Local Readout and Control of Current and Kinetic Energy Operators in Optical Lattices.

Quantum gas microscopes have revolutionized quantum simulations with ultracold atoms, allowing one to measure local observables and snapshots of quantum states. However, measurements so far were mostly carried out in the occupation basis. Here, we demonstrate how all kinetic operators, such as kinetic energy or current operators, can be measured and manipulated with single-bond resolution. Beyond simple expectation values of these observables, the single-shot measurements allow one to access full counting statistics and complex correlation functions. Our work paves the way for the implementation of efficient quantum state tomography and hybrid quantum computing protocols for itinerant particles on a lattice. In addition, we demonstrate how site-resolved programmable potentials enable a spatially selective, parallel readout in different bases as well as the engineering of arbitrary initial states.

High-Fidelity Detection of Large-Scale Atom Arrays in an Optical Lattice.

Recent advances in quantum simulation based on neutral atoms have largely benefited from high-resolution, single-atom sensitive imaging techniques. A variety of approaches have been developed to achieve such local detection of atoms in optical lattices or optical tweezers. For alkaline-earth and alkaline-earth-like atoms, the presence of narrow optical transitions opens up the possibility of performing novel types of Sisyphus cooling, where the cooling mechanism originates from the capability to spatially resolve the differential optical level shifts in the trap potential. Up to now, it has been an open question whether high-fidelity imaging could be achieved in a "repulsive Sisyphus" configuration, where the trap depth of the ground state exceeds that of the excited state involved in cooling. Here, we demonstrate high-fidelity (99.971(1)%) and high-survival (99.80(5)%) imaging of strontium atoms using repulsive Sisyphus cooling. We use an optical lattice as a pinning potential for atoms in a large-scale tweezer array with up to 399 tweezers and show repeated, high-fidelity lattice-tweezer-lattice transfers. We furthermore demonstrate loading the lattice with approximately 10 000 atoms directly from the MOT and scalable imaging over >10 000 lattice sites with a combined survival probability and classification fidelity better than 99.2%. Our lattice thus serves as a locally addressable and sortable reservoir for continuous refilling of optical tweezer arrays in the future.

Ultracold field-linked tetratomic molecules.

Ultracold polyatomic molecules offer opportunities1 in cold chemistry2,3, precision measurements4 and quantum information processing5,6, because of their rich internal structure. However, their increased complexity compared with diatomic molecules presents a challenge in using conventional cooling techniques. Here we demonstrate an approach to create weakly bound ultracold polyatomic molecules by electroassociation7 (F.D. et al., manuscript in preparation) in a degenerate Fermi gas of microwave-dressed polar molecules through a field-linked resonance8-11. Starting from ground-state NaK molecules, we create around 1.1 × 103 weakly bound tetratomic (NaK)2 molecules, with a phase space density of 0.040(3) at a temperature of 134(3) nK, more than 3,000 times colder than previously realized tetratomic molecules12. We observe a maximum tetramer lifetime of 8(2) ms in free space without a notable change in the presence of an optical dipole trap, indicating that these tetramers are collisionally stable. Moreover, we directly image the dissociated tetramers through microwave-field modulation to probe the anisotropy of their wavefunction in momentum space. Our result demonstrates a universal tool for assembling weakly bound ultracold polyatomic molecules from smaller polar molecules, which is a crucial step towards Bose-Einstein condensation of polyatomic molecules and towards a new crossover from a dipolar Bardeen-Cooper-Schrieffer superfluid13-15 to a Bose-Einstein condensation of tetramers. Moreover, the long-lived field-linked state provides an ideal starting point for deterministic optical transfer to deeply bound tetramer states16-18.

Field-linked resonances of polar molecules.

Scattering resonances are an essential tool for controlling the interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances1, which have been extensively studied in various platforms1-7, are not expected to exist in most ultracold polar molecules because of the fast loss that occurs when two molecules approach at a close distance8-10. Here we demonstrate a new type of scattering resonance that is universal for a wide range of polar molecules. The so-called field-linked resonances11-14 occur in the scattering of microwave-dressed molecules because of stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium-potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole-dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids15 and molecular supersolids16, as well as assembling ultracold polyatomic molecules.

Magnetically mediated hole pairing in fermionic ladders of ultracold atoms.

Conventional superconductivity emerges from pairing of charge carriers-electrons or holes-mediated by phonons1. In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations2, as captured by models of mobile charges in doped antiferromagnets3. However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems4-8, in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions9. Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings10, we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole-hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.

Ultracold Sticky Collisions: Theoretical and Experimental Status.

Collisional complexes, which are formed as intermediate states in molecular collisions, are typically short-lived and decay within picoseconds. However, in ultracold collisions involving bialkali molecules, complexes can live for milliseconds, completely changing the collision dynamics. This can lead to unexpected two-body loss in samples of nonreactive molecules. During the past decade, such "sticky" collisions have been a major hindrance in the preparation of dense and stable molecular samples, especially in the quantum-degenerate regime. Currently, the behavior of the complexes is not fully understood. For example, in some cases, their lifetime has been measured to be many orders of magnitude longer than recent models predict. This is not only an intriguing problem in itself but also practically relevant, since understanding molecular complexes may help to mitigate their detrimental effects. Here, we review the recent experimental and theoretical progress in this field. We treat the case of molecule-molecule as well as molecule-atom collisions.

Exploring the Regime of Fragmentation in Strongly Tilted Fermi-Hubbard Chains.

Intriguingly, quantum many-body systems may defy thermalization even without disorder. One example is so-called fragmented models, where the many-body Hilbert space fragments into dynamically disconnected subspaces that are not determined by the global symmetries of the model. In this Letter we demonstrate that the tilted one-dimensional Fermi-Hubbard model naturally realizes distinct effective Hamiltonians that are expected to support nonergodic behavior due to fragmentation, even at resonances between the tilt energy and the Hubbard on site interaction. We find that the effective description captures the observed dynamics in experimentally accessible parameter ranges of moderate tilt values. Specifically, we observe a pronounced dependence of the relaxation dynamics on the initial doublon fraction, which directly reveals the microscopic processes of the fragmented model. Our results pave the way for future studies of nonergodic behavior in higher dimensions.

Practical quantum advantage in quantum simulation.

The development of quantum computing across several technologies and platforms has reached the point of having an advantage over classical computers for an artificial problem, a point known as 'quantum advantage'. As a next step along the development of this technology, it is now important to discuss 'practical quantum advantage', the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers. Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to modern materials science, high-energy physics and quantum chemistry. This would impact several important real-world applications, such as developing materials for batteries, industrial catalysis or nitrogen fixing. Much as aerodynamics can be studied either through simulations on a digital computer or in a wind tunnel, quantum simulation can be performed not only on future fault-tolerant digital quantum computers but also already today through special-purpose analogue quantum simulators. Here we overview the state of the art and future perspectives for quantum simulation, arguing that a first practical quantum advantage already exists in the case of specialized applications of analogue devices, and that fully digital devices open a full range of applications but require further development of fault-tolerant hardware. Hybrid digital-analogue devices that exist today already promise substantial flexibility in near-term applications.

Evaporation of microwave-shielded polar molecules to quantum degeneracy.

Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter1-9, implement quantum information schemes10-12 and test the fundamental symmetries of nature13. Realizing their full potential requires cooling interacting molecular gases deeply into the quantum-degenerate regime. However, the intrinsically unstable collisions between molecules at short range have so far prevented direct cooling through elastic collisions to quantum degeneracy in three dimensions. Here we demonstrate evaporative cooling of a three-dimensional gas of fermionic sodium-potassium molecules to well below the Fermi temperature using microwave shielding. The molecules are protected from reaching short range with a repulsive barrier engineered by coupling rotational states with a blue-detuned circularly polarized microwave. The microwave dressing induces strong tunable dipolar interactions between the molecules, leading to high elastic collision rates that can exceed the inelastic ones by at least a factor of 460. This large elastic-to-inelastic collision ratio allows us to cool the molecular gas to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such cold and dense samples of polar molecules open the path to the exploration of many-body phenomena with strong dipolar interactions.

Realizing the symmetry-protected Haldane phase in Fermi-Hubbard ladders.

Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain1,2. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter3,4. More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement5-7. Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.

Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion.

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, KPZ universality was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We tested this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We found that domain-wall relaxation is indeed governed by the KPZ dynamical exponent z = 3/2 and that the occurrence of KPZ scaling requires both integrability and a nonabelian SU(2) symmetry. Finally, we leveraged the single-spin-sensitive detection enabled by the quantum gas microscope to measure an observable based on spin-transport statistics. Our results yield a clear signature of the nonlinearity that is a hallmark of KPZ universality.

Suppression of Unitary Three-Body Loss in a Degenerate Bose-Fermi Mixture.

We study three-body loss in an ultracold mixture of a thermal Bose gas and a degenerate Fermi gas. We find that at unitarity, where the interspecies scattering length diverges, the usual inverse-square temperature scaling of the three-body loss found in nondegenerate systems is strongly modified and reduced with the increasing degeneracy of the Fermi gas. While the reduction of loss is qualitatively explained within the few-body scattering framework, a remaining suppression provides evidence for the long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions mediated by fermions between bosons. Our model based on RKKY interactions quantitatively reproduces the data without free parameters, and predicts one order of magnitude reduction of the three-body loss coefficient in the deeply Fermi-degenerate regime.

Realizing Distance-Selective Interactions in a Rydberg-Dressed Atom Array.

Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.

Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid.

The competition between antiferromagnetism and hole motion in two-dimensional Mott insulators lies at the heart of a doping-dependent transition from an anomalous metal to a conventional Fermi liquid. We observe such a crossover in Fermi-Hubbard systems on a cold-atom quantum simulator and reveal the transformation of multipoint correlations between spins and holes upon increasing doping at temperatures around the superexchange energy. Conventional observables, such as spin susceptibility, are furthermore computed from the microscopic snapshots of the system. Starting from a magnetic polaron regime, we find the system evolves into a Fermi liquid featuring incommensurate magnetic fluctuations and fundamentally altered correlations. The crossover is completed for hole dopings around 30%. Our work benchmarks theoretical approaches and discusses possible connections to lower-temperature phenomena.

Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains.

The thermalization of isolated quantum many-body systems is deeply related to fundamental questions of quantum information theory. While integrable or many-body localized systems display non-ergodic behavior due to extensively many conserved quantities, recent theoretical studies have identified a rich variety of more exotic phenomena in between these two extreme limits. The tilted one-dimensional Fermi-Hubbard model, which is readily accessible in experiments with ultracold atoms, emerged as an intriguing playground to study non-ergodic behavior in a clean disorder-free system. While non-ergodic behavior was established theoretically in certain limiting cases, there is no complete understanding of the complex thermalization properties of this model. In this work, we experimentally study the relaxation of an initial charge-density wave and find a remarkably long-lived initial-state memory over a wide range of parameters. Our observations are well reproduced by numerical simulations of a clean system. Using analytical calculations we further provide a detailed microscopic understanding of this behavior, which can be attributed to emergent kinetic constraints.

Crossed optical cavities with large mode diameters.

We report on a compact, ultrahigh-vacuum compatible optical assembly to create large-scale, two-dimensional optical lattices for use in experiments with ultracold atoms. The assembly consists of an octagon-shaped spacer made from ultra-low-expansion glass, to which we optically contact four fused silica cavity mirrors, making it highly mechanically and thermally stable. The mirror surfaces are nearly plane-parallel, which allows us to create two perpendicular cavity modes with diameters ∼1m m. Such large mode diameters are desirable to increase the optical lattice homogeneity, but lead to strong angular sensitivities of the coplanarity between the two cavity modes. We demonstrate a procedure to precisely position each mirror substrate that achieves a deviation from coplanarity of d=1(5)µm. Creating large optical lattices at arbitrary visible and near-infrared wavelengths requires significant power enhancements to overcome limitations in the available laser power. The cavity mirrors have a customized low-loss mirror coating that enhances the power at a set of relevant visible and near-infrared wavelengths by up to 3 orders of magnitude..

A subradiant optical mirror formed by a single structured atomic layer.

Versatile interfaces with strong and tunable light-matter interactions are essential for quantum science1 because they enable mapping of quantum properties between light and matter1. Recent studies2-10 have proposed a method of controlling light-matter interactions using the rich interplay of photon-mediated dipole-dipole interactions in structured subwavelength arrays of quantum emitters. However, a key aspect of this approach-the cooperative enhancement of the light-matter coupling strength and the directional mirror reflection of the incoming light using an array of quantum emitters-has not yet been experimentally demonstrated. Here we report the direct observation of the cooperative subradiant response of a two-dimensional square array of atoms in an optical lattice. We observe a spectral narrowing of the collective atomic response well below the quantum-limited decay of individual atoms into free space. Through spatially resolved spectroscopic measurements, we show that the array acts as an efficient mirror formed by a single monolayer of a few hundred atoms. By tuning the atom density in the array and changing the ordering of the particles, we are able to control the cooperative response of the array and elucidate the effect of the interplay of spatial order and dipolar interactions on the collective properties of the ensemble. Bloch oscillations of the atoms outside the array enable us to dynamically control the reflectivity of the atomic mirror. Our work demonstrates efficient optical metamaterial engineering based on structured ensembles of atoms4,8,9 and paves the way towards controlling many-body physics with light5,6,11 and light-matter interfaces at the single-quantum level7,10.

Robust Bilayer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy.

Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly stable vertical superlattice and subsequent charge pumping to separate the layers by 21 µm. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods, or the realization of tunable bilayer systems.

Tune-Out and Magic Wavelengths for Ground-State

We demonstrate a versatile, state-dependent trapping scheme for the ground and first excited rotational states of ^{23}Na^{40}K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering rates.

Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains.

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.