This work presents a substantial advancement on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. More specifically, this work introduces a generalized mathematical reconciliation to recover exact effective quantized resistances found by simulation and measurement. Furthermore, this work explores the concept of fractal dimension, clarifying the benefits of both full and partial recursions in QHARS devices. Three different partial recursion cases are visited for a near-1 G Ω QHARS device. These partial recursions, analyzed in the context of their fractal dimensions, offer increased flexibility in accessing desired resistances within a specific neighborhood of values compared to full recursion methods, though at the cost of the number of required elements.

In electrical metrology, the quantum Hall effect is accessed at the Landau level filling factor ν = 2 plateau to define and disseminate the unit of electrical resistance (ohm). The robustness of the plateau is only exhibited at this Landau level filling factor and thus places a constraint on the quantized resistances that are accessible when constructing quantized Hall array resistance standards (QHARS) using epitaxial graphene on SiC. To overcome devices constrained by using Hall elements in series or in parallel, this work approaches the fabrication of a cross-square network configuration, which is similar to but departs slightly from conventional wye-delta designs and achieves significantly higher effective quantized resistance outputs. Furthermore, the use of pseudofractal-like recursion amplifies the ability to reach high resistances. QHARS devices designed as the ones here are shown to achieve an effective resistance of 55.81 MΩ in one configuration and 27.61 GΩ in another, with a hypothetically projected 317.95 TΩ that could be accessed with more specialized equipment. Teraohmmeter measurements reveal the limits of conventional wet cryogenic systems due to resistance leakage. Ultimately, this work builds on the capability of realizing exceptionally high-value quantum resistance standards.

This work introduces a pseudofractal analysis for optimizing high-resistance graphene-based quantized Hall array resistance standards (QHARS). The development of resistance standard device designs through star–mesh transformations is detailed, aimed at minimizing element count. Building on a recent mathematical framework, the approach presented herein refines QHARS device concepts by considering designs incorporating pseudofractals (which may be expressed as star–mesh transformations). To understand how future QHARS pseudofractal designs enable varying sizes of neighborhoods of available quantized resistance, Minkowski–Bouligand algorithms are used to analyze fractal dimensions of the device design topologies. Three distinct partial recursion cases are explored in addition to the original full recursion design, and expressions for their total element counts are derived. These partial recursions, assessed through their fractal dimensions, offer enhanced flexibility in achieving specific resistance values within a desired neighborhood compared to full recursion methods, albeit with an increased number of required elements. The formalisms presented are material-independent, making them broadly applicable to other quantum Hall systems and artifact standards.

In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm’s law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here we report a unified realization of the volt, ohm and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 μV V−1. The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 μΩ Ω−1. We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33–252 nA, and our lowest uncertainty is 4.3 μA A−1 at 83.9 nA. For other current values, a systematic error that ranges from −10 μA A−1 to −30 μA A−1 is present due to the imperfect isolation of the PJVS microwave bias. A unified realization of the volt, ohm and ampere can be achieved by integrating a quantum anomalous Hall resistor and a programmable Josephson voltage standard in a single cryostat.

A 1G Omega star-mesh quantized Hall array resistance standard (QHARS) assembled from 37 individual elements, each exhibiting the quantum Hall effect (QHE), was fabricated and tested. The 1G Omega QHARS has three orders of magnitude fewer elements than a largely series 1G Omega QHARS, which would require approximately 77480 elements. A dual source bridge (DSB), using a nanovolt detector and a modified algorithm using least-squares analysis was used to interpolate a bridge null from five measurement points taken near the null of the linear measurement system. The 1G Omega star-mesh QHARS was used as a standard to calibrate 100 M Omega , 1G Omega , and 10 G Omega high resistance standards. The star-mesh measurements agreed within the combined standard uncertainties of the values of these standards based on traditional high resistance scaling from the i=2 quantized Hall resistance value of 12906.4037...Omega , where guarded Hamon transfer standards and DSBs are used to build-up to high resistance ranges from 1 M Omega standard resistors.

We report the 2022 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at https://physics.nist.gov/cuu/Constants/. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2022. A discussion of the major improvements as well as inconsistencies within the data is given. (c) 2025 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved.

This work introduces a pseudofractal analysis for optimizing high-resistance graphene-based quantized Hall array resistance standards (QHARS). The development of resistance standard device designs through star-mesh transformations is detailed, aimed at minimizing element count. Building on a recent mathematical framework, the approach presented herein refines QHARS device concepts by considering designs incorporating pseudofractals (which may be expressed as star-mesh transformations). To understand how future QHARS pseudofractal designs enable varying sizes of neighborhoods of available quantized resistance, Minkowski-Bouligand algorithms are used to analyze fractal dimensions of the device design topologies. Three distinct partial recursion cases are explored in addition to the original full recursion design, and expressions for their total element counts are derived. These partial recursions, assessed through their fractal dimensions, offer enhanced flexibility in achieving specific resistance values within a desired neighborhood compared to full recursion methods, albeit with an increased number of required elements. The formalisms presented are material-independent, making them broadly applicable to other quantum Hall systems and artifact standards.

This work elaborates on how one may develop high-resistance quantized Hall array resistance standards (QHARS) by using star-mesh transformations for element count minimization. Refinements are made on a recently developed mathematical framework optimizing QHARS device designs based on full, symmetric recursion by reconciling approximate device values with exact effective quantized resistances found by simulation and measurement. Furthermore, this work explores the concept of fractal dimension, clarifying the benefits of both full and partial recursions in QHARS devices. Three distinct partial recursion cases are visited for a near-1 Gigaohm QHARS device. These partial recursions, analyzed in the context of their fractal dimensions, offer increased flexibility in accessing desired resistance values within a specific neighborhood compared to full recursion methods, though at the cost of the number of required devices.

A new Kibble balance is being built at the National Institute of Standards and Technology (NIST). For the first time in one of the highly accurate versions of this type of balance, a single passive flexure mechanism is used for both modes of operation: the weighing mode and the velocity mode. The mechanism is at the core of the new balance design as it represents a paradigm shift for NIST away from using knife edge-based balance mechanisms, which exhibit hysteresis in the measurement procedure of the weighing mode. Mechanical hysteresis may be a limiting factor in the performance of highly accurate Kibble balances approaching single digit nanonewton repeatability on a nominal 100 g mass, as targeted in this work. Flexure-based mechanisms are known to have very good static hysteresis when used as a null detector. However, for larger and especially longer lasting deformations, flexures are known to exhibit anelastic drift. We seek to characterize, and ideally compensate for, this anelastic behavior after deflections during the velocity mode to enable a 10 - 8 accurate Kibble balance-measurement on a nominal 100 g mass artifact with a single flexure-based balance mechanism. A measurement of the anelastic after-effect after static excitation hints that the apparatus produced a result for anelastic relaxation comparable to previously published work. Furthermore, a series of oscillatory displacements similar to those occurring in a velocity mode of a Kibble balance measurement are imposed upon the flexure mechanism and show a significant anelastic relaxation torque resulting in multiple micronewton of force relaxation. The amplitude of this force relaxation could be reduced by counterbending the flexures before performing a force measurement.

A recent mathematical framework for optimizing resistor networks to achieve values in the MO through GO levels was employed for two specific cases. Objectives here include proof of concept and identification of possible apparatus limitations for future experiments involving graphene-based quantum Hall array resistance standards. Using fractal-like, or recursive, features of the framework allows one to calculate and implement network designs with substantially lower-valued resistors. The cases of 100 M Omega and 1 G Omega demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances.

Following the 2019 redefinition of the International System of Units (SI), the kilogram, as the unit of mass, transitioned from being tied to a physical artifact to a fixed value based on the Planck constant [1]. The adoption of simplified and compact metrology instruments has streamlined the traditional mass dissemination chain, making primary mass realization capabilities particularly valuable for calibration laboratories. For the past two years, the National Institute of Standards and Technology (NIST) has been developing a second generation tabletop Kibble balance (KIBB-g2) aimed at realizing gram-level masses to ASTM E617 Class 3 uncertainties [2]. This paper provides an overview of the design and advancements of KIBB-g2, presents performance results, and outlines planned design changes for a third generation tabletop Kibble Balance (KIBB-g3).

This paper describes the characterization of the quantum anomalous Hall (QAH) effect resistor with Chromium-doped Bismuth Antimony Telluride with the efforts in coupling directly to a programmable Josephson voltage standard (PJVS) at zero magnetic field. The precision measurement of the QAH resistance was performed under the presence of microwave signal biased to the PJVS. Understanding such effect will help to improve the experimental set-up for integrating multiple quantum electrical standards in a single system.

This paper describes the next generation prototype of the Electronic NIST Torque Realizer (ENTR) project. The first prototype version (ENTR-v1) has been able to realize low-range torques (on the order of 1x10-3 Nm) to uncertainties of less than 1000 parts in 1x106. The second generation prototype (ENTR-v2) has been designed and constructed specifically with the goal of realizing at least 1Nm of torque utilizing a direct current, direct-drive design and traceability to quantum standards without the need for physical mass and length standard artifacts. The paper will describe some of the design decisions of ENTR-v2 in order to reach this higher range of operation, and we aim to present results of torque realization verification with a full uncertainty budget within the coming months.

The National Institute of Standards and Technology (NIST) is building a robust open-source hardware and software Quantum Electro-Mechanical Metrology Suite (QEMMS) that can provide quantum voltage, resistance, current, mass, and force dissemination directly traceable to the new SI. The goal is to develop a self-calibrating SI system that is turn- key and fit-for-purpose for primary standard laboratories and other national metrology institutes.

For the past several years, we have been using the torsion balance developed at the Bureau International des Poids et Mesures (BIPM) to measure the gravitational constant G. The most notable feature of the apparatus is that it allows the measurement of G with two different methods: the Cavendish method and the Servo method.The systematic effects are different in several important variables, leading to an improved combined result. In the past year, we have identified a gas pressure effect that hampered previous measurements at the National Institute of Standards and Technology

A recent mathematical framework for optimizing resistor networks to achieve values in the MΩ through GΩ levels was employed for two specific cases. Objectives here include proof of concept and identification of possible apparatus limitations for future experiments involving graphene-based quantum Hall array resistance standards. Using fractal-like, or recursive, features of the framework allows one to calculate and implement network designs with substantially lower-valued resistors. The cases of 100 MΩ and 1 GΩ demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances.

Ten years ago, B. Kibble and I. Robinson published an article that promised a simplification of the Kibble balance experiment. According to this theory, the effect of parasitic forces and non-vertical motions cancel if the position and orientation of the coil are given by a single degree of freedom. We reiterate the derivation of the Kibble-Robinson theory (KRT) and then paraphrase the theory to emphasize the assumptions and conclusions. From there, we discuss the implications of the difference measurement in force mode, the effect of corner loading, the addition of relief gimbals, and the non-verticality of the sensing direction.

Theoretically wye-delta transformation can be used to realize ultra-high resistances up to PO. For graphene-based quantum Hall array resistance standards fabricated to utilize the wye-delta transformation, a few challenges present themselves, including the unique quantized resistance in a graphene Hall bar and the limitation of the area of homogeneous high-quality graphene. In this paper, we discuss approaches to optimize the transformation for quantum Hall array resistance standard and propose a dual-output design for 1 M Omega and 100 M Omega as an alternative to other build-up techniques, shortening the path from quantum resistance standards.

By directly integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) into a single cryostat, we have implemented a unified quantum electrical instrument that provides a realization of the volt, ohm, and ampere in accordance with the revised International System of Units (SI). The quantum voltage output from this prototype ranged from (0.24 to 6.5) mV with combined relative uncertainties (k = 1) down to 3 mu V/V. The colocated QAHR provided a realization of the ohm at zero magnetic field with uncertainties near 1 mu Omega/Omega at R-yx approximate to 25.9 k Omega. For the ampere, a longitudinal current applied to the QAHR is converted to a quantized Hall voltage, which was directly compared to the Josephson voltage, providing measurements of the ampere that are directly traceable to the revised SI. We determined currents in the range (9.33 to 252) nA with uncertainties of (41 to 4.3) mu A/A, respectively. Limitations and improvements are discussed to aid the reproduction of similar instruments at other national metrology institutes.

A primary force standard is implemented to realize the watt through Planck's constant by means of radiation pressure at the kilowatt level. The high amplification laser-pressure optic, or HALO, is a multiple reflection radiation pressure apparatus used for absolute radiometry of high-power lasers. In this work, a primary standard electrostatic force balance is used to measure the reflection-enhanced optical forces. With this configuration, the HALO is used to measure laser powers in the range of 100 W-5000 W from a 1070 nm fiber laser. The expanded uncertainty of the 5 kW measurement is 0.12%, which is both the lowest uncertainty multi-kW measurement and radiation pressure-based measurement to-date. The HALO result was validated against a thermal primary standard using a calibrated transfer standard at 2 kW. The degree of equivalence was 0.78% +/- 1.12%, which demonstrates agreement within the uncertainties of these two primary standards.