Richard L. Steiner

History and progress on accurate measurements of the Planck constant

The measurement of the Planck constant, h, is entering a new phase. The CODATA 2010 recommended value is 6.626 069 57 × 10(-34) J s, but it has been a long road, and the trip is not over yet. Since its discovery as a fundamental physical constant to explain various effects in quantum theory, h has become especially important in defining standards for electrical measurements and soon, for mass determination. Measuring h in the International System of Units (SI) started as experimental attempts merely to prove its existence. Many decades passed while newer experiments measured physical effects that were the influence of h combined with other physical constants: elementary charge, e, and the Avogadro constant, N(A). As experimental techniques improved, the precision of the value of h expanded. When the Josephson and quantum Hall theories led to new electronic devices, and a hundred year old experiment, the absolute ampere, was altered into a watt balance, h not only became vital in definitions for the volt and ohm units, but suddenly it could be measured directly and even more accurately. Finally, as measurement uncertainties now approach a few parts in 10(8) from the watt balance experiments and Avogadro determinations, its importance has been linked to a proposed redefinition of a kilogram unit of mass. The path to higher accuracy in measuring the value of h was not always an example of continuous progress. Since new measurements periodically led to changes in its accepted value and the corresponding SI units, it is helpful to see why there were bumps in the road and where the different branch lines of research joined in the effort. Recalling the bumps along this road will hopefully avoid their repetition in the upcoming SI redefinition debates. This paper begins with a brief history of the methods to measure a combination of fundamental constants, thus indirectly obtaining the Planck constant. The historical path is followed in the section describing how the improved techniques and discoveries in quantum mechanics steadily reduced the uncertainty of h. The central part of this review describes the technical details of the watt balance technique, which is a combination of the mechanical and electronic measurements that now determine h as a direct result, i.e. not requiring measured values of additional fundamental constants. The first technical section describes the basics and some of the common details of many watt balance designs. Next is a review of the ongoing advances at the (currently) seven national metrology institutions where these experiments are pursued. A final summary of the recent h determinations of the last two decades shows how history keeps repeating itself; there is again a question of whether there is a shift in the newest results, albeit at uncertainties that are many orders of magnitude less than the original experiments. The conclusion is that there is room for further development to resolve these differences and find new ideas for a watt balance system with a more universal application. Since the next generation of watt balance experiments are expected to become kilogram realization standards, the historical record suggests that there is yet a need for proof that Planck constant results are finally reproducible at an acceptable uncertainty.

Towards an electronic kilogram: an improved measurement of the Planck constant and electron mass

The electronic kilogram project of NIST has improved the watt balance method to obtain a new determination of the Planck constant h by measuring the ratio of the SI unit of power W to the electrical realization unit W90, based on the conventional values for the Josephson constant KJ−90 and von Klitzing constant RK−90. The value h = 6.626 069 01(34) × 10−34 J s verifies the NIST result from 1998 with a lower combined relative standard uncertainty of 52 nW/W. A value for the electron mass me = 9.109 382 14(47) × 10−31 kg can also be obtained from this result. With uncertainties approaching the limit of those commercially applicable to mass calibrations at the level of 1 kg, an electronically-derived standard for the mass unit kilogram is closer to fruition.

A practical Josephson voltage standard at 1 V

A series array of 1484 pairs of Josephson junctions, biased by microwaves at 72 GHz, is demonstrated to provide stable quantized voltages at the 1 V level. The niobium/lead-alloy junctions used in the array are not affected by thermal cycling.

Details of the 1998 Watt Balance Experiment Determining the Planck Constant

The National Institute of Standards and Technology (NIST) watt balance experiment completed a determination of Planck constant in 1998 with a relative standard uncertainty of 87 × 10−9 (k = 1), concurrently with an upper limit on the drift rate of the SI kilogram mass standard. A number of other fundamental physical constants with uncertainties dominated by this result are also calculated. This paper focuses on the details of the balance apparatus, the measurement and control procedures, and the reference calibrations. The alignment procedures are also described, as is a novel mutual inductance measurement procedure. The analysis summary discusses the data noise sources and estimates for the Type B uncertainty contributions to the uncertainty budget. Much of this detail, some historical progression, and a few recent findings have not been included in previous papers reporting the results of this experiment.

NBS determination of the fine-structure constant, and of the quantized Hall resistance and Josephson frequency-to-voltage quotient in SI units

Results of US National Bureau of Standards (NBS) experiments to realize the ohm and the watt, to determine the proton gyromagnetic ratio by the low-field method, to determine the time dependence of the NBS representation of the ohm using the quantum Hall effect, and to maintain the NBS representation of the volt using the Josephson effect, are appropriately combined to obtain an accurate value of the fine-structure constant and of the quantized Hall resistance in SI units, and values in SI units of the Josephson frequency-to-voltage quotient, Planck constant and elementary charge. >

Determination of the Planck constant using a watt balance with a superconducting magnet system at the National Institute of Standards and Technology

For the past two years, measurements have been performed with a watt balance at the National Institute of Standards and Technology (NIST) to determine the Planck constant. A detailed analysis of these measurements and their uncertainties has led to the value h = 6.626 069 79(30) × 10−34 J s. The relative standard uncertainty is 45 × 10−9. This result is 141 × 10−9 fractionally higher than h90. Here h90 is the conventional value of the Planck constant given by , where KJ-90 and RK-90 denote the conventional values of the Josephson and von Klitzing constants, respectively.

Josephson array voltage calibration system: operational use and verification

A Josephson array system that maintains the US legal volt is described. This system is almost fully automated, operates with a typical precision of 0.009 mu V, and readily allows US legal volt measurements weekly, or more frequently if desired. This system was compared to the previous volt-maintenance system, and agreement was found to within 0.03 p.p.m. This verification is limited by uncertainties in the resistive divider instruments of the previous system. >

The NBS Josephson array voltage standard

A Josephson voltage standard based on a series array of 2076 junctions is described. When irradiated with a 15-mW signal at a frequency of 96 GHz, the array produces 15 000 quantized levels between −1.5 and 1.5 V. Initial results on high-precision comparisons with a Zener reference standard are given.

A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer

A new refractometer with a variable length vacuum cell has been developed to eliminate errors caused by deformations in optical windows of the cell. The refractive index of air is determined by measuring the changes in the optical path difference between the air of interest and a vacuum as a function of the changes in the cell length. An optical phase modulation technique and a dark fringe detection method are used to obtain a high resolution in measuring the optical path difference by a double-pass Michelson interferometer. A combined standard uncertainty of 5/spl times/10/sup -9/ in the measurement of the refractive index of air has been achieved.

A summary of the Planck constant measurements using a watt balance with a superconducting solenoid at NIST

Researchers at the National Institute of Standards and Technology have been using a watt balance, NIST-3, to measure the Planck constant