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713 records · Page 34

Stellar Population Properties in the Stellar Streams around SPRC047

Abstract We have investigated the properties (e.g., age, metallicity) of the stellar populations of a ringlike tidal stellar stream (or streams) around the edge-on galaxy SPRC047 (z= 0.031) using spectral energy distribution (SED) fits to integrated broadband aperture flux densities. We used visual images in six different bands and Spitzer/IRAC 3.6μm data. We have attempted to derive best-fit stellar population parameters (metallicity, age) in three noncontiguous segments of the stream. Due to the very low surface brightness of the stream, we have performed a deconvolution with a Richardson–Lucy–type algorithm of the low spatial resolution 3.6μm IRAC image, thereby reducing the effect of the point-spread function aliasedemissionfrom the bright edge-on central galaxy at the locations of our three stream segments. Our SED fits that used several different star formation (SF) history priors, from an exponentially decaying SF burst to continuous SF, indicate that the age–metallicity–dust degeneracy is not resolved, most likely because of inadequate wavelength coverage and low signal-to-noise ratios of the low surface brightness features. We also discuss how future deep visual–near-infrared observations, combined with absolute flux calibration uncertainties at or below the 1% level, complemented by equally well absolute flux-calibrated observations in ultraviolet and mid-infrared bands, would improve the accuracy of broadband SED fitting results for low surface brightness targets, such as stellar streams around nearby galaxies that are not resolved into stars.

Astronomy & Astrophysics

Future Projection of Tropical Upper-Tropospheric Troughs and Implications for Tropical Cyclone Activity

Summertime tropical upper-tropospheric troughs (TUTTs) provide a unified framework to better understand how extratropical and tropical forcings jointly modulate basin-scale tropical cyclone (TC) activity. In this study, we examine future changes in TUTTs and their implications for TC activity. Multimodel ensemble-mean projections from 45 Coupled Model Intercomparison Project phase 6 (CMIP6) models suggest a contraction of the Pacific TUTT and an expansion of the Atlantic TUTT as the climate warms. Consistently, future changes in environment-based TC indices indicate that the large-scale conditions will become more favorable for TC genesis and intensification over the central North Pacific but less favorable over the tropical North Atlantic and Gulf of Mexico. Utilizing a TC-permitting large-ensemble dataset [i.e., the Database for Policy Decision-Making for Future Climate Change (d4PDF)] that adequately captures the observed interannual TUTT–TC relationships, we further confirm the impacts of projected TUTT changes on the TC activity in a warmer climate. In contrast, the TUTT–TC relationship is poorly represented in most CMIP6 High-Resolution Model Intercomparison Project (HighResMIP) models; such deficiencies call for caution when assessing future TC risk based on explicitly tracked TCs in these models. Additionally, CMIP6 projections show large intermodel spread in TUTT changes, implying uncertainty in projected TC activity, especially over the central-to-eastern Pacific and the North Atlantic. This intermodel spread is associated with interhemispheric sea surface temperature warming asymmetry, which leads to a meridional shift of the intertropical convergence zone (ITCZ) and the simultaneous weakening or strengthening of TUTTs in the North Pacific and North Atlantic. The potential contributions of anthropogenic aerosol forcing and oceanic circulation to this interhemispheric warming asymmetry are briefly examined.

Climate Change

Enhanced Optical Contrast and Switching in Near‐Infrared Electrochromic Devices by Optimizing Conjugated Polymer Oligo(Ethylene Glycol) Sidechain Content and Gel Electrolyte Composition

Abstract A detailed investigation addressing the effects of functionalizing conjugated polymers with oligo(ethylene glycol) (EG n ) sidechains on the performance and polymer‐electrolyte compatibility of electrochromic devices (ECDs) is reported. The electrochemistry for a series of donor‐acceptor copolymers having near‐infrared (NIR)‐optical absorption, where the donor fragment is 3,4‐ethylenedioxythiophene (EDOT) or an EG n functionalized bithiophene (g2T) and the acceptor fragment is diketopyrrolopyrrole (DPP) functionalized with branched alkyl or EG n sidechains, is extensively probed. ECDs are next fabricated and it is found that EG n sidechain incorporation must be finely balanced to promote polymer‐electrolyte compatibility and provide efficient ion exchange. Proper electrolyte‐cation pairing and polymer structural tuning affords a 2x increase in optical contrast (from 12% to 24%) and >60x reduction in switching time (from 20 to 0.3 s). Atomic force microscopy (AFM)/grazing incidence wide‐angle X‐ray scattering (GIWAXS) characterization of the polymer film morphology/microstructure reveals that an over‐abundance of EG n sidechains generates large polymer crystallites, which can suppress ion exchange. Lastly, time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) indicates sidechain/electrolyte identity does not influence the electrolyte penetration depth into the films, and EG n sidechain inclusion increases electrolyte cation uptake. The material structural design insight and guidelines regarding the polymer‐electrolyte ion insertion/expulsion dynamics reported here should be of significant utility for developing next‐generation mixed ionic‐electronic conducting materials.

Chemistry

Three-dimensional nucleation and growth of deformation twins in magnesium

At two-thirds the weight of aluminum, magnesium alloys have the potential to reduce the fuel consumption of transportation vehicles. These advancements depend on our ability to optimize the desirable versus undesirable effects of deformation twins, which are three-dimensional (3D) microstructural domains that form under mechanical stresses. Previously only characterized through surface or thin-film measurements, we here present 3D in situ characterization of deformation twinning inside an embedded grain over mesoscopic fields of view using dark-field x-ray microscopy supported by crystal plasticity finite element analysis. The results revealed the role of triple junctions on twin nucleation and the sequence and irregularity of twin growth and showed that twin-grain junctions, twin-twin junctions, and twin boundaries were the sites of localized dislocation accumulation.

Lee, Sangwon [Univ. of Michigan, Ann Arbor, MI (Un

Coordinated Natural Gas and Electric Planning: Case Studies of Current Approaches and Practices

This paper examines how natural gas and electric utilities across eight U.S. states and two Canadian provinces are beginning to coordinate historically separate planning processes in response to growing system interdependencies, policy mandates, aging infrastructure, and changing customer energy choices. Electricity planning has long relied on robust integrated resource planning frameworks that weigh numerous objectives, risks, and costs. Natural gas planning, on the other hand, is typically less transparent and more narrowly focused on safety and system integrity. As economic, reliability, and policy drivers place new and shared demands on both systems, jurisdictions and utilities are experimenting with approaches such as coordinated forecasting, non pipeline alternatives, and combined planning pilots. A few have issued regulatory or statutory directives for greater data sharing and methodological alignment. Case studies from British Columbia, California, Colorado, Illinois, Massachusetts, Minnesota, New York, Québec, Rhode Island, and Washington illustrate a wide range of approaches to rethinking siloed planning. The paper identifies several common themes across the jurisdictions examined. It provides observations on the methods, processes, and organizational steps that may be needed in the future to address the challenges being faced by states and utilities. Lastly, it identifies some initial steps that states and utilities can consider if they would like to pursue more integrated, cost-effective, policy-aligned energy system planning.

03 NATURAL GAS

Fingerprinting Uranium Oxides with Electron Energy Loss Spectroscopy Supported by Theoretical Computations

Uranium oxides occur in a variety of phases that differ in crystal structure and uranium oxidation states. Electron energy loss spectroscopy (EELS) is one of the few techniques that has sufficient spatial resolution and sensitivity to electronic structure to distinguish amongst phases at the nanoscale. However, beam-sensitive materials such as uranium oxides are subject to spectral modification due to interactions with the electron beam. Therefore, theory support is essential to reliably exclude the impact of beam damage and generate true reference datasets. Here we use a comparison of theoretical and experimental spectra to probe the impact of beam damage on O K-edge and U N-edge (N6,7 and N4,5) EELS spectra of various single-valent and mixed-valence uranium oxide bulk phases. Using a low-dose experimental set-up, we show that the O K-edge theoretical spectra are in excellent agreement with experiment for both peak positions and relative intensities of respective peaks. In contrast, U N-edge features are less distinguishing due to the partially localized nature of the U 5f orbitals and overlapping multiplet and spin–orbit coupling effects. This work demonstrates that O K-edge EELS is sufficiently diagnostic to distinguish a wide range of uranium oxides and that the experimental approach used here minimizes beam damage and allows valence state discrimination across the U(IV), U(V) and U(VI) series. When combined with imaging modes available in electron mi-croscopy, the work enables detailed investigation and characterization of uranium redox transformations at the nanoscale.

Carbone, Jacopo

Monolayer Films of Binary Metal Oxide Nanoparticles for Carbon Nanotube Synthesis

Binary metal oxide nanoparticles (biMO-NPs) combining transition and main-group metals with well-organized atomic architectures have unique potential as robust and economical heterogeneous catalysts. Herein, metal oxide nanoparticles (CoAlxOy) using cobalt and aluminum were synthesized, and their structure, morphology, and chemical composition were investigated using various characterization techniques. The biMO-NPs, which had a Gaussian-type size distribution (∼6 nm), were assembled on plain silicon substrates modified chemically with linker molecules bearing suitable end groups. Surface analysis revealed an ordered, uniform, close-packed arrangement of biMO-NPs forming a monolayer architecture with nanoscale thickness (∼12 nm), high surface uniformity, and negligible defects. The nanoparticle monolayer film (NP-MF) was employed as a catalyst to grow carbon nanotube (CNT) forests via the thermal chemical vapor deposition (CVD) method, similar to those grown from catalyst thin films deposited by physical vapor deposition. Structural characterization confirmed the growth of a dense, uniform, high-quality vertically aligned carbon nanotube (VA-CNT) forest with a length of ∼125 µm, which is comparable to the VA-CNTs grown from expensive thin films. Thus, CNT growth was successfully catalyzed by the biMO-NPs, highlighting a simple and inexpensive alternative for catalyst deposition. In this innovative wet-chemistry approach, the catalyst and catalyst support are combined within a single nanoparticle before NP-MF assembly. Interestingly, this approach provides a scalable and cost-effective pathway for CNT growth, eliminating the need for expensive thin deposition techniques.

Regmi, Bishow [University of Cincinnati]

Investigating permafrost carbon dynamics in Alaska with artificial intelligence

Abstract Positive feedbacks between permafrost degradation and the release of soil carbon into the atmosphere impact land–atmosphere interactions, disrupt the global carbon cycle, and accelerate climate change. The widespread distribution of thawing permafrost is causing a cascade of geophysical and biochemical disturbances with global impacts. Currently, few earth system models account for permafrost carbon feedback (PCF) mechanisms. This research study integrates artificial intelligence (AI) tools and information derived from field-scale surveys across the tundra and boreal landscapes in Alaska. We identify and interpret the permafrost carbon cycling links and feedback sensitivities with GeoCryoAI, a hybridized multimodal deep learning (DL) architecture of stacked convolutionally layered, memory-encoded recurrent neural networks (NN). This framework integratesin-situmeasurements and flux tower observations for teacher forcing and model training. Preliminary experiments to quantify, validate, and forecast permafrost degradation and carbon efflux across Alaska demonstrate the fidelity of this data-driven architecture. More specifically, GeoCryoAI logs the ecological memory and effectively learns covariate dynamics while demonstrating an aptitude to simulate and forecast PCF dynamics—active layer thickness (ALT), carbon dioxide flux (CO 2 ), and methane flux (CH 4 )—with high precision and minimal loss (i.e. ALT RMSE : 1.327 cm [1969–2022]; CO 2 RMSE : 0.697µmolCO 2 m −2 s −1 [2003–2021]; CH 4 RMSE : 0.715 nmolCH 4 m −2 s −1 [2011–2022]). ALT variability is a sensitive harbinger of change, a unique signal characterizing the PCF, and our model is the first characterization of these dynamics across space and time.

Environmental Sciences & Ecology

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE

In Situ Tracking of Nonthermal Plasma Etching of ZIF-8 Films

Surface characterization is critical for understanding the processes used for preparing catalysts, sorbents, and membranes. Nonthermal plasma (NTP) is a process that achieves high reactivity at low temperatures and is used to tailor the surface properties of materials. In this work, we combine the capabilities of infrared reflection absorption spectroscopy (IRRAS) with NTP for the in situ interrogation of zeolitic imidazolate framework-8 (ZIF-8) thin films to probe modifications in the material induced by oxygen and nitrogen plasmas. The IRRAS measurements in oxygen plasma reveal etching of organic ligands with sequential removal of the methyl group and imidazole ring and with the formation of carbonyl moieties (C═O). In contrast, nitrogen plasma induces mild etching and grafting of nitrile groups (−C≡N). Scanning electron microscopy imaging shows that oxygen plasma, at prolonged times, significantly degrades the ZIF-8 film at the grain boundaries. Treatment of ZIF-8 membranes using mild plasma conditions yields a fivefold enhancement for H 2 /N 2 and CO 2 /CH 4 ideal selectivities and an eightfold enhancement for CO 2 /N 2 ideal selectivity. Additionally, the new tools described here can be used for spectroscopic in situ tracking of plasma-induced chemistry on thin films in general.

IRRAS

Multiscale and multidimensional modeling of particle acceleration and transport in solar flares

Multi-messenger, multi-viewpoint, and time-resolved observations of solar flares are now providing unprecedented constraints on particle acceleration sites, energy conversion, and energy transport. The interpretation of current observations, including microwave imaging spectroscopy from EOVSA, hard x-ray (HXR) imaging from Solar Orbiter/STIX, gamma-ray diagnostics from Fermi, and in situ measurements from Parker Solar Probe and Solar Orbiter, collectively demands modeling frameworks that go beyond traditional spatially unresolved, one-zone models or single-mechanism descriptions. This review surveys multiscale and multidimensional modeling approaches, including kinetic, magnetohydrodynamic (MHD), and macroscopic particle models, that are being developed to meet the need. Kinetic simulations reveal that three-dimensional (3D) effects, including field-line chaos and self-generated turbulence, are essential for sustained power-law particle acceleration. MHD simulations now capture flux-rope eruptions, plasmoid-unstable current sheets, and turbulent flare regions in realistic magnetic topologies. Macroscopic models coupling MHD with energetic-particle models produce spatially resolved electron distributions and synthetic HXR and microwave emissions for direct comparison with observations. Despite these advances, outstanding challenges remain in bridging kinetic and global scales, improving MHD simulations and macroscopic particle models, and achieving quantitative model-observation closure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Tailoring Ion Transport in Li 3‐3y Ho 1+y Cl 6‐x Br x via Transition‐Metal Free Structural Planes and Charge Carrier Distribution

Abstract Localized atomistic disorder in halide‐based solid electrolytes (SEs) can be leveraged to boost Li + mobility. In this study, Li + transport in structurally modified Li 3 HoCl 6 , via Br − introduction and Li + deficiency, is explored. The optimized Li 3‐3 y Ho 1+ y Cl 6‐ x Br x achieves an ionic conductivity of 3.8 mS cm −1 at 25 °C, the highest reported for holmium halide materials. 6,7 Li nuclear magnetic resonance and relaxometry investigations unveil enhanced ion dynamics with bromination, attaining a Li + motional rate neighboring 116 MHz. X‐ray diffraction analyses reveal mixed‐anion‐induced phase transitions with disproportionate octahedral expansions and distortions, creating Ho‐free planes with favorable energetics for Li + migration. Bond valence site energy analysis highlights preferred Li + transport pathways, particularly in structural planes devoid of Ho 3+ blocking effects. Molecular dynamics simulations corroborate enhanced Li + diffusion with Br − introduction into Li 3 HoCl 6 . Li‐Ho electrostatic repulsions in the (001) plane presumably drive Li + diffusion into the Ho‐free (002) layer, enabling rapid intraplanar Li + motion and exchange between the 2d and 4h sites. Li 3‐3 y Ho 1+ y Cl 6‐ x Br x also demonstrates good battery cycling stability. These findings offer valuable insights into the intricate correlations between structure and ion transport and will help guide the design of high‐performance fast ion conductors for all‐solid‐state batteries.

Chemistry

Simulation to a Newborn Supernova Remnant from a Low-mass Iron Core Star

Supernova remnant observations show a high degree of asymmetry, mixing, and inhomogeneity. These asymmetries are seeded during the early seconds of the explosion and are further enhanced and modified as the shock and ejecta move through the stellar progenitor and into the circumstellar medium. We present simulations of a 9.6 M⊙ zero-metallicity progenitor initialized after shock revival and evolved for several years when the ejecta is in the circumstellar medium. A suite of 1D and 2D simulations examines the effects of neutron-star wind and radioactive decay heating. In 1D, decay heating forms a low-density bubble that suppresses the reverse shock. While in 2D, the heating is localized to metal-rich pockets, inflating them and compressing the surrounding material into dense shells. In 3D, the neutron-star wind and decay heating modify the plume morphology, producing more large-scale structures. The extended plume morphology leads to an asymmetrical shock breakout. After breakout, the leading plumes cannot keep up with the shock front, resulting in deceleration and fragmentation by the reverse shock while retaining the large-scale asymmetry. The projected ejecta morphology and velocities are strongly viewing angle dependent. The relatively uniform metal-rich distribution does not resemble the strongly inhomogeneous ejecta structure of Cas A. The 160-isotope decay network shows that 24.4% of the radioactive heating comes from decay chains other than the canonical 56Ni chain. The low explosion energy, low 56Ni yield, and Ni/Fe ratio greater than unity suggest an observational signature similar to an electron capture supernova.

Neopane, Sudarshan [University of Tennessee (UT)]

A strong and ductile Super Kovar alloy via fully coherent nanoprecipitates

Emerging high-precision technologies demand materials with exceptional dimensional stability and mechanical robustness, as even microscopic thermomechanical deformation can cause functional failure. However, a fundamental trilemma exists: High strength, ductility, and low thermal expansion are mutually exclusive, as strengthening-induced lattice distortions compromise the spin-lattice coupling, which is essential for low thermal expansion. Here, we overcome this trilemma by designing “Super Kovar,” an Fe-Ni-Co-Al-Ta alloy, featuring fully coherent nanoprecipitates. It unifies a 1.0-gigapascal ultimate tensile strength and ∼39% elongation with a Kovar-grade thermal expansion of 3.81 × 10−6 K−1 (100 to 410 K). The key is a dense dispersion of L12 nanoprecipitates that form an almost strain-free coherent interface with the ferromagnetic matrix. Beyond providing precipitation strengthening, these coherent interfaces suppress intrinsic phonons of nanoprecipitates via elastic coupling while avoiding magnetic domain pinning to preserve the Invar effect of the matrix. This reduces the thermal expansion of the precipitates by 56% and achieves a fourfold enhancement in the strength-ductility product, establishing a paradigm for dimensionally stable, ultrastrong alloys.

Yu, Chengyi [University of Science and Technology

Emergence of low-energy spin waves in superconducting electron-doped cuprates

In order to fully utilize the technological potential of unconventional superconductors, an enhanced understanding of the superconducting mechanism is necessary. In the best performing superconductors, the cuprates, superconductivity is intimately linked with magnetism, although the details of this coupling remain elusive. Here, we address this gap by studying the electron-doped cuprate Nd 1.85 Ce 0.15 CuO 4−δ that has an antiferromagnetic ground state when synthesized and only becomes superconducting after a reductive annealing process. Using neutron spectroscopy, we show that the as-grown crystal exhibits a large spin pseudogap in the magnetic fluctuation spectrum. Annealing removes defects introduced by the commonly employed synthesis method and significantly reduces the spin pseudogap. While the spin pseudogap in the annealed sample likely arises from superconductivity, in the as-grown sample it results from the absence of long-wavelength spin waves. These results reveal a direct connection between defects, magnetism, and superconductivity, offering new insight into the mechanisms underlying high-temperature superconductivity and guiding the design of improved superconducting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Large moiré superstructure of stacked incommensurate charge density waves

This article reports how two different charge density waves with slightly different wavevectors can exist in the same crystal and create moiré superstructure. Advances in heterostructure fabrication have opened new frontiers in moiré physics. Here we extend moiré engineering from artificially assembled thin flakes with mismatched lattice parameters to materials that host incommensurate orders, presenting a long-period moiré superlattice in a layered charge-density-wave compound, EuTe 4 . Using high-momentum-resolution X-ray diffraction, we found two coexisting incommensurate charge density waves with slightly mismatched in-plane wavevectors. The interaction between these two charge density waves leads to joint commensuration with the lattice and a moiré superstructure with a period of ~13.6 nm, offering key insights into the unique properties of EuTe4, such as the temperature-invariant incommensurate wavevectors and unconventional in-gap states. Owing to interlayer phase shifts, the moiré superstructure exhibits a clear thermal hysteresis, accounting for the large hysteresis in electrical resistivity and numerous metastable states. Our findings open new directions for moiré engineering based on incommensurate lattices and highlight the important role of interlayer ordering in stacked structures.

36 MATERIALS SCIENCE

Cobalt-free and high-rate stable 5V lithium nickel manganese oxide spinel cathodes enabled via surface oxygen vacancies

Spinel LiNi 0.5 Mn 1.5 O 4 offers both the high-rate, low-cost and safety advantages of LiFePO 4 and the high energy density of LiNiₓMnᵧCo₁₋ₓ₋ᵧO₂ and LiNiₓCoᵧAlzO₂ cathodes. However, the large operating voltage of these materials induces electrolyte oxidation, which degrades the interface and drives Mn dissolution. These reactions are further exacerbated at high rates due to temperature rise. In this study, we discover that ammoniacal treatment followed by annealing introduces a high density of oxygen vacancies in the “near-surface region” of LiNi 0.5 Mn 1.5 O 4 particles. These vacancies release electrons changing the oxidation state of Mn and suppressing its tendency to oxidize the electrolyte. Further, these vacancies enhance the electrode’s electronic conductivity (by ∼3-fold) and Li + diffusivity (by ∼2-fold) greatly improving charge transport, especially when operated at high rates. This results in an across-the-board improvement in self-discharge, specific capacity, energy density, rate capability, coulombic efficiency and cycling stability. When cycled at ∼200 mA g −1 , the capacity fade averaged over 3000 cycles for the surface vacancy-enriched material is ∼0.0167% per cycle compared to an order of magnitude higher fade rate for the baseline material. In conclusion, these findings reveal the potential of targeted surface oxygen vacancy doping to develop cobalt-free and high energy density cathodes that tolerate fast charging and deliver improved cycle life.

Cobalt-free cathodes

Dressed-State Hamiltonian Engineering in a Strongly Interacting Solid-State Spin Ensemble

In quantum science applications, ranging from many-body physics to quantum metrology, dipolar interactions in spin ensembles are often controlled via Floquet engineering. However, this technique typically reduces the interaction strength between spins and effectively weakens the coupling to a target sensing field, limiting the metrological sensitivity. In this Letter, we develop and demonstrate an alternative method that directly tunes the native dipolar interaction in an ensemble of nitrogen-vacancy (NV) centers in diamond, thereby overcoming these limitations inherent to Floquet engineering. Our approach utilizes dressed-state qubit encoding under a bias magnetic field applied perpendicular to the crystal lattice orientation. This method leads to a 3.2× enhancement of the dimensionless coherence parameter JT 2 compared to state-of-the-art Floquet engineering and a 2.6× (8.3 dB) enhanced sensitivity in ac magnetometry. Furthermore, our results provide a powerful Hamiltonian engineering tool for future studies with NV ensembles and other interacting higher-spin (S > $\frac{1}{2}$) systems.

Quantum control