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Metal‐organic frameworks (MOFs) and MOF‐derived materials have attracted great attention as alternatives to noble‐metal based electrocatalysts owing to their intriguing structure properties, especially for high efficiency and stable oxygen reduction reaction (ORR). Herein, we employed a one‐pot reaction to make a multimetal (Fe, Co, Cu, and Zn) mixed zeolitic imidazolate framework (MM‐ZIF) via adopting a simple in situ redox reaction. Further pyrolysis of the target MM‐ZIF, a highly porous carbon polyhedron (FC‐C@NC) grafted with abundant carbon nanotubes was obtained, in which ultrasmall Co nanoparticles with partial lattice sites substituted by Fe and Cu were embedded. The obtained FC‐C@NC possessed large surface area, highly porous structure, widely‐spread metal active sites, and conductive carbon frameworks, contributing to outstanding ORR activity and long‐term stability. It displayed superior tolerance to methanol crossover and exceeded the commercial Pt/C catalyst and most previously reported non‐noble‐metal catalysts. Impressively, the as‐produced FC‐C@NC‐based zinc‐air battery afforded an open‐circuit potential of 1.466 V, a large specific capacity of 659.5 mAh/g, and a high gravimetric energy density of 784.3 Wh/kgZn, significantly outperforming the Pt/C‐based cathode. Highly porous carbon frameworks supported abundant Co nanoparticles with partial lattice sites substituted by Fe and Cu showed excellent performance for oxygen reduction reaction, and the assembled zinc‐air battery exceeded commercial benchmark Pt/C catalyst, which showed great potentials for applications in energy storage and conversion process.

Doping metal ions offer a promising strategy to tune the intrinsic and surface properties of BiVO4 for enhanced photoelectrochemical (PEC) activity. Given this, experimental and theoretical studies on cadmium (Cd) doping to BiVO4 photoanode were studied for PEC water splitting applications. The spectroscopic and PEC results indicate that the substitution of Cd at Bi lattice sites causes the reduction in the valence state of V5+ to V4+ that creates hole trap states below the Fermi level of BiVO4. The introduced hole trap states at the BiVO4 surface suppress the charge recombination and provide effective hole transfer sites for the facile water oxidation reactions. The Cd-BiVO4 exhibited significantly higher photocurrent compared to the pristine BiVO4 reaching 3.5 ​mA ​cm₋2 (with a hole scavenger) at 1.23 ​V vs RHE. Furthermore, doping increases the carrier density in the bulk of BiVO4 leading to improved charge separation, and charge transfer while reducing the hole transfer resistance at the interface. The Cd-doped BiVO4 exhibited a charge separation efficiency of 80 ​% and with a 90 ​% of overall water splitting faradaic efficiency. Importantly, the results of this work propose the advantages of doping metal ions at Bi lattice sites in BiVO4 for improved PEC activity.

After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space. An interconnected network made of superconducting microwave resonators is created as a step towards quantum simulations of interacting particles in hyperbolic space.

Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly correlated electrons in solids. In this work, we realize the Hubbard Hamiltonian and search for specific patterns within the individual images of many realizations of strongly correlated ultracold fermions in an optical lattice. Upon doping a cold-atom antiferromagnet, we find consistency with geometric strings, entities that may explain the relationship between hole motion and spin order, in both pattern-based and conventional observables. Our results demonstrate the potential for pattern recognition to provide key insights into cold-atom quantum many-body systems.

Adding irregularity to a system can lead to a transition from a more orderly to a less orderly phase. Meier et al. demonstrated a counterintuitive transition in the opposite direction: Controlled fluctuations in the system's parameters caused it to become topologically nontrivial. The starting point was a one-dimensional lattice of ultracold rubidium atoms in momentum space whose band structure was topologically trivial. The researchers then introduced fluctuations in the tunneling between the lattice sites and monitored the atomic “wires” as the amplitude of the fluctuations increased. The wires first became topologically nontrivial and then went back to trivial for sufficient disorder strengths. Science , this issue p. 929 Controlled fluctuations in the tunneling between the sites of an atomic wire in momentum space cause a topological transition. Topology and disorder have a rich combined influence on quantum transport. To probe their interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic Hamiltonian engineering, based on the laser-driven coupling of discrete momentum states of ultracold atoms. Measuring the bulk evolution of a topological indicator after a sudden quench, we observed the topological Anderson insulator phase, in which added disorder drives the band structure of a wire from topologically trivial to nontrivial. In addition, we observed the robustness of topologically nontrivial wires to weak disorder and measured the transition to a trivial phase in the presence of strong disorder. Atomic interactions in this quantum simulation platform may enable realizations of strongly interacting topological fluids.

The Hubbard model is widely believed to contain the essential ingredients of high-temperature superconductivity. However, proving definitively that the model supports superconductivity is challenging. Here, we report a large-scale density matrix renormalization group study of the lightly doped Hubbard model on four-leg cylinders at hole doping concentration δ = 12.5%. We reveal a delicate interplay between superconductivity and charge density wave and spin density wave orders tunable via next-nearest neighbor hopping t′. For finite t′, the ground state is consistent with a Luther-Emery liquid with power-law superconducting and charge density wave correlations associated with half-filled charge stripes. In contrast, for t′ = 0, superconducting correlations fall off exponentially, whereas charge density and spin density modulations are dominant. Our results indicate that a route to robust long-range superconductivity involves destabilizing insulating charge stripes in the doped Hubbard model.

We demonstrate site-resolved imaging of individual bosonic atoms in a Hubbard-regime two-dimensional optical lattice with a short lattice constant of 266 nm. To suppress the heating by probe light with the 1S0-1P1 transition of the wavelength λ = 399 nm for high-resolution imaging and preserve atoms at the same lattice sites during the fluorescence imaging, we simultaneously cool atoms by additionally applying narrow-line optical molasses with the 1S0-3P1 transition of the wavelength λ = 556 nm. We achieve a low temperature of , corresponding to a mean oscillation quantum number along the horizontal axes of 0.22(4) during the imaging process. We detect, on average, 200 fluorescence photons from a single atom within a 400 ms exposure time, and estimate a detection fidelity of 87(2)%. The realization of a quantum gas microscope with enough fidelity for Yb atoms in a Hubbard-regime optical lattice opens up the possibilities for studying various kinds of quantum many-body systems such as Bose and Fermi gases, and their mixtures, and also long-range-interacting systems such as Rydberg states.

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold 84 Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials. Synthetic dimensions, states of a system engineered to act as if they were a reconfigurable extra spatial dimension, have been demonstrated with different systems previously. Here the authors create a synthetic dimension using Rydberg atoms and configure it to support topological edge states.

We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.

Atomically defined assemblies of dye molecules (such as H and J aggregates) have been of interest for more than 80 years because of the emergence of collective phenomena in their optical spectra 1 – 3 , their coherent long-range energy transport, their conceptual similarity to natural light-harvesting complexes 4 , 5 , and their potential use as light sources and in photovoltaics. Another way of creating versatile and controlled aggregates that exhibit collective phenomena involves the organization of colloidal semiconductor nanocrystals into long-range-ordered superlattices 6 . Caesium lead halide perovskite nanocrystals 7 – 9 are promising building blocks for such superlattices, owing to the high oscillator strength of bright triplet excitons 10 , slow dephasing (coherence times of up to 80 picoseconds) and minimal inhomogeneous broadening of emission lines 11 , 12 . So far, only single-component superlattices with simple cubic packing have been devised from these nanocrystals 13 . Here we present perovskite-type (ABO 3 ) binary and ternary nanocrystal superlattices, created via the shape-directed co-assembly of steric-stabilized, highly luminescent cubic CsPbBr 3 nanocrystals (which occupy the B and/or O lattice sites), spherical Fe 3 O 4 or NaGdF 4 nanocrystals (A sites) and truncated-cuboid PbS nanocrystals (B sites). These ABO 3 superlattices, as well as the binary NaCl and AlB 2 superlattice structures that we demonstrate, exhibit a high degree of orientational ordering of the CsPbBr 3 nanocubes. They also exhibit superfluorescence—a collective emission that results in a burst of photons with ultrafast radiative decay (22 picoseconds) that could be tailored for use in ultrabright (quantum) light sources. Our work paves the way for further exploration of complex, ordered and functionally useful perovskite mesostructures. Through precise structural engineering, perovskite nanocrystals are co-assembled with other nanocrystal materials to form a range of binary and ternary perovskite-type superlattices that exhibit superfluorescence.