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Discrete Open-Shell Tris(bipyridinium radical cationic) Inclusion Complexes in the Solid State
In the solid state the properties of organic radicals depend heavily on radical-radical interactions that are influenced by the superstructure of the crystalline phase. Here, we report the synthesis and characterization of a substituted tetracationic cyclophane, cyclobis(paraquat-p-1,4- dimethoxyphenylene), and outline how its bisradical dicationic redox state associates with the methyl viologen radical cation (MV •+ ) to give a trisradical tricationic inclusion complex. The (super)structures of the reduced cyclophane and this 1:1 complex in the solid-state deviate from the analogous (super)structures observed for the reduced state of cyclobis(paraquat-p-phenylene) and that of its trisradical tricationic complex. Titration experiments with a range of guests reveal that the methoxy substituents on the para-xylenyl do not influence significantly of the binding affinity of the cyclophane for small neutral guests, whereas the affinity decreases by an order of magnitude for larger radical cationic guests such as MV •+ . X-Ray diffraction reveals that the solid- state structures of the tricationic trisradical complexes to be a discrete entity with weak intermolecular orbital overlap between the neighboring complexes. Transient nutation EPR experiment and DFT calculations confirm that the complex has a doublet spin configuration in the ground state as a result of the strong orbital overlap within the complex, while the quartet-state spin configuration is higher in energy and so is inaccessible at ambient temperature. The superconducting quantum interference device (SQUID) measurement reveals that trisradical tricationic complexes interact antiferromagnetically (J/k = - 2.33 K) and form a 1D Heisenberg antiferromagnetic chain along the a-axis in the crystal. Furthermore, these results offer new insights into the design and synthesis of organic magnetic materials based on host-guest inclusion complexes.
Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe 2
Fifty years after Anderson’s resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe 2 , first proving the Heisenberg character of the interactions and quantifying the second-neighbor coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120°-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials.
Linear-frequency conversion with time-varying metasurfaces
Frequency conversion is a hallmark of nonlinearity. The spectral manifestations, emergent within a system, can typically be attributed to a marked nonlinearity within the material properties, complex geometric configurations, and/or the unique functional form of interactions taking place in the constitutive subsystems. These phenomena, irrespective of their origins, have been harnessed and exploited in applications ranging from the generation of entangled photons, a cornerstone in quantum technologies, to nanomechanical frequency mixing, advancing subsurface scanning probe microscopy. Here, we propose a frequency conversion mechanism based on time-varying metasurfaces, an emerging frontier in metamaterial research. We show how temporal properties of metasurfaces can effectively emulate a nonlinear medium, thereby facilitating frequency conversion. The proposed material configuration has the potential not only to advance integrated photonics and quantum optics, but also to create opportunities in quantum sensing, quantum materials, and crucially quantum communications. Published by the American Physical Society 2024
Emergent flat band electronic structure in a VSe 2 /Bi 2 Se 3 heterostructure
Flat band electronic states are proposed to be a fundamental tool to achieve various quantum states of matter at higher temperatures due to the enhanced electronic correlations. However, materials with such peculiar electronic states are rare and often rely on subtle properties of the band structures. Here, by using angle-resolved photoemission spectroscopy, we show the emergent flat band in a VSe 2 / Bi 2 Se 3 heterostructure. Our photoemission study demonstrates that the flat band covers the entire Brillouin zone and exhibits 2D nature with a complex circular dichroism. In addition, the Dirac cone of Bi 2 Se 3 is not reshaped by the flat band even though they overlap in proximity of the Dirac point. These features make this flat band distinguishable from the ones previously found. Thereby, the observation of a flat band in the VSe 2 / Bi 2 Se 3 heterostructure opens a promising pathway to realize strongly correlated quantum effects in topological materials.
Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network
A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.
Ultimate Strength of Metals
We present a theoretical model that predicts the peak strength of polycrystalline metals based on the activation energy (or stress) required to cause deformation via amorphization. Building on extensive earlier work, this model is based purely on materials properties, requires no adjustable parameters, and is shown to accurately predict the strength of four exemplar metals (fcc, bcc, and hcp, and an alloy). This framework reveals new routes for design of more complex high-strength materials systems, such as compositionally complex alloys, multiphase systems, nonmetals, and composite structures.
Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials
Since their introduction in 1929, Pauling’s five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al. (2020), who performed a statistical analysis of the performance of Pauling’s five rules for about 5000 oxide crystal structures. They concluded that only 13% of the oxides satisfy the last four rules simultaneously and that the second rule has the most exceptions. They also found that Pauling’s first rule is satisfied for only 66% of the coordination environments tested and concluded that no simple rule linking ionic radius to coordination environment will be predictive due to the variable quality of univalent radii. We address these concerns and discuss quantum mechanical calculations that complement Pauling’s rules, particularly his first (radius sum and radius ratio rule) and second (electrostatic valence rule) rules. We also present a more realistic view of the bonded radii of atoms, derived by determining the local minimum in the electron density distribution measured along trajectories between bonded atoms known as bond paths, i.e., the bond critical point (rc). Electron density at the bond critical point is a quantum mechanical observable that correlates well with Pauling bond strength. Moreover, a metal atom in a polyhedron has as many bonded radii as it has bonded interactions, resulting in metal and O atoms that may not be spherical. O atoms, for example, are not spherical in many oxide-based crystal structures. Instead, the electron density of a bonded oxygen is often highly distorted or polarized, with its bonded radius decreasing systematically from ~1.38 Å when bonded to highly electropositive atoms like sodium to 0.64 Å when bonded to highly electronegative atoms like nitrogen. Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al. (2020) is not surprising. We offer a modified, more fundamental version of Pauling’s first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction. Pauling’s second rule implicitly assumes that bond strength is invariant with bond length for a given pair of bonded atoms. Many studies have since shown that this is not the case, and Brown and Shannon (1973) developed an equation and a set of parameters to describe the relation between bond length and bond strength, now redefined as bond valence to avoid confusion with Pauling bond-strength. Brown (1980) used the valence-sum rule, together with the path rule and the valence-matching principle, as the three axioms of bond-valence theory (BVT), a powerful method for understanding many otherwise elusive aspects of crystals and also their participation in dynamic processes. We show how a priori bond-valence calculations can predict unstrained bond-lengths and how bond-valence mapping can locate low-Z atoms in a crystal structure (e.g., Li) or examine possible diffusion pathways for atoms through crystal structures. In addition, we briefly discuss Pauling’s third, fourth, and fifth rules, the first two of which concern the sharing of polyhedron elements (edges and faces) and the common instability associated with structures in which a polyhedron shares an edge or face with another polyhedron and contains high-valence cations. The olivine [α-(MgxFe1–x)2SiO4] crystal structure is used to illustrate the distortions from hexagonal close-packing of O atoms caused by metal-metal repulsion across shared polyhedron edges. We conclude by discussing several applications of BVT to Earth materials, including the use of BVT to: (1) locate H+ ions in crystal structures, including the location of protons in the crystal structures of nominally anhydrous minerals in Earth’s mantle; (2) determine how strongly bonded (usually anionic) structural units interact with weakly bonded (usually cationic) interstitial complexes in complex uranyl-oxide and uranyl-oxysalt minerals using the valence-matching principle; (3) calculate Lewis acid strengths of cations and Lewis base strengths of anions; (4) determine how (H2O) groups can function as bond-valence transformers by dividing one bond into two bonds of half the bond valence; (5) help characterize products of sorption reactions of aqueous cations (e.g., Co2+ and Pb2+) and oxyanions [e.g., selenate (Se6+O4)2- and selenite (Se4+O3)2-] at mineral-aqueous solution interfaces and the important role of protons in these reactions; and (6) help characterize the local coordination environments of highly charged cations (e.g., Zr4+, Ti4+, U4+, U5+, and U6+) in silicate glasses and melts.
Synthetic Pathways to gamma-Graphyne and Related Allotropes of Carbon
Graphynes, two-dimensional carbon lattices combining sp 1 and sp 2 hybridized atoms, were predicted theoretically more than three decades ago, but few structures have been realized to date. These carbons are believed to possess remarkable mechanical and electronic properties, including high charge carrier mobilities comparable to those in graphene (10 4 to 10 5 cm 2 V -1 s -1 ). Unlike graphene, certain graphynes are predicted to be intrinsic semiconductors. Among these intriguing structures, γ-graphyne stands out as the structurally simplest and most symmetric sp 1 /sp 2 lattice. γ-Graphyne was first theorized in 1987. In contrast with graphene, γ-graphyne will be a semiconductor with a small band gap suitable for fabrication of electronic devices. This solves one of the fundamental problems of carbon-based electronics, the necessity for inducing a band gap in graphene. γ-Graphyne has the potential to form the basis for the next generation of carbon-based electronics operating at speeds unattainable by traditional silicon chips. Unlike silicon, γ-graphyne is a direct band gap semiconductor, and it will feature exceptional strength comparable to that of other 2D carbon allotropes. Such combination of properties may enable a new generation of highly efficient, ultra-light and flexible solar cells. Despite being a potentially “magical” material, γ-graphyne remained synthetically elusive for over three decades. The primary goals of this project were: (1) Synthesis of bulk γ-graphyne phases through solution-phase 2D polymerizations; (2) Experimental exploration of the physical and chemical properties of γ-graphyne; and (3) Mechanistic and theoretical studies of the novel chemical transformations developed in Goal 1. Common pyrolytic and vapor-deposition methodologies used for the synthesis of graphitic allotropes are unsuitable for graphyne and other sp 1 -contaning structures, as acetylenes readily convert to graphene and amorphous carbon at high temperatures. In contrast, this proposal is based on solution-based 2D polymerization. The major advantages of this approach over the traditional high temperature techniques are the potential to adjust the structure of the material with atomic precision, and the possibility of using structurally complex and relatively fragile repeat units. The outcomes of this research can revolutionize carbon nanotechnology, expanding the field’s structural toolbox beyond primarily graphitic and benzenoid structures. Understanding the chemistry of sp 1 carbon allotropes can lead to entirely new classes of structures with unique properties, including graphyne ribbons, nanotubes, quantum dots, and heterostructures with other 2D materials. Furthermore, the development of reliable and robust synthetic pathways towards periodic covalent molecular sheets with atomically precise structures shall have a profound impact on chemistry and materials science.
Renewal: Coherent control of spin states in organic electronics – discovery and investigation of complex room-temperature magnetic quantum excitations
In the course of four funding cycles of this project, its research focused on the exploration and understanding of spin-dependent electronic processes in organic semiconductors. It aimed to investigate the potential of harnessing the spin degree of freedom in organic materials for various applications such as spin electronics, quantum information, sensors, and as well as quantum coherent spin phenomena of charge carrier states in organic semiconductors, with the aim to develop room-temperature-based quantum applications. Specifically, the project aimed to: Apply new diagnostic tools, i.e. spin spectroscopy techniques, for paramagnetic charge carrier states in organic semiconductors, based on coherent control with pulsed electron spin resonance to understand spin relaxation and spin mixing mechanisms in organic semiconductor materials and devices such as OLEDs. Explore the nature of charge carrier spin-coupling and pathways for its manipulation to control the physical behaviors of these materials. This involves investigating spin interactions through materials structure, composition, morphological dependencies, isotopic effects, and externally applied electric and magnetic fields, with the goal to manipulate electrical and optical material properties by adjusting spin-orbit, spin-dipolar, spin-exchange, as well as spin-hyperfine interactions to open up this materials class for new applications. Study spin-dependent charge carrier transport and recombination and how these observables are governed by spin-propagation, especially coherent spin propagation as well as collective spin-effects such as the spin-Dicke effect and resonant multi-photon magnetic dipole transitions. The project utilized pulsed electrically detected magnetic resonance (pEDMR) and pulsed optically detected magnetic resonance (pODMR) techniques over a wide frequency range. These techniques enabled the observation and quantification of various spin-spin coupling types, including spin-exchange, spin-dipolar, hyperfine, and spin-orbit interactions. The project will leverage low- to mid-frequency pEDMR/pODMR facilities and collaboration with the National High Magnetic Field Laboratory.
Unconventional excitonic states with phonon sidebands in layered silicon diphosphide
Complex correlated states emerging from many-body interactions between quasiparticles (electrons, excitons and phonons) are at the core of condensed matter physics and material science. In low-dimensional materials, quantum confinement affects the electronic, and subsequently, optical properties for these correlated states. Here, by combining photoluminescence, optical reflection measurements and ab initio theoretical calculations, we demonstrate an unconventional excitonic state and its bound phonon sideband in layered silicon diphosphide (SiP 2 ), where the bound electron–hole pair is composed of electrons confined within one-dimensional phosphorus–phosphorus chains and holes extended in two-dimensional SiP 2 layers. The excitonic state and emergent phonon sideband show linear dichroism and large energy redshifts with increasing temperature. Our ab initio many-body calculations confirm that the observed phonon sideband results from the correlated interaction between excitons and optical phonons. With these results, we propose layered SiP2 as a platform for the study of excitonic physics and many-particle effects.
A Lattice Litany for Transition Metal Oxides
In this tribute to K Alex Müeller, I describe how his early insights have influenced future decades of research on perovskite ferroelectrics and more broadly transition metal oxides (TMOs) and related quantum materials. I use his influence on my own research journey to discuss impacts in three areas: structural phase transitions, precursor structure, and quantum paraelectricity. I emphasize materials functionality in ground, metastable, and excited states arising from competitions among lattice, charge, and spin degrees of freedom, which results in highly tunable landscapes and complex networks of multiscale configurations controlling macroscopic functions. I discuss competitions between short- and long-range forces as particularly important in TMOs (and related materials classes) because of their localized and directional metal orbitals and the polarizable oxygen ions. I emphasize crucial consequences of elasticity and metal–oxygen charge transfer
Ionic Modulation at the LaAlO 3 /KTaO 3 Interface for Extreme High-Mobility Two-Dimensional Electron Gas
Due to the coexistence of many emergent phenomena, including 2D superconductivity and a large Rashba spin-orbit coupling, 5d transition metal oxides-based two-dimensional electron systems (2DESs) have been prospected as one of the potential intrants for modern electronics. However, despite the lighter electron mass, the mobility of carriers, a key requisite for high-performance devices, in 5d-oxides devices remains far behind their 3d-oxides analogs. The carriers’ mobility in these oxides is significantly hampered by the inevitable presence of defects. Here, in this study, very high mobility (≈22 650 cm 2 V –1 s –1 ) of 5d-2DES confined at the LaAlO 3 /KTaO 3 interface is reported. The high mobility, which is beyond the values observed in SrTiO 3 2DESs in the same carrier-density range, is achieved using the ionic-liquid gating at room temperature. The authors postulate that the ionic-liquid gating affects the oxygen vacancies and efficiently reduces any disorder at the interface. Investigating density and mobility in a broad range of back-gate voltage, the authors reveal that the mobility follows the power-law µ ∝ n 1.2 , indicating the very high quality of ionic-liquid-gated LaAlO 3 /KTaO 3 devices, consistent with the postulate. Furthermore, the analysis of the quantum oscillations confirms that the high-mobility electrons occupy the electronic sub-bands emerging from the Ta:5d orbitals of KTaO 3 .
Toward improved property prediction of 2D materials using many-body quantum Monte Carlo methods
The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.
Noncollinear spin order, field-induced transitions, and short-range correlations in Cu 4 SO 4 (OH) 6
We report a comprehensive study of spin-$\frac{1}{2}$ quantum magnet brochantite, Cu 4 SO 4 (OH) 6 , combining high-field thermodynamic measurements, polarized neutron diffraction, inelastic neutron scattering, and nuclear magnetic resonance spectroscopy. Using bulk magnetization and specific heat measurements we construct the magnetic 𝐻−𝑇 phase diagram for magnetic fields applied along main crystallographic directions up to 24.1 T. Polarized neutron diffraction reveals a noncollinear magnetic ground state confined to the 𝑎𝑏 plane. A field-induced transition is observed for magnetic fields in the 𝑎𝑏 plane whose critical field and character evolve continuously with field direction in the 𝑎𝑏 plane. While the transition for 𝐻 ∥ 𝑏 might be a spin-flop-like transition, the one for 𝐻 ∥ 𝑎 resembles the short-range correlated state above 𝑇 N , suggesting a magnetic configuration related to the quasi-two-dimensional correlations in the 𝑏𝑐 planes. The experimental results demonstrate that the ground-state and field-induced phases cannot be explained by a simple XXZ model with a single dominant exchange interaction and that weaker interchain and anisotropic interactions have to be taken into account. Our work establishes brochantite as a low-symmetry Cu-based quantum magnet with noncollinear order and complex field-induced behavior.
Highly Asymmetric Graphene Layer Doping and Band Structure Manipulation in Rare Earth–Graphene Heterostructure by Targeted Bonding of the Intercalated Gadolinium
Heterostructures consisting of vertically stacked two-dimensional (2D) materials have recently gained large attention due to their highly controllable electronic properties and resulting quantum phases. In contrast to the mechanically stacked multilayered systems, which offer exceptional control over a stacking sequence or interlayer twist angles, the epitaxially grown 2D materials express unprecedented quality and stability over wafer-scale lengths. However, controlling the growth conditions remains a major obstacle toward the formation of complex, epitaxial heterostructures with well-defined electronic properties. Here, we synthesized a trilayer graphene heterostructure on the SiC(0001) substrate with two specific interlayer locations occupied by gadolinium. We applied multitechnique methodology based on low-temperature scanning tunneling microscopy/spectroscopy (STM/S) and angle-resolved photoelectron spectroscopy (ARPES) to determine the intercalant’s locations in the complex, epitaxial graphene heterostructure. Our approach relies on very high quality and large, micrometer-scale homogeneity of the synthesized system. The experimentally determined electronic structure is dominated by the two topmost graphene layers. Overall, our spectroscopic results show quantitative agreement between global ARPES, local STM/S, and density functional theory predictions. The characterized electronic properties primarily reflect highly anisotropic doping levels between the two corresponding graphene layers, which significantly affect the band structure topology. Two pairs of hybridized massive Dirac bands from our initial synthesis–the bilayer graphene on the SiC(0001) substrate–are transformed upon Gd intercalation into two pairs of massless Dirac bands with a new hybridization region in between. Our results open perspectives in the realization of exotic 2D quantum materials via atomically precise synthesis of epitaxial, multilayered graphene–rare earth heterostructures.
Principles of two-dimensional terahertz spectroscopy of collective excitations: The case of Josephson plasmons in layered superconductors
Two-dimensional terahertz spectroscopy (2DTS), a terahertz analog of nuclear magnetic resonance, is a new technique poised to address many open questions in complex condensed matter systems. The conventional theoretical framework used ubiquitously for interpreting multidimensional spectra of discrete quantum level systems is, however, insufficient for the continua of collective excitations in strongly correlated materials. Here, in this work, we develop a theory for 2DTS of a model collective excitation, the Josephson plasma resonance in layered superconductors. Starting from a mean-field approach at temperatures well below the superconducting phase transition, we obtain expressions for the multidimensional nonlinear responses that are amenable to intuition derived from the conventional single-mode scenario. We then consider temperatures near the superconducting critical temperature T c , where dynamics beyond mean-field become important and conventional intuition fails. As fluctuations proliferate near T c , the dominant contribution to nonlinear response comes from an optical parametric drive of counterpropagating Josephson plasmons, which gives rise to 2D spectra that are qualitatively different from the mean-field predictions. As such, and in contrast to one-dimensional spectroscopy techniques, such as third harmonic generation, 2DTS can be used to directly probe thermally excited finite-momentum plasmons and their interactions. Our theory can readily be tested in cuprates, and we discuss implications beyond the present context of Josephson plasmons.
SIREN: Scaling Ion-Traps by REquiring iNnovative Heterogenous Integration
The SIREN (Scaling Ion Traps by Requiring iNnovative heterogenous integration) project explores the feasibility of heterogeneous integration (HI) as a transformative approach to scaling ion traps, a critical technology for advancing quantum computers and atomic clocks. Traditional ion trap architectures face significant challenges in scalability due to limitations in optical access, fabrication techniques, and material constraints. SIREN addresses these challenges by leveraging HI, which combines different materials and fabrication processes to create more complex and efficient ion trap structures. HI integrated structures can be manufactured without compromising the process to maintain compatibility to ion traps. This project focuses on integrating a separately fabricated waveguide with a fully functional ion trap. The respective alignment between the pieces needs to be accurate to less than 2 µm to ensure that the light from the waveguide can overlap with the trapping region. The fine alignment must also be maintained through an ultra-high vacuum bake, a critical step in preparing an ion trap experiment. The project's outcomes suggest that heterogeneous integration is a promising pathway for overcoming current scalability barriers, paving the way for the next generation of quantum technologies. SIREN's findings contribute significantly to the field, offering a scalable solution that could accelerate the development of practical quantum computers and highly accurate atomic clocks.