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.

https://iopscience.iop.org/article/10.1088/0034-4885/76/1/016101/pdf

History and progress on accurate measurements of the Planck constant

Since 1889 the international prototype of the kilogram has served as the definition of the unit of mass in the International System of Units (SI). It is the last material artefact to define a base unit of the SI, and it influences several other base units. This situation is no longer acceptable in a time of ever increasing measurement precision.It is therefore planned to redefine the unit of mass by fixing the numerical value of the Planck constant. At the same time three other base units, the ampere, the kelvin and the mole, will be redefined. As a first step, the kilogram redefinition requires a highly accurate determination of the Planck constant in the present SI system, with a relative uncertainty of the order of 1 part in 108.The most promising experiment for this purpose, and for the future realization of the kilogram, is the watt balance. It compares mechanical and electrical power and makes use of two macroscopic quantum effects, thus creating a relationship between a macroscopic mass and the Planck constant.In this paper the background for the choice of the Planck constant for the kilogram redefinition is discussed and the role of the Planck constant in physics is briefly reviewed. The operating principle of watt balance experiments is explained and the existing experiments are reviewed. An overview is given of all presently available experimental determinations of the Planck constant, and it is shown that further investigation is needed before the redefinition of the kilogram can take place.

http://iopscience.iop.org/article/10.1088/0026-1394/50/1/R1/pdf

Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram

The redefinition of the SI unit of mass in terms of a fixed value of the Planck constant has been made possible by the Kibble balance, previously known as the watt balance. Once the new definition has been adopted, the Kibble balance technique will permit the realisation of the mass unit over a range from milligrams to kilograms. We describe the theory underlying the Kibble balance and practical techniques required to construct such an instrument to relate a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at present, in the region of 2 parts in 10^8. A number of Kibble balances have either been built or are under construction and we compare the principal features of these balances.

https://iopscience.iop.org/article/10.1088/0026-1394/53/5/A46/pdf

The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass.

The METAS watt balance project was initiated slightly more than a decade ago. Over this time, the apparatus has been through an uninterrupted series of upgrades that have improved its reliability to a point where continuous series of measurements can be taken fully automatically over periods of several months. A comprehensive analysis of possible systematic errors has now been completed and a large set of data has been analysed to calculate a value for the Planck constant h. This paper describes the watt balance in detail, explains the data acquisition and analysis thoroughly and presents the uncertainty budget. The value of the Planck constant determined with our apparatus is h = 6.626?069?1(20) ? 10?34?J?s with a relative standard uncertainty of 0.29 ? 10?6. This value differs from the 2006 CODATA adjustment by 0.024??W?W?1.

https://iopscience.iop.org/article/10.1088/0026-1394/48/3/007/pdf

Determination of the Planck constant with the METAS watt balance

/pdf/high-resolution-spectroscopy-36s8wtkhul.pdf

High Resolution Spectroscopy

This paper summarizes the various improvements to and new developments for the Bureau International des Poids et Mesures (BIPM) watt balance, which have been implemented over the past two years. The main distinctive feature of the BIPM apparatus is its capability for simultaneous force and velocity measurements. Our first campaign of measurements in air at atmospheric pressure has been carried out with simultaneous force-velocity measurements. The results obtained among 11 series showed a relative reproducibility of the Planck constant h of 5.0 × 10-6. The relative difference between our Planck constant result and the CODATA 2006 recommended value is -4.8 × 10-6, with a relative uncertainty of 4.8 × 10-5.

The BIPM Watt Balance: Improvements and Developments

The International Bureau of Weights and Measures (BIPM) is developing a novel watt balance based on a simultaneous measurement scheme for the forthcoming redefinition of the kilogram The two distinct measurement phases in a conventional watt balance are carried out in a single phase where all quantities are measured simultaneously The main characteristics of this simultaneous measurement approach are described An analysis of the advantages and the drawbacks is carried out

https://iopscience.iop.org/article/10.1088/0026-1394/51/2/S80/pdf

A watt balance based on a simultaneous measurement scheme

Since beginning the construction early in 2005, considerable progress has been made on the watt balance of the Bureau International des Poids et Mesures (BIPM). We have continued the development of a room-temperature version to test the feasibility of simultaneous force and velocity measurements. Preliminary measurements of the voltage-velocity ratio have been carried out with a reproducibility of the order of 1 part in 104. The coil suspension has been improved to reduce the undesired coil movement in the 5 degrees of freedom different from a perfectly vertical movement. Further work on the current source has reduced its long-term drift to a few parts in 109 per minute with a satisfactory short-term stability. A technique needed to separate the voltage induced in the coil from the voltage drop due to the current flow based on the use of a second noninductive coil has been tested. The second coil is now being integrated into the apparatus. Work has started on the geometrical and magnetic characterizations of a large precision solenoid that will become the reference for the magnetic field alignment. The collaboration with a university on the fabrication of our magnetic circuit is being continued. This paper briefly outlines the main ideas of the BIPM watt balance and reports the progress to date.

Progress on the BIPM watt balance

The Kibble balance is expected to become an important instrument in the near future for realizing the unit of mass, the kilogram, in the revised international system of units (SI). The Kibble balance assumes an equality of two magnetic profiles measured in the weighing and velocity phases. A recent study conducted in the Kibble balance group at the Bureau International des Poids et Mesures (BIPM) showed that the coil current could significantly affect the magnetic profile, which should be carefully taken into account in the Kibble balance experiment. This paper gives a deeper understanding and investigation of the effect, and discusses the magnetic profile change due to the coil current, for both the classical two-mode and the one-mode Kibble balances. The coil current effect has been theoretically and experimentally investigated based on a typical magnet design with an air gap. One important conclusion found in the one-mode Kibble balance is that the magnetic profile change measured in the velocity phase is twice the change in the weighing phase. A compensation suggestion, to minimize the profile change due to the coil current in a BIPM-type magnet, is presented.

https://iopscience.iop.org/article/10.1088/1681-7575/aa9a8e/pdf

Coil-current effect in Kibble balances: analysis, measurement, and optimization

This paper presents the progress made to improve and develop the Bureau International des Poids et Mesures (BIPM) watt balance during the last two years. A reduction by a factor of five of the type A uncertainty was achieved by refining the velocity measurement. The BIPM simultaneous weighing and moving approach was experimentally compared to a bifilar coil technique. The relative difference to the Planck constant determination between the two approaches is $2 \times 10^{-7}$ with a type A uncertainty of $3 \times 10^{-7}$ . A vacuum enclosure located in a dedicated laboratory with better thermal and vibrational isolation is ready to receive the present apparatus for further improvement.

A. Kiss

Papers

The BIPM Watt Balance: Improvements and Developments

A watt balance based on a simultaneous measurement scheme

Progress on the BIPM watt balance

Coil-current effect in Kibble balances: analysis, measurement, and optimization

Status of the BIPM Watt Balance