The 2019 revision of the International System of Units (SI) allowed for improved experiments consolidating mechanical and quantum electrical metrology. Previously, the ampere's definition relied on complex mechanical experiments, but the Josephson and quantum Hall effects offered quantum electrical standards. While the Kibble balance successfully rationalized the kilogram, it involved separate experiments and transfer standards. This research utilizes two quantum electrical standards within a single Kibble balance setup to levitate a mass, directly linking macroscopic mass to quantum standards. This represents a significant advance in precision metrology, potentially leading to a more accessible and democratized system of units.

The paper reviews previous work on quantum Hall array resistance standards (QHARS), noting limitations in current capacity before quantization breaks down. It also references the use of single-electron transistors for current measurement, but their nanoampere range limits broader application. The authors cite the Kibble balance and the original quantum electrical metrology triangle, highlighting the replacement of single-electron tunneling with the Kibble balance in this new approach. Existing methods for mass dissemination, including the international consensus value of the kilogram, are also discussed. The work builds upon prior research in graphene quantum Hall effect, Josephson voltage standards and Kibble balance techniques.

The experiment uses three NIST-designed components: a programmable Josephson voltage standard (PJVS), a graphene quantum Hall array standard (QHARS), and a Kibble balance. The QHARS, composed of 13 graphene quantum Hall arrays in parallel, provides a resistance of Rk/26 (where Rk is the von Klitzing constant). Quantization was verified using magnetic field reversal measurements. The PJVS converts a microwave reference frequency to a DC voltage standard using the Josephson constant (2e/h). The Kibble balance operates in two modes: force mode (comparing electromagnetic force to weight) and velocity mode (measuring induced voltage and velocity). The experiment measures 50g and 100g masses. The current passing through the QHARS, also used to levitate the mass in the Kibble balance, is determined quantum mechanically via current-to-voltage conversion using the QHARS and PJVS. Standard resistors (100Ω and 1000Ω) were also used for comparison. Data analysis included drift corrections for standard resistors and accounting for experimental disruptions (e.g., power outage). The measurements use primary standards of time and length traceable to fundamental constants.

The QHARS devices exhibited excellent quantization at currents suitable for mass measurement (0.35 mA and 0.7 mA for 50g and 100g masses, respectively). Mass measurements yielded relative uncertainties (k=1) on the order of 3 × 10⁻⁸ for both 50g and 100g masses. The deviation between mass values obtained using QHARS and traditional resistors was small, indicating the validity of the quantum approach. The experiment demonstrates the closure of the metrology triangle, connecting macroscopic mass to the Planck constant through quantum voltage and resistance standards. By incorporating quantum standards, artifact resistance standards can be gradually eliminated from the measurement chain. The achieved current levels (mA range) bring the quantum ampere closer to practical use.

The results demonstrate the feasibility of directly linking macroscopic mass to quantum standards within a single experimental setup. This eliminates the need for intermediary transfer standards, improving accuracy and potentially simplifying calibration processes. The low uncertainties achieved highlight the precision and stability of the graphene-based QHARS devices at relatively high currents. The work contributes to the ongoing effort to refine and consolidate the SI system, making fundamental units more accessible and less dependent on physical artifacts. The ability to measure mass using quantum standards in this integrated approach has significant implications for various fields of metrology and fundamental physics research.

This study successfully integrates quantum voltage and resistance standards into a Kibble balance for direct mass measurement. The high precision and accuracy achieved demonstrate a significant step towards a more robust and accessible SI system based on fundamental constants. Future work could focus on extending this methodology to other mass ranges and exploring the use of different quantum technologies for even more precise measurements.

The study primarily focused on 50g and 100g masses. While the results are promising, further research is needed to validate the approach across a broader range of mass values. The experiment was susceptible to external factors such as power outages, which affected data quality. Future iterations should focus on improving environmental control to minimize such disturbances. The small deviation between QHARS and standard resistors suggests potential refinements in the characterization and calibration procedures to further minimize uncertainties.