Electrical quantum standards and their role in the SI

The International System of Units, SI, is poised to make a quantum change and become a measurement system based entirely on the fundamental properties of the natural world. In the next version of the SI, the Planck constant h , the elementary charge e , the Avogadro constant N A and the Boltzmann constant k will be fixed, in addition to the already fixed values of the speed of light c and the ground state hyperfine splitting in caesium-133. As a result, six out of the seven base units of the SI will be based directly on true invariants of nature. A major part of this change has been enabled by the ready availability of electrical quantum standards of exquisite precision and mechanisms for using them to make measurements outside the electrical arena. The overall effect will be to eliminate the remaining imprecise definitions of physical units associated with the use of artefact standards and aid direct SI measurements without problems of scaling. Fixing the Planck constant and the elementary charge will have the effect of incorporating the best physical realizations of electrical quantities into the SI, providing a system of units fit for the 21st century. The purpose of this special feature is to review the status of electrical quantum standards and report the latest developments in those areas and their applications to other areas of metrology. The special feature coincides with the 50th anniversary of the seminal paper of Josephson, 'Possible new effects in superconductive tunnelling' [1], which established the basic physical principle upon which the quantum voltage standards are based. Josephson voltage standards are based on the inverse Josephson effect. When a junction of two superconducting electrodes, weakly linked through a thin insulator or a normal metal, is irradiated with a radiofrequency electromagnetic field of frequency f and is biased by a dc current, then the voltage across the junction is quantized (i.e. small changes in either the dc current or the power of the rf irradiation, or both, do not change the voltage). The value of this quantized Josephson voltage is equal to nfh /2 e , where n is the quantum step of the current–voltage characteristic curve. In this special feature there are three papers on dc Josephson voltage standards. Solve and Stock review the programme conducted by the Bureau International des Poids et Mesures (BIPM) to perform on-site comparisons of Josephson voltage standards, and give a comprehensive analysis of the possible sources of errors of such comparisons. Behr et al summarize the developments of Josephson voltage standards at Physikalisch-Technische Bundesanstalt (PTB) and their applications in dc voltage and other areas of metrology. Finally, Georgakopoulos et al report a reduction, by a factor of a thousand, in the smallest voltage that can be generated by dc Josephson voltage standards. Although dc voltage standards are well established, significant challenges exist when extending this extremely precise technology to ac. There are two approaches to producing accurate ac voltages using the inverse Josephson effect: the programmable Josephson voltage standard (PJVS) and the pulse-driven ac voltage standard. The PJVS contains an array of Josephson junctions, organized into independently biased segments. By biasing chosen, binary-related, segments on the first quantum step (positive or negative) or zero, the array can be made to behave as a quantum digital to analogue converter. The PJVS approach can produce stepwise approximated sine waves with rms values of some volts, but it suffers from parasitic capacitances and inductances distributed in the different parts of the system and, more importantly, the voltage is not quantized during the finite transition time between successive voltage levels. Hence the output frequency of PJVS-based systems is limited to a few kilohertz. In this special feature, Jeanneret et al review the Josephson locked synthesizer, a PJVS-based system where the effect of transients between successive steps on the output voltage is reduced. This special feature also presents two applications of PJVS-based quantum voltage standards: the evaluation of conventional ac voltage standards based on thermal converters (Budovsky et al ) and the measurement of the settling time of a high resolution digital voltmeter (Henderson et al ). In the pulse-driven ac voltage standard, arbitrary voltages can be produced by modulating the rf irradiation of an array of Josephson junctions by a series of high frequency pulses, usually by means of Δ–Σ modulation. The output voltage of the array of junctions is a series of quantized voltage pulses that correspond to the desired waveform after the high frequency components are removed. The pulse-driven standard can operate at much higher frequencies than the PJVS. Eliminating the effects of parasitic impedances of the, necessarily long, connecting leads therefore becomes a significant challenge. In this special feature, van den Brom and Houtzager report a voltage lead correction technique. Quantum resistance standards are based on the quantum Hall effect in which the resistance of a two-dimensional electron gas in a strong magnetic field is quantized. The value of the quantized Hall resistance is h / ie 2 , where i is the number of the quantum step in the resistance–magnetic field curve. Quantum Hall resistance devices can be combined in series to form a resistive voltage divider with low uncertainty in the ratio. In this special feature, Domae et al report the realization of such a resistive voltage divider on a chip. Quantum Hall resistance standards have been routinely used at dc for over two decades. However, the operation of quantum Hall devices at ac is complicated by the flow of current in capacitances around the device, which can compromise measurement of its resistance. Schurr et al review the status of ac quantum Hall resistance standards and their role in the SI. Ohm's law can be applied to quantum realizations of voltage, resistance and current to test their consistency. Active research into this 'metrological triangle' is underway and, at present, there is no evidence to indicate a discrepancy at any level. However, work is continuing on current sources which utilize a countable flow of electrons (the electric current produced is proportional to ef , f being the operating frequency of the device), but the work has some way to go before the question of consistency can be resolved at levels approaching 1 part in 10 9 . In this special feature, Scherer and Camarota review the state-of-the-art of metrological triangle experiments and Devoille et al report on the status of the metrological triangle experiment at the Laboratoire National de Métrologie et d'Essais (LNE), France. The availability of precise representations of the volt and the ohm based on quantum mechanics has enabled the watt balance, an apparatus which relates electrical and mechanical power, to link the kilogram to the Planck constant. This has paved the way for the proposed redefinition of the kilogram, the last artefact standard in the SI, in terms of a fixed value of the Planck constant. In the past few years a number of papers, e.g. [2, 3], have been published describing the working principles of the watt balance and the characteristics of the existing implementations of the experiment. The measurements of the principal quantities—mass, velocity, gravitational acceleration, resistance and voltage—are reasonably well documented but the ultimate precision of the apparatus depends on a number of techniques that are required to eliminate second-order effects. In this special feature, Robinson provides details of these general alignment techniques with special reference to the NPL Mark II watt balance. Acknowledgments We would like to thank the authors for supporting the special feature with their excellent contributions; the guardians of the quality of a scientific paper, the referees, for their valuable comments and suggestions; Professor Wuqiang Yang and the members of the editorial board of Measurement Science and Technology for their support. Finally, we would like to thank Dr Sharon D'Souza, James Dimond and all the editorial and publication staff at Measurement Science and Technology , for their help in making the special feature a reality. References [1] Josephson B D 1962 Possible new effects in superconductive tunnelling Phys. Lett. 1 251–3 [2] Li S, Han B, Li Z and Lan J 2012 Precisely measuring the Planck constant by electromechanical balances Measurement 45 1–13 [3] Stock M 2011 The watt balance: determination of the Planck constant and redefinition of the kilogram Phil. Trans. R. Soc. A 369 3936–53