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Quantum Electromagnetics Division
The Quantum Electromagnetics Division develops measurement devices, standards, and methodologies for use with electronic, magnetic, photonic, and quantum technologies that have national strategic importance. The division has four technical focus areas: advanced computing, new analytical tools and reference data, instrumentation for astrophysics and cosmology, and quantum information science. The division’s researchers take advantage of the quantum-mechanical, electronic, magnetic, and photonic properties of materials and their interaction with electromagnetic radiation to create a wide variety of measurement tools used for such things as quantum-based electrical standards, energy-efficient spintronic devices, and high-resolution photon sensors used in imaging and spectroscopy. Innovations in metrology and in micro- and nanofabrication originating from the division have helped propel critical advances in high-performance superconducting electronics, data storage, materials development, quantum processing and engineering, nuclear forensics, and astronomical observations and have also contributed to a deeper understanding of fundamental physics. Furthermore, hardware designed and built by the division is important in such areas as artificial intelligence, superconducting quantum information, and hyperspectral imaging.
The division has five research groups: the Device Microfabrication Group, the Quantum Calorimeters Group, the Long Wavelength Sensors and Applications Group, the Quantum Electronics Group, and the Spin Electronics Group. The division has 70 staff members, including more than 40 scientists, plus technicians, engineers, and students, to carry out pioneering research in such areas as superconducting transition-edge sensors (TESs), superconducting quantum interface device (SQUID) multiplexing, parametric amplifiers, microwave kinetic inductance detectors, and several types of advanced refrigerators.
The Device Microfabrication Group builds a wide range of microfabricated circuits including TESs, MKIDs, SQUIDs, and parametric amplifiers for both internal and external sensing and metrology needs worldwide. The Group specializes in the development of large arrays of cryogenics sensors.
The Quantum Calorimeters Group develops highly sensitive calorimetric detectors of high-energy X ray and gamma-ray radiation using highly sensitive TES devices. The high-sensitivity spectrometers form a core capability at the National Institute of Standards and Technology (NIST) and answer external needs for super-fine-energy resolution to detect isotopes, in particular, for residual low-volume isotope compositions in nuclear materials and nuclear medicines.
The Long Wavelength Sensors and Applications Group explores and implements devices and spectrometers for long wavelength low energy electromagnetic radiation with super-high sensitivity at absolute energy scale by using TES and microwave kinetic induction detector-based devices. These devices achieved an unprecedented sensitivity of 6 × 10–19 W/Hz1/2 in the long-wavelength region and provided absolute power measurement metrology at low power levels relevant to quantum computing.
The Quantum Electronics Group develops low-noise readout techniques to enable larger arrays of more sensitive detectors. The Group designs low-noise amplifiers, multiplexing circuits, and custom room-temperature electronics in order to perform end-to-end readout of cryogenic sensors.
The Spin Electronics Group is exploring a next-generation technology to replace conventional semiconductor electronics for high-capacity data processing applications. Electron-spin torque is being explored for use in switching magnetic memory elements; if successful, the new technique could provide
higher switching speeds, greater reliability, and scalability to smaller device dimensions for lower-power switching of memory bits with magnetic fields. Theoretical and experimental investigations have been performed on spin and thermal transport, interfacial structure, and the transfer dynamics of spin angular momentum in devices and across interfaces with newly developed high-frequency and optical measurement capabilities to create and characterize new materials.
The division works with stakeholders in industry, academia, and other government agencies to understand and be responsive to their measurement needs in such areas as quantum electrical standards; advanced materials analysis using X-ray sensor arrays; superconducting electronics and nanomagnetics for high-speed, energy-efficient, future-generation computing; and quantitative medical diagnostic imaging.
ASSESSMENT OF TECHNICAL PROGRAMS
The Quantum Electromagnetics Division’s focuses include, among others, high-performance sensors for long-wavelength detection, X-ray detection, large-scale TES detector fabrication, and interconnects.
The Device Microfabrication Group has recently fabricated 300 wafers for sensors and interconnects yearly. The mix includes TESs, microwave kinetic inductance detectors, SQUID arrays, time-division SQUID multiplexers, microwave SQUID multiplexers, Josephson parametric amplifiers, kinetic inductance traveling wave parametric amplifiers, normal-insulator-superconductor tunnel junctions, tunable inductance bridges, and microresonators.
The TES activity at the Quantum Electromagnetics Division has matured over the past few years and ranks among the best in the world. This activity’s success with larger research and development programs (e.g., the Simons Observatory and ATHENA satellite) can be a true sign of success for NIST. However, the TES activity has become very successful and is very strongly supported by a few outside programs. This is good, but the scientific and technical community at large has not taken advantage of the TES capability. It would be very satisfying to see a broadly based appreciation of TES, which would impact more than just a very small number of major named programs. Such penetration would also shield TES activity from changes in the small number of programs. It would be good if, in the coming years, the success with a small number of “name” programs would transition into programs that affect the scientific, technical, and industrial community broadly.
That the sensors and interconnect program is so successful speaks to the scientific and technical expertise behind it. However, it is important to disseminate the results to broader communities and industry beyond the current stakeholders. This would generate new needs and technology directions which will require additional support and a focus on staffing and resources.
The current funding profile of the groups in the division appears highly skewed, with 65 percent of the funding coming from outside non-NIST sources. While the panel applauds the high level of interaction of the group with the practical needs of outside stakeholders, questions arise regarding the possibility of such high levels of external funding redirecting the real priorities of the division away from NIST. There is a real danger that the level of outside funding and the outsize success of the sensor/interconnect activity could obscure new opportunities that should be pursued.
Conclusion 5-1: The Quantum Electrodynamics Division’s resources, specifically funding, are currently inadequate to pursue interesting new lines of inquiry in quantum electronics and explore new opportunities should those opportunities fall in line with the Physical Measurement Laboratory’s mission. Quantum electronics is a very broad field with many areas to be explored beyond what the division currently explores.
Device Microfabrication Group
The fabrication activity perhaps ranks among the best-in-class, in terms of both breadth and quality of the output, which is attested by the fact that the sensors and amplifiers produced by this group are sought by users worldwide and form the critical components of two well-known astrophysics programs—the Simons Observatory and the ATHENA (Advanced Telescope for High Energy Astrophysics) satellite program for space X-ray spectroscopy.
Wafers with many high-pixel-count TES sensor arrays are required for Simons Observatory. The group has successfully transitioned many processes to 150 mm wafer size. Achievement of readout for so many complex sensors is a tour de force for the quantum electronics group and other divisions. The device fabrication group works intimately with other groups on device design, read-out, testing, packaging, and system users to optimize the TES devices and circuits to deliver the world’s best performance for the stakeholders.
Opportunities and Challenges
Fabrication facilities appear to be state-of-the-art for the current fabrication needs. However, questions remain regarding continuous upgrade of the capabilities, especially two dedicated special superconductor deposition systems are needed to meet future advances in performance requirement and capacity needs.
Recommendation 5-1: The Physical Measurement Laboratory should prioritize renovations and improvements to the device fabrication facility of the Quantum Electromagnetics Division. The present facilities are fully used and aged to the point that they require major renovations to increase the capacity to deliver on current expanding research projects and to acquire new capabilities to embark on leading-edge research in the future.
Quantum Calorimeters Group
The extension of TES applications to highly sensitive calorimetric detection of X rays and gamma rays promises to revolutionize precision detection. The group develops and disseminates sensors and spectrometer instruments to detect single photons, particles, and radioactive decays, particularly active in X-ray and gamma-ray wavebands, and in decay energy spectroscopy. These devices are used for internal metrology projects including X-ray tomography of integrated circuits and efforts to improve the realization of the becquerel.3 X-ray and gamma-ray spectrometers are also used for collaborative external projects at X-ray light sources and nuclear facilities. The high sensitivity spectrometer instruments are a core capability of NIST, used for determining more precise and more accurate reference data for both internal (NIST) and external needs of other government agencies, for example.
Accomplishments
The TES calorimeter demonstrated the ability to reduce thermal noise at ultra-low temperatures (less than 100 mK). The high sensitivity provides super energy resolution to detect isotopic composition, in particular, the ratio of Pu-238/Pu-239/Pu-240, which is critical to detecting residual low-volume isotope compositions in nuclear materials and nuclear medicines.
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3 The becquerel is a measure of radioactive decay. More information can be found at https://www.nrc.gov/readingrm/basic-ref/glossary/becquerel-bq.html, last accessed January 17, 2024.
Long-Wavelength Sensors and Applications Group
This group is responsible for the high-sensitivity infrared detectors, whose success with the Simons Observatory was described above. The most remarkable success was clearly the unprecedented achievement of detection sensitivity of approximately 6 × 10–19 W/Hz1/2 in the long-wavelength region together with the capability of absolute power measurement. The group develops arrays of multichroic microwave polarimeters for very challenging detection of faint infrared radiation from the cosmic microwave background. These new devices and measurement techniques are well suited to perform new spectroscopic metrology into the deep long wavelengths which are absent today beyond the micron-scale infrared regime. The long wavelength measurement techniques will provide detailed characterization and understanding of materials and compounds to develop many industrial and bio-medical applications.
Recommendation 5-2: The Quantum Electromagnetics Division should broaden its advanced long-wavelength sensing technologies to many other long-wavelength applications at elevated temperatures, such as for far-infrared long wavelengths and nuclear isotopic compositions.
Accomplishments
The group demonstrated TES bolometers and SQUID multiplexed readout to advance cosmology for measurements of the cosmic microwave background radiation by supplying more than 80,000 units of TES sensors and more than 130,000 units of SQUID multiplexed readout channels to U.S. research collaboration partners to perform detailed mapping of dark matter. Arrays of microwave kinetic inductance detectors enable new astrophysics applications.
The group demonstrated a highly sensitive TES bolometer intended to achieve absolute power sensitivities as small as 100 aW in support of quantum computing. The high sensitivity is enabled by achieving ultralow thermal conductance between the thermal bath and the sensing element. Similar devices would enable single photon counting at frequencies of tens of terahertz.
A new, highly sensitive microwave kinetic inductance detector was implemented to enable measurement of far-infrared radiation (0.1–10 mm). Advanced silicon platelet feedhorn arrays and meta-material lenslet arrays have been developed for coupling long-wavelength radiation to sensors.
Opportunities and Challenges
The mix of technical talent in the Long-Wavelength Sensors and Applications Group is outstanding. However, it would be valuable for the group to explore long-term plans for maintaining cutting-edge technology. It would also be useful if the team considered increasing their exposure to reach broader audiences to help recruiting. As the current experienced workforce are aging with limited additions of junior and mid-career staff, succession plans should be developed to close experience gaps.
Quantum Electronics Group
The Quantum Electronics Group develops advanced, world-class, low-noise, high-bandwidth multiplexed readouts for cryogenic quantum sensor arrays. It also performs fundamental research on the detection of weak signals based on quantum coherence and quantum entanglement. The group has strong capabilities in designing firmware, analog and microwave electronics, highly sensitive low-noise readout electronics, and parametric amplifiers, with close collaborations with internal and external partners for applications. For example, TES arrays with SQUID multiplexers have been inserted in X-ray spectrometers for the Intelligence Advanced Research Projects Activity’s RAVEN (Rapid Analysis of Various Emerging Nano-electronics) and the BESSY-II (Berliner Elektronenspeicherring-Gessellschaft fur Synchrotronsstrahlung) synchrotron; gamma-ray spectrometers for the Los Alamos, Oak Ridge, and
Idaho National Laboratories; in microwave polarimeters for the Simons Observatory, and for the ATHENA X-ray satellite being developed by the National Aeronautics and Space Administration (NASA) and the European Space Agency.
Accomplishments
The group developed time-division SQUID multiplexers to read out TESs for the ATHENA satellite’s X-ray integral field unit (X-IFU), which were certified as technology readiness level (TRL) 5 by NASA in 2023.
The group demonstrated highly sensitive and compact microwave readout design and instrument deployment for mixing baseband signals up to 4–8 GHz for 1,054 channels. It implemented high-bandwidth readout of near-infrared and optical TESs used for quantum information science.
Single-photon detection was demonstrated with a new integration of microwave SQUID multiplexing and kinetic inductance current sensors. The integration of traveling wave parametric amplifiers and TES array provides amplification and mode selection to enable high-detection sensitivity approaching the standard quantum limit (SQL) and dissipates less power.
The Boulder Cryogenic Quantum Testbed is a project within the Quantum Electronics Group that is intended to explore materials limitations to the performance of supercomputing quantum computers. There appears to be good collaboration with a Google group that has been at the forefront of commercial quantum supercomputing activities. The team also engages with at least one of the Department of Energy quantum centers. The program is at the starting gate, and the panel sees a great future here if nurtured properly. The partnership with academia has helped to educate young students and to train junior researchers from the University of Colorado and other universities to utilize this unique testbed. Many industrial companies are participating to perform experiments at the testbeds and transferring some knowledge back to the companies. Additional staff support to optimize the loss and readouts in the testbed and funding of students and junior postdoctoral researchers with additional operational expenses to strengthen the collaboration for this effort should be strongly considered.
Recommendation 5-3: The Boulder Cryogenic Quantum Testbed should add additional personnel and resources. In particular, it should seek to develop an enhanced capability that offers a unique resource by funding additional staff for the testbed and adding internships for students and junior researchers to strengthen and broaden the collaborations and partnerships with academia and with the emerging quantum computing and sensing industry.
Spin Electronics Group
After the 2018 National Academies’ assessment (NASEM 2018), the Nanoscale Spin Dynamics Group was dissolved. The current Spin Electronics Group is planned to move to the Applied Physics Division in fiscal year (FY) 2023. The technical focus areas are to develop novel electrical and optical metrology techniques for microelectronics and to explore novel devices relevant to advanced and future computing. In FY 2023, the group has four active projects on nanoscale magnetic devices, extreme ultraviolet optical metrology, cryogenic neuromorphic circuits, and hybrid ferromagnetic and superconductor systems. The group also developed 3D X-ray tomography techniques to provide high resolution images of layers metal interconnections in a microelectronic integrated circuit.
Accomplishments
The group demonstrated spin sensitivity and can resolve a single spin in 1019 using a hybrid superconductor-ferromagnet system. They are developing time-resolved measurement of stochastic spin-torque magnetic tunneling junction devices for application of random code generation for novel stochastic
computing applications. They are using extreme ultraviolet pulses to image the dynamics of nanoscopic heat flow and material properties in active microelectronic devices.
Opportunities and Challenges
Since the previous reorganization, the group has initiated many new diverse research directions on in situ characterization of dynamic properties of spin-based materials, and highly sensitive quantum sensing and quantum computing with promising advances. This small group is spread very thin and it is not adequate to cover these new areas in stochastic spin-based computing. It will require additional personnel and resources to attain a critical mass for it to be truly competitive worldwide.
Recommendation 5-4: The Spin Electronics Group should add additional personnel and resources. In particular, it should consider increasing exposure to reach broader audiences in recruiting. With a small and aging workforce to cover many new and competitive research directions, it should also consider succession and recruitment plans to establish a critical mass and close experience gaps in pursuing new research fields in spin-based quantum computing and device characterization.
ASSESSMENT OF SCIENTIFIC EXPERTISE
The Quantum Electromagnetics Division has world-class expertise in harnessing electromagnetic technologies for practical and fundamental scientific use cases. This is demonstrated, in part, by the awards won by division staff. These include the 2023 Keithley Award from the American Physical Society, a 2022 R&D100 award, two Nancy Grace Roman Technology fellowships, an Institute for Electrical and Electronics Engineers (IEEE) Magnetics Distinguished Lectureship, and various Department of Commerce medals. There have been 21 awards in total since the past assessment.
The division is delivering unique and complex sensing systems in a research environment that is simultaneously multi-disciplinary, multi-institution, and multi-agency. The scientific innovation of the division ranges from applied material science to technologies for quality assurance of integrated assemblies. The panel finds that the U.S. scientific ecosystem continues to be accelerated by the products of the division.
The Quantum Electromagnetics Division has used its unique sensor expertise to underpin a shared mission among U.S. agencies to foster broad American technical superiority. Advancing nuclear material accountancy is a key achievement for the division; which includes mobile spectrometers fielded at Oak Ridge National Laboratory, the analytical laboratory at Idaho National Laboratory, and soon the Pacific Northwest National Laboratory. Engaging in an interdisciplinary manner, the division has introduced a leap forward for detector resolution in the Microcalorimeter Gamma Spectrometer—a new platform for nondestructive nuclear material analysis.
The division successfully takes advantage of longstanding NIST leadership—for instance, the design and fabrication of SQUID arrays—while innovating on new sensing modalities and materials. One encouraging finding is that by acting as the central hub of sensing activity, the division is proactively extending its capabilities through calibration, for example, through the development and integration of phonon band-gap filters within bolometer sensors, which has been initially explored through external collaborations.
A major milestone for the division has been the recognition of a TRL assessment of TRL-5 by NASA for the sensor baselined for the upcoming ATHENA space mission, meaning that the sensor and readout component has passed the bar for integrated system testing. This accomplishment is the culmination of decades of accumulated experience and expertise and an important waypoint toward a successful space mission.
Indeed, the collaboration with NASA and other astrophysics projects is a key driving force behind the group’s groundbreaking work. The panel was encouraged to see that in most cases, clear and ambitious targets were set for new technology development. Additional internal resources could bolster the balance between work in the service of specific science missions and work that is strictly curiosity-driven exploration.
Accomplishments
The Quantum Electromagnetics Division is tackling ambitious programmatic targets at the forefront of science. This focus has resulted in new expertise and innovations, such as the frequency trimming of multiplexed resonators after precharacterization, as well as new sensing capabilities, such as absolute power measurement for atto-watt, and new directions, such as a standard for the becquerel unit. The division effectively shares expertise between sensing modalities such as electronics, firmware, and component design, accumulating incremental progress to extend its leadership.
Opportunities and Challenges
The work of the division relies on an increasingly rare set of scientific expertise. It is remarkable what the division has accomplished at the size of the current group. A key challenge remains recruiting and retention. In some areas, such as cryogenics development, the division’s expertise resides in a single individual whose technical background is increasingly sought after by the industry. The additional workforce could enable succession planning for critical expertise and extend the division’s efforts to apply sensing technologies in new directions, such as applications in the development of quantum computing components.
The collective expertise of the people in the division is extraordinary, and extra care needs to be given to recruit and retain them, especially the guest staff. Researcher morale is high, and many temporary researchers have been employed for a long time and express a desire to stay. If would be useful if the Physical Measurement Laboratory were to institute clear and open policies and practices for guest postdoctoral and visiting researchers to obtain permanent government employee positions. Furthermore, given that many researchers work in their own small groups with little interaction with the broader NIST community, the institute could improve retention and achieve broader research collaborations by encouraging broader interactions among researchers through NIST-wide seminar series and activities and the development of common meeting areas such as a cafeteria.
Conclusion 5-2: Clear and open policies and practices across the organization on recruiting permanent government employee positions and promoting interactions and collaborations would be useful in helping the Physical Measurement Laboratory in recruiting and retaining the world-class workforce that it needs. In particular, the open positions could be made available to staff and guest researchers across the organization. NIST-wide seminars and activities to promote inter-group interactions and collaborations could also be helpful.
BUDGET, FACILITIES, EQUIPMENT, AND HUMAN RESOURCES
The division’s budget is approximately $28 million, but only one-third of that is provided by NIST. The division’s budget is adequate for its current work. However, the majority of the budget is connected to specific projects with expected deliverables that are funded by external organizations (e.g., the Simons Observatory, and NASA for the ATHENA Project). The amount of external funding speaks to the importance and quality of the science and engineering research and technology development done in the division. At the same time, a low ratio of internal to external funding prevents the division and, as a result, the organization from reinvesting in facilities.
The facilities housing the division’s laboratories are well used and fully equipped with state-of-the-art equipment. Most of the equipment is uniquely designed to provide metrology for the projects under way. Most of this equipment (i.e., the cryogenic testbed open to government scientists and engineers) is unique in the country or plays unique roles and needs to be sustained. It may be appropriate to seek funding from other federal programs dedicated to the further development and sustainment of unique instrumentation and infrastructure that can be available to users funded by federal funds, centers, hubs, or commons. The present facilities are fully utilized and aged to the point that they require major renovations to increase the capacity to deliver current expanding research projects and to acquire new capabilities to embark on future research.
The Quantum Electromagnetics Division develops highly precise measurements and instrumentation using devices such as SQUID amplifiers, microcalorimeters, and microbolometers fabricated in the Boulder Microfabrication Facility. This designed and developed equipment is a marvel of engineering and science, reflecting the fact that the quality of the researchers in the division is unique and important to the future of NIST. The quality of the technology and engineering solutions is superb and difficult to find in any other laboratory in this area. The collective expertise of the people is extraordinary, and extra care needs to be given to retaining them. However, the science and engineering staff see their positions as temporary, and they need more assurance than rather vague promises for possible retention. Without a well-developed plan for turning their qualified science and engineering employees into permanent positions, the team risks losing significant technical expertise. The division has the opportunity to retain the highly talented guest researchers, who all expressed interest in remaining with NIST. However, clearer policies and practices are needed for moving from a guest researcher to a permanent government employee position.
There appears to be a disconnect between the NIST leadership comments on the difficulties with recruiting and retention permanent staff versus the panelist discussions with guest researchers. There does not appear to be a retention problem for guest researchers, as their morale was high, and many guest researchers have been employed for a long time and expressed no desire to leave. For recruitment for permanent staff, NIST has ample opportunity to select from the many outstanding guest researchers they currently employ. Many postdocs said they are interested in government positions but must learn to identify and apply for permanent positions. A predictable path for postdoctoral and visiting researchers to become permanent NIST employees would be useful. Discussions with the researchers identified the need for a clear policy for becoming a permanent NIST employee. In addition, NIST may want to use its relationship with the University of Colorado Boulder (CU) and JILA to identify graduate student opportunities. Several students the panel talked to said they felt isolated and commented that there was no strong sense of community among the graduate students at NIST. One consideration could be a targeted seminar series open to all CU graduate students to foster community, expand their understanding of NIST’s work, and give early career researchers a venue to speak. Perhaps this could be opened to CU as an additional recruiting opportunity. NIST also does not appear to have a mechanism to support “gap year” students between receiving their bachelor’s degree and applying to graduate school. A formal program may bolster workforce development and allow a new onboarding process to introduce early career researchers to NIST.
EFFECTIVENESS OF DISSEMINATION EFFORTS
The Quantum Electromagnetics Division has an impressive dissemination record. Its staff has authored 423 total publications in the past 4 years. The division’s publications have been cited a total of 5,379 times in 69 journals and the division’s staff has an h-index of 35 over the past 4 years. In addition, there have been 659 co-authored papers in the past 4 years with collaborators such as the Department of Energy, NASA, Stanford University, Cardiff University, the University of Chicago, and the University of California, Berkeley. The division has 3 licenses, 20 patents, and 9 disclosures since the past assessment.
Stakeholders are the primary drivers of the research portfolios of the Quantum Electromagnetics Division, as 65 percent of the funding ($15.6 million) comes from external sources. The team noted that this percentage of external funding was unusually high for PML. In FY 2023, 31 out of 70 group members are guest researchers, and the team has three National Research Council postdoctoral fellows.
The team disseminates its results via high-visibility publications and by transitioning technology to the stakeholders. Some technology transfer efforts are occurring through patents and licensing agreements. Currently, the groups work extensively with academia, industry, and government agencies so future technology dissemination and transfer efforts can be further accelerated, particularly in areas of quantum sensing and readout. NIST has sufficient technology transfer mechanisms, some of which are used by the team.
The team works effectively with stakeholders to develop critical technologies to attain program goals. Because most of the work is supported by stakeholder investment, the team is in close contact to delineate technical plans to meet stakeholders’ system requirements. The team also uses previous program outputs to implement next-generation devices and plan future research directions. No improvements are needed in this process.
Opportunities and Challenges
The sensors and interconnect program is very successful in meeting the goals of the stakeholders with great transmission of the scientific and technical expertise behind it. Outside of some good publications in selective scientific and technical journals, however, it is important to disseminate the results to a broader audience and industry beyond the current stakeholders and associated communities. This could generate new research projects to support industrial needs while helping recruit future staff. For example, this may be realized by a NIST-led industry–academia partnership program to develop advanced design, measurement, and metrology technologies in emerging devices and materials or quantum sensing and computing applications by using resources from academic centers, investment of commercial partners, and ongoing government initiatives such as the Quantum Initiative and CHIPS program.
The members of the division must disseminate their advanced quantum electromagnetic metrology and measurement standards through active participation in pan-industry standard bodies such as IEEE, the International Telecommunication Union, etc.
REFERENCE
NASEM (National Academies of Sciences, Engineering, and Medicine). 2018. An Assessment of Four Divisions of the Physical Measurement Laboratory at the National Institute of Standards and Technology: Fiscal Year 2018. Washington, DC: The National Academies Press. https://doi.org/10.17226/25281.