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DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗

DOE OSTI2022

Comparing the extraction performance of cyclodextrin-containing supramolecular deep eutectic solvents versus conventional deep eutectic solvents by headspace single drop microextraction

A headspace single drop microextraction (HS-SDME) method coupled with high performance liquid chromatography was developed to compare the extraction of eighteen aromatic organic pollutants from aqueous solutions using cyclodextrin-based supramolecular deep eutectic solvents (SUPRADESs) and alkylammonium halide-based conventional deep eutectic solvents (DESs). Different derivatives of beta-cyclodextrin (β-CD) were employed as hydrogen bond acceptors (HBA) in SUPRADESs and the extraction performance investigated. SUPRADES comprised of the 20 wt% native β-CD HBA provided the highest enrichment factors of analytes compared to SUPRADESs comprised of other derivatives of β-CD (random methylated β-cyclodextrin, heptakis(2,3,6-tri-O-methyl)-β-cyclodextrin, and 2-hydroxypropyl β-cyclodextrin). In addition, native β-CD and its derivatives were dissolved in the neat DESs and their effect on the extraction of analytes examined. Dissolution of 20 wt% native β-CD in the choline chloride ([Ch + ][Cl - ]):2Urea DES resulted in a significant increase in the extraction efficiencies of target analytes compared to the neat [Ch + ][Cl - ]:2Urea DES. Under optimum conditions, the extraction method required a solvent microdroplet of 6.5 μL, 1000 rpm stir rate, 30% (w/v) salt concentration, and a temperature of 40 °C. The tetrabutylammonium chloride: 2 lactic acid DES resulted in the highest enrichment factors while the [Ch + ][Cl - ]:2Urea DES had the lowest for most of the analytes among the evaluated solvents. The method provided limits of detection (LODs) down to 35 μg L -1 . Finally, the developed method was applied for the analysis of spiked tap and lake water, where relative recoveries ranging from 83.7% -119.7% and relative standard deviations lower than 19.2% were achieved.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract : Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Robinson, Alex W.↗

DOE OSTI2023

Phase diagram of twisted bilayer graphene at filling factor $v = ±3$

Here, we study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $v = ±3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing translation symmetry breaking terms, we obtain the phase diagram with respect to the ratio of AA interlayer hopping (w 0 ) and AB interlayer hopping (w 1 ). When the interlayer hopping ratio is close to the chiral limit (w 0 /w 1 ≲ 0.5), a quantum anomalous Hall state with Chern number v c = ±1 can be observed consistent with previous studies. Around the realistic value w 0 /w 1 ≈ 0.8, we find a spin and valley polarized, translation symmetry breaking, state with C 2⁢z T symmetry, a charge gap and a doubling of the moiré unit cell, dubbed theC 2⁢z T stripe phase. The real-space total charge distribution of this C 2⁢z T stripe phase in the flat band limit does not have modulation between different moiré unit cells, although the charge density in each layer is modulated, and the translation symmetry is strongly broken. Other symmetries, including C 2⁢z , C 2⁢x , particle-hole symmetry P, and the topology of the C 2⁢z T stripe phase, are also discussed in detail. We observed braiding and annihilation of the Dirac nodes by continuously turning on the order parameter to its fully self-consistent value, and provide a detailed explanation of the mechanism for the charge gap opening despite preserving C 2⁢z T and valley U⁡(1) symmetries. In the transition region between the quantum anomalous Hall phase and the C 2⁢z T stripe phase, we find an additional competing state with comparable energy corresponding to a phase with a tripling of the moiré unit cell.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Glycolate Analysis in Tank 22: Developing and Testing Analytical Methods for the Savannah River Site Liquid Waste System

Researchers developed and tested a range of techniques to support a low mg/L Limit of Quantitation (LOQ) of glycolate in radioactive Tank 22 waste solution by Ion Chromatography (IC) and by proton NMR. For the IC method, Dionex OnGuard II cartridges were tested as a means of removing alkali earth and transition metals that can interfere during ion chromatography applications especially when analyzing for low-concentration, chelating analytes. Additionally, concentrations of nitrate in the raw Tank 22 sample (5,000 to 10,000 mg/L) were managed by using reasonable levels of sample dilution. The resulting IC performance quality was enhanced by improving the baseline, increasing sensitivity [Limit of Quantitation (LOQ) of 12 mg/L and Limit of Detection (LOD) of 4.0 mg/L], and resolving analytes into well-defined Gaussian peaks when using the Dionex OnGuard II H⁺ cartridges to remove matrix interferences. High concentrations of nitrate limited the performance of the IC method. To achieve an acceptable baseline, samples with high nitrate content require more dilution, resulting in higher detection limits. Tests on samples with higher concentrations of nitrate (Tank 30 and 32 supernate with approximately 150000 mg/L nitrate) suggested that IC detection limits for glycolate in these samples would be > 500 mg/L. Thus, an LOQ of 12 mg/L is not feasible by this IC method on evaporator feed samples. An alternative method of glycolate analysis, using proton nuclear magnetic resonance (H NMR), was developed by the research team. In initial tests, the H NMR technique provided reasonable quantitation of glycolate in Tank 22 conditions by direct observation of the liquid. The H NMR method may provide improved detection limits for solutions with higher nitrate concentrations. We recommend further development of this analysis for high nitrate LWS samples such as evaporator feed and evaporator drop tank content. A method for pretreatment of samples using crystalline silicotitanate (CST) was developed and tested. The objective of the pretreatment was to facilitate analysis of samples with higher levels of radioactivity. The pretreatment did not influence the glycolate concentration in solution, and the pretreatment is projected to reduce Cs 137 activity in a sample by a factor of 16,200. The double strike CST pretreatment was demonstrated and would allow milliliters of higher activity samples to be transferred from the Shielded Cells and handled in a containment unit for glycolate analysis. The various studies validated IC and H NMR methods for glycolate analysis, defined the range of applicability, and demonstrated key supporting analytical protocols. Based on the results, high quality glycolate analysis of Tank 22 is feasible down to approximately 12 mg/L, with the potential for broader applicability of the methods to other conditions in the Savannah River Site Liquid Waste System (LWS).

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Polarization-dependent electrocaloric and pyroelectric effects in ferroelectric BaTiO 3 thin films

In this paper we examine the influence of controllable polarization reversal and built-in electric fields on pyroelectric and electrocaloric effects in a BaTiO 3 thin film using a modified indirect method. We find that the magnitude of the sample's change in polarization with temperature is sensitive to the degree of polarization reversal. The pyroelectric response is small at low fractions of switched polarization and grows larger by several factors as larger fractions of polarization are reversed. This polarization reversal-sensitive pyroelectric behavior is the result of an internal built-in field, which has the effect of destabilizing low fractions of switched polarization and producing diminished pyroelectric effect. Greater fractions of switched polarization are more stable against backswitching and permit a larger pyroelectric response. Our findings highlight a characterization method for polarization-dependent pyroelectric effects in ferroelectric thin films, where built-in field effects are also present.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid

This paper investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. Furthermore, in order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. Additionally, the performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

42 ENGINEERING↗

DOE OSTI2024

Field‐representative evaluation of PID‐polarization in TOPCon PV modules by accelerated stress testing

Abstract Potential‐induced degradation‐polarization (PID‐p) can reduce module power, but how to project the extent to which PID‐p may occur in field conditions considering the factors of system voltage, condensed moisture, temperature, and illumination has not been clarified. Using tunnel oxide passivated contact (TOPCon) modules, this work demonstrates a method to test full‐size crystalline silicon PV modules for PID‐p to provide field‐representative results. In initial screening tests with positive or negative 1000 V electrical bias applied at 60°C for 96 h using Al foil electrodes on the glass surfaces, the module type exhibited reversible PID‐p only on the front face when the cell circuit was in negative voltage potential. No PID was detected on the rear after testing in either polarity. We then evaluated the PID‐p sensitivity on the front side under different UV irradiances while maintaining the glass surface wet to estimate real‐world susceptibility to PID‐p. The magnitude of the observed behavior was fit using a previously developed charge transfer and depletion by light model. Whereas power loss with −1000 V applied to the cell circuit at 60°C for 96 h in the dark was about 30%, testing the module front under 0.051 W·m −2 nm −1 at 340 nm UVA irradiation using fluorescent tubes, the mean degradation was only 3%. When the modules were tested in the dark for PID‐p with in situ dark current–voltage (I‐V) characterization, the thermal activation energy for degradation was 0.71 eV; for recovery in the dark, it was 0.58 eV. Whereas recovery from the degraded state at 60°C in the dark without voltage bias was 5% absolute in 38 h, rapid recovery of about 5% absolute was observed with 1000 W·s/m 2 exposure at 25°C using a flash tester.

14 SOLAR ENERGY↗

DOE OSTI2022

Hydrodynamics of countercurrent flow in an additive-manufactured column with triply periodic minimal surfaces for carbon dioxide capture

Computational investigation of the countercurrent flows in an additively manufactured (AM) column packed with triply periodic minimal surface (TPMS) is challenging. Multiphase flow simulations using the volume of fluid (VOF) method can explain the column’s hydrodynamic characteristics, including interfacial area, liquid holdup, pressure drop, flow regime, etc. The interfacial area is a key factor dictating the mass transfer via the absorption process, and thereby the overall efficiency of the column. The impacts of a solvent's physical properties, liquid and gas loads, and contact angle on the hydrodynamics are extensively explored. The solvents include traditional solvent (monoethanolamine [MEA]) used in industry as well as a water-lean solvent (EEMPA) as prospective solvents for carbon capture. As expected, interfacial area and liquid holdup increase with increasing liquid loads (q L ). The EEMPA exhibits higher values for the interfacial area and liquid holdup compared to those for the MEA. The dry and wet pressure drops per unit length in the column at different gas loads (F G ) are calculated and further compared with the empirical correlations for traditional packings. At low gas loads, i.e., in the preloading regime, the predicted values of the wet and dry pressure drops match well with the corresponding values calculated from available correlations. The gas load has a marginal impact on the interfacial area at its lower value, but the higher value of F G (>2.18 $\sqrt{Pa}$) causes flooding in the column. The effect of varying contact angles on the interfacial area and liquid holdup in the preloading regime is also studied. Both interfacial area and liquid holdup decrease with the increase in the value of the contact angle. Altogether, the effect of the contact angle on interfacial area is more pronounced than other parameters influencing the interfacial area.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Factors controlling pore network development of thermally mature Early Palaeozoic mudstones from the Baltic Basin (N Poland)

Understanding the formation of pore space, especially in low porosity shales (as source rocks and as unconventional resources), is critical to the oil and gas industry, since pores control the space available for hydrocarbon and participate in hydrocarbon transport. We examined 87 Ordovician and Silurian mudstone samples collected from four wells located in the Pomeranian part of the Baltic Basin (northern Poland), one of the primary Polish targets for hydrocarbon exploration. These samples represent the Pelplin, the Paslek, the Jantar, the Prabuty, and the Sasino Formations, which still requires more detailed porosity studies. Our study aimed to identify factors controlling porosity development, by applying bulk techniques (organic petrology and TOC analyses, quantitative mineralogy, and porosimetry) as well as nano- to microscale techniques (thin section petrography, electron microscopy). The studied samples are mainly argillaceous mudstones. The results of porosimetry measurements, combined with image analysis, indicate that the pores of all studied rocks are dominated by micropores (pores < 2 nm in diameter), mesopores (2-50 nm in diameter) and small macropores. The SEM images showed three main pore types: a) voids related to clay mineral aggregates, b) pores inside organic matter particles, and c) pores between other mineral grains. In the Jantar and Sasino mudstones, the organic matter content and its thermal maturity control porosity. The occurrence of solid bitumen in the rocks from these formations reduces samples’ mesoporosity because of the pore-clogging effect. In contrast, in the Paslek and Prabuty Formations, there is low organic matter content and specific surface area and the volume of mesopores increase with clay minerals content. In the Pelplin mudstones, there are no prevailing factors controlling porosity. As a result, we suggest that a combination of SEM image analysis and dual liquid porosity (DLP) measurements is a powerful method to assess porosity available for petroleum flow in mudstones.

03 NATURAL GAS↗

DOE OSTI2023

From ash to oxides: Recovery of rare-earth elements as a step towards valorization of coal fly ash waste

Coal fly ash (CFA) is both a valuable waste material and a potential source of environmental contamination. The inclusion of metals such as rare-earth elements offer a possible incentive towards waste valorization if the metals can be extracted and recovered in an economical manner. Rare-earth elements (REEs) have many technological applications and are critically important in the manufacture of electric vehicles, communication devices, and industrial magnets. However, the global supply of rare-earth elements has faced shortages and price shocks. Current methods for separating and isolating individual rare-earth elements use large amounts of energy and organic solvents, raising concerns over environmental impacts. These factors have led to the investigation of nontraditional sources and separation techniques for these elements. Here, we describe a column-based system that uses a newly developed ligand-associated organosilica sorbent to concentrate and separate rare-earth elements from fly ash leachate. The fly ash used in this study originally contained 0.024 wt% rare-earth elements and the final oxide powder after enrichment contained > 10 wt% rare-earth elements, which is a enrichment of > 400 times. This process requires no additional organic solvents after the sorbent media has been synthesized, offering an alternative to the current standard using solvent extraction for rare-earth element recovery.

42 ENGINEERING↗

DOE OSTI2025

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES↗

DOE OSTI2021

Atom Equivalent Energies for the Rapid Estimation of the Heat of Formation of Explosive Molecules from Density Functional Tight Binding Theory

Atom equivalent energies have been derived from which the gas-phase heat of formation of explosive molecules can be estimated from fast, semiempirical density functional tight binding total energy calculations. The root-mean-square deviation and maximum deviation of the heats of formation from the experimental values for the set of 45 energetic molecules compiled by Byrd and Rice [ J. Phys. Chem. A, 2006, 110, 1005–1013] are 10.4 and 25.5 kcal/mol, respectively, using 4 atom equivalent energies and 7.4 and 15.0 kcal/mol, respectively, using 7 atom equivalent energies. These errors are around a factor of 2–3 larger than those obtained from density functional theory calculations but are smaller than those obtained from other semiempirical electronic structure methods. Heats of formation calculated with density functional tight binding theory using the 4 and 7 atom equivalent energies, the Byrd and Rice scheme, and the atom pair contribution method for a new set of 531 energetic molecules that contain only carbon, hydrogen, nitrogen, and oxygen are provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Kβ X-ray Emission Spectra Analysis Using Bayesian Optimization

The Kβ X-ray emission spectrum of 3 d transition metals is rich with electronic and structural information due to strong exchange interactions with the valence shell of the metal, and has become crucial for understanding their spin and oxidation states. The spectrum is commonly treated using crystal-field multiplet theory, a semi-empirical theory that uses tunable parameters to control the strength of the effects present in X-ray emission spectroscopy (XES). However, determining the experimental values of these parameters remains a challenge. We present a methodology that applies Bayesian optimization to crystal-field multiplet theory to determine parameter values. The algorithm is tested on the X-ray emission spectra of a collection of Mn, Co, and Ni oxides. We are able to find optimal values for the four most impactful parameters: Slater−Condon reduction factors F dd , F pd , and G pd , and crystal field splitting 10 Dq . The algorithm produces significantly improved accuracy compared to current analysis methods, and probes interparameter dependencies by modeling the error landscape. This advancement enhances XES analysis by offering an approach of obtaining quantitative electronic structural information on 3 d transition metal valence shells, facilitating applications across various scientific fields.

Bayesian optimization↗

DOE OSTI2026

Collection of fluorescence from an ion using trap-integrated photonics

Spontaneously emitted photons are entangled with the electronic and nuclear degrees of freedom of the emitting atom, so interference and measurement of these photons can entangle separate matter-based quantum systems as a resource for quantum information processing. Since confinement in a single-mode facilitates the photon interference needed for generating entanglement, the dipole emission patterns relevant in spontaneous emission present a mode-matching challenge. Current demonstrations rely on bulk photon-collection and manipulation optics that suffer from large component size and system-to-system variability—factors that impede scaling to the large numbers of entangled pairs needed for quantum information processing. To address these limitations, we demonstrate a collection method that enables passive phase stability, straightforward photonic manipulation, and intrinsic reproducibility. Specifically, we engineer a waveguide-integrated grating to couple photons emitted from a trapped ion into a single optical mode within a microfabricated ion-trap chip. Using the integrated collection optic, we characterize the collection efficiency, image the ion, and detect the ion’s quantum state. The integrated optic covers 2.18% of the solid angle and collects 1.97 ± 0.3% of the spontaneously emitted light incident on the grating for a total collection efficiency of 0.043% into a single-mode waveguide. This proof-of-principle demonstration lays the foundation for leveraging the inherent stability and reproducibility of integrated photonics to create, manipulate, and measure multipartite quantum states in arrays of quantum emitters.

Optical physics↗

DOE OSTI2024

Ab initio electroweak corrections to superallowed β decays and their impact on V ud

Radiative corrections are essential for an accurate determination of V ud from superallowed β decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for V ud . In this work, we provide a detailed account of the electroweak corrections to superallowed β decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. Here, we present a first numerical evaluation of the dominant corrections in light nuclei based on quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parametrize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in V ud , as illustrated in detail for the 14 O → 14 N transition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

High-bandwidth image-based predictive laser stabilization via optimized Fourier filters

Controlling the delivery of kHz-class pulsed lasers is of interest in a variety of industrial and scientific applications, from next-generation laser-plasma acceleration to laser-based x-ray emission and high-precision manufacturing. The transverse position of the laser pulse train on the application target is often subject to fluctuations by external drivers (e.g., room cooling and heating systems, motorized optics stages and mounts, vacuum systems, chillers, and/or ground vibrations). For typical situations where the disturbance spectrum exhibits discrete peaks on top of a broad-bandwidth lower-frequency background, traditional PID (proportional-integral-derivative) controllers may struggle, since as a general rule PID controllers can be used to suppress vibrations up to only about 5%–10% of the sampling frequency. Here, a predictive feed-forward algorithm is presented that significantly enhances the stabilization bandwidth in such laser systems (up to the Nyquist limit at half the sampling frequency) by online identification and filtering of one or a few discrete frequencies using optimized Fourier filters. Furthermore, the system architecture demonstrated here uses off-the-shelf CMOS cameras and piezo-electric actuated mirrors connected to a standard PC to process the alignment images and implement the algorithm. To avoid high-end, high-cost components, a machine-learning-based model of the piezo mirror’s dynamics was integrated into the system, which enables high-precision positioning by compensating for hysteresis and other hardware-induced effects. A successful demonstration of the method was performed on a 1 kHz laser pulse train, where externally-induced vibrations of up to 400 Hz were attenuated by a factor of five, far exceeding what could be done with a standard PID scheme.

Natal, Joseph↗

DOE OSTI2023

Nearly-frustration-free ground state preparation

Solving for quantum ground states is important for understanding the properties of quantum many-body systems, and quantum computers are potentially well-suited for solving for quantum ground states. Recent work [1] has presented a nearly optimal scheme that prepares ground states on a quantum computer for completely generic Hamiltonians, whose query complexity scales as δ − 1 , i.e. inversely with their normalized gap. Here we consider instead the ground state preparation problem restricted to a special subset of Hamiltonians, which includes those which we term "nearly-frustration-free": the class of Hamiltonians for which the ground state energy of their block-encoded and hence normalized Hamiltonian α − 1 H is within δ y of -1, where δ is the spectral gap of α − 1 H and 0 ≤ y ≤ 1 . For this subclass, we describe an algorithm whose dependence on the gap is asymptotically better, scaling as δ y / 2 − 1 , and show that this new dependence is optimal up to factors of log ⁡ δ . In addition, we give examples of physically motivated Hamiltonians which live in this subclass. Finally, we describe an extension of this method which allows the preparation of excited states both for generic Hamiltonians as well as, at a similar speedup as the ground state case, for those which are nearly frustration-free.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗