, bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental quantum platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.

The most efficient and most versatile technique for producing highly charged ions (HCI) with high atomic numbers is electron stripping in-flight at high kinetic energies. While this requires relativistic velocities, many experiments call for trapped or at least slowly moving ions. For example, studies of fundamental interactions would significantly improve in precision when performed in an ion trap while studies on slow HCI for material science are not yet feasible due to the lack of availability. The goal of the HITRAP project at the GSI Helmholtzzentrum für Schwerionenforschung GmbH is to decelerate accelerator-produced heavy HCI and prepare them in a Penning trap via electron cooling for subsequent experiments. We present the trapping of accelerator-produced HCI. Fully stripped ${{}^{36}\mathrm{Ar}}^{18+}$ were decelerated from the production energy of $45\mathrm{MeV}/\mathrm{u}$ to $6\mathrm{keV}/\mathrm{u}$ followed by trapping in the HITRAP Cooling Trap for the duration of several seconds. The Cooling Trap is a nested Penning trap that allows for the simultaneous storage of HCI ions with a cold electron plasma. It was commissioned with HCI from a local electron beam ion source, which led to the first observation of electron cooling of highly charged ions in a Penning trap, marking a significant advancement in the field. These developments constitute a major step toward a worldwide unique facility with unparalleled capabilities in heavy-ion research and already enable the first experimental studies at HITRAP.

Heavy polar molecules are sensitive probes of physics beyond the standard model. However, uncontrolled external electromagnetic fields pose challenges to achieving precise and accurate measurements. Minimizing susceptibility to these fields is therefore critical and has played an important role in all precision experiments of this type. Here we devise and demonstrate clock transitions engineered to realize robust symmetry violation searches in the polyatomic molecule YbOH. Sensitivities to external fields can be suppressed by orders of magnitude while preserving high sensitivity to the electron electric dipole moment. We perform Ramsey measurements on these clock transitions and observe suppression of electric and magnetic sensitivities by at least factors of 700 and 200, respectively, and demonstrate the robustness of their spin coherence against large electromagnetic-field fluctuations. We further identify and employ selected quantum states to make sensitive measurements of external magnetic and electric fields, another critical feature for highly accurate measurements. This approach of molecular engineering is broadly applicable to diverse molecular species and states, including those with complex nuclei and those that are compatible with state-of-the-art cooling and trapping techniques, thereby offering the potential to significantly improve experimental sensitivity to a wide range of new physics while expanding the chemical design space for molecular quantum science.

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon, it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to individual measurements and revealed only through joint readout of both oscillators, in stark contrast to the system in the (deterministic) classical limit where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of ${10}^{19}$ and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

We explore a two-node, entanglement-enhanced sensor network for differential phase sensing that exploits decoherence-free subspaces to suppress common-mode noise, a primary limitation of many state-of-the-art quantum sensors. We identify a class of entangled states that, while not strictly optimal, achieve the same asymptotic sensitivity scaling as optimal states and can be prepared efficiently from initially unentangled atomic ensembles. Importantly, the preparation time decreases with increasing system size, which makes the states compatible with realistic noise processes in present-day quantum sensors that operate with large particle numbers but lack full error correction. We illustrate these ideas using two cavity-mediated preparation protocols: (i) coherent, unitary entanglement generation analogous to bosonic two-mode squeezing, yielding Heisenberg scaling, and (ii) dissipative preparation through collective emission into a shared cavity mode, providing a square-root improvement beyond the standard quantum limit. Numerical simulations show that both approaches remain effective at experimentally realistic cavity cooperativities, establishing a practical path toward scalable, quantum-enhanced differential phase sensing.

Full coherent control and generation of nonclassical superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology, and continuous-variable quantum computation. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear interactions with midcircuit spin measurements that herald the probabilistic preparation of superpositions of squeezed, trisqueezed, and quadsqueezed states, which have not previously been experimentally demonstrated. We achieve independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full-state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.

Among the thriving quantum computation and quantum simulation platforms based on arrays of Rydberg atoms, those using circular Rydberg atoms are particularly promising. These atoms uniquely combine the strong dipole-dipole interactions typical of Rydberg states with long lifetimes. However, low-angular-momentum ($\ell$) laser-accessible Rydberg levels have been so far mostly used, because circular Rydberg atoms have no optical transitions, hindering their individual detection and manipulation. We remove this limitation with a hybrid platform, combining an array of data laser-trapped circular Rydberg atoms of rubidium with an auxiliary array of Rb ancilla atoms transiently excited to a low-$\ell$ Rydberg level. We perform a quantum nondemolition detection of the data qubit with the ancilla, through the blockade of the ancilla optical excitation induced by a Förster resonance. Conversely, we locally manipulate the data qubit through the excitation of the ancilla. This dual-Rydberg platform is highly promising for quantum computation and simulation. It adds to the circular-atom toolbox the midcircuit measurements, essential for error correction. More strikingly, it gives access to time correlations in long-term quantum simulations, uniquely accessible to circular Rydberg atoms.

The fidelity and quantum nondemolition character of the dispersive readout in circuit QED are limited by unwanted transitions to highly excited states at specific photon numbers in the readout resonator. This observation can be explained by multiphoton resonances between computational states and highly excited states in strongly driven nonlinear systems, analogous to multiphoton ionization in atoms and molecules. In this work, we utilize the multilevel nature of high-$E_J/E_C$ transmons to probe the excited-state dynamics induced by strong drives during readout. With up to ten resolvable states, we quantify the critical photon number of ionization, the resulting state after ionization, and the fraction of the population transferred to highly excited states. Moreover, using pulse shaping to control the photon number in the readout resonator in the high-power regime, we tune the adiabaticity of the transition and verify that transmon ionization is a Landau-Zener-type transition. We further extend these methods to a typical transmon with $E_J/E_C\approx 55$ and probe the offset-charge dependence of ionization dynamics in a timed-resolved manner. Our experimental results agree well with the theoretical prediction from a semiclassical driven transmon model and may guide future exploration of strongly driven nonlinear oscillators.

Nonlinear phenomena underpin a broad array of technologies, from electronic frequency mixers and harmonic generation to parametric amplification and optical frequency doubling. Conventional schemes for generating microwave frequency combs are constrained by intrinsic material or junction properties that require high driving powers. Here, we overcome these limitations via phase-transition physics. We show that a hybrid quantum system—composed of a solid-state spin ensemble and a nonlinear oscillator—exhibits a distinct bistable phase transition point (BP) where system response becomes both highly enhanced and nonlinear. The nonlinearity around the BP is higher order than other phase transitions, such as exceptional points, critically producing high-order frequency response which enhances nonlinear processes. Approaching the BP, we demonstrate a frequency comb with a record number of teeth at unprecedentedly low driving powers, surpassing previous results using magnonic systems and traditional diode-based approaches. These findings highlight the potential of hybrid quantum systems in advancing high-performance frequency manipulation.

Collisions between ultracold calcium monohydroxide (CaOH) molecules are realized and studied. Inelastic collision rate constants are measured for CaOH prepared in ground and excited vibrational states, and the electric field dependence of these rates is measured for molecules in single quantum states of the parity-doubled bending mode. Theoretical calculations of collision rate coefficients are performed and found to agree with measured values. The lowest collisional loss rates are for states with repulsive long-range potentials that shield ultracold molecules from loss channels at short distance. These results unveil the collisional behavior of parity-doublet molecules in the ultracold regime and lay the foundation for future experiments to evaporatively cool polyatomic molecules to quantum degeneracy.

We propose high-spin $\mathrm{\Sigma }$-state polar molecules assembled from ultracold atoms to probe charge-parity-violating physics beyond the standard model. We identify YbCr as a prime candidate to search for the electric dipole moment of the electron. We show that the combination of relativistic ytterbium and high-spin chromium, amenable to magnetoassociation, leads to molecules with easy-to-polarize parity doublets and large intramolecular electric fields. Based on ab initio results for molecular constants, we predict a sensitivity of $\delta d_{\mathrm{e}}=(6\times {10}^{-31}/\sqrt{n_{\mathrm{day}}})e\mathrm{cm}$ via standard spin-precession measurements, assess the experimental feasibility, and discuss potential extensions to more advanced quantum control as well as searches of the nuclear magnetic quadrupole moment. This work paves the way to next-generation searches for new physics with ultracold molecules in both the leptonic and hadronic sectors.

Traditional x-ray photoelectron spectroscopy (XPS) relies upon a direct mapping between the photoelectron binding energies and the local chemical environment, which is well characterized by an electrostatic partial charges (PC) model for systems in equilibrium. However, the extension of this technique to out-of-equilibrium systems has been hampered by the lack of x-ray sources capable of accessing multiple atomic sites with high spectral and temporal resolution, as well as the lack of simple theoretical procedures to interpret the observed signals. In this work we employ XPS with a narrow band femtosecond x-ray probe to unravel different ultrafast dissociation processes of a polyatomic molecule, fluoromethane (${\mathrm{CH}}_3\mathrm{F}$). We demonstrate that the PC model can be successfully applied to describe the C-F and C-H dissociation dynamics after strong-field ionization, with excellent agreement between experimental measurements and ab initio simulations. These results enable the application of this technique to out-of-equilibrium systems of higher complexity, by correlating real-time information from multiple atomic sites and interpreting the measurements through a viable theoretical modeling.

Light-induced quantum phases offer the potential for simple and powerful tuning of material properties. For example, simply illuminating 2D materials in the integer quantum Hall regime with polarized light is predicted to drive quantum phase transitions. Such phenomena are largely beyond the current frontier of solid state experiments due to technical limitations on laser intensity and material purity. However, the Harper-Hofstadter mapping which relates a two-dimensional integer quantum Hall system to a 1D quasicrystal enables the same polarization-dependent light-induced phase transitions to be observed using a quantum gas in a driven quasiperiodic optical lattice. We report results of such an experiment. We observe an interlaced phase diagram of localization-delocalization phase transitions as a function of drive polarization and amplitude. Elliptically polarized driving can stabilize an extended critical phase featuring multifractal wave functions; we observe signatures of this phenomenon in anomalous polarization-dependent subdiffusive transport. In this regime, increasing the strength of the quasiperiodic potential can enhance rather than suppress transport. These experiments demonstrate a simple method for synthesizing exotic multifractal states and exploring light-induced quantum phases across different dimensionalities.

Computing high-dimensional potential energy surfaces for molecular systems and materials is considered to be a great challenge in computational chemistry with potential impact in a range of areas including the fundamental prediction of reaction rates. In this paper, we design and discuss an algorithm that has similarities to large language models in generative AI and natural language processing. Specifically, we represent a molecular system as a graph which contains a set of nodes, edges, faces, etc. Interactions between these sets, which represent molecular subsystems in our case, are used to construct the potential energy surface for a reasonably sized chemical system with 51 nuclear dimensions. For this purpose, a family of neural networks that pertain to the graph-theoretically obtained subsystems get the job done for this 51 nuclear dimensional system. We then ask if this same family of lower-dimensional graph-based neural networks can be transformed to provide accurate predictions for a 186-dimensional potential energy surface. We find that our algorithm does provide accurate results for this larger-dimensional problem with sub-kcal/mol accuracy for the higher-dimensional potential energy surface problem. Indeed, as a result of these developments, here we produce efforts toward a full-dimensional potential energy surface for the protonated 21-water cluster (186 nuclear dimensions) at coupled-cluster single and double level accuracy.