The International System of Units (SI) will soon undergo a major change, when the units of measurement are redefined on the basis of fundamental physical constants [1, 2].
It now seems possible, or even probable, that this long-term metrology goal of the revision of the SI system, will be achieved in 2018. The base unit of time, the second, is already defined in terms of the properties of single atoms, by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium-133 atom, and the metre is based on the second and an agreed numerical value for the speed of light.
However, in the current SI system the kilogram is still based on the International Prototype of the Kilogram, which is kept behind locks and keys at the BIPM (International Bureau of Weights and Measures) close to Paris. The magnitude of the unit of electric current, the ampere, is defined based on the per-metre force between two conductors, via which the magnitude of an ampere, in turn, depends on the prototype of the kilogram.
However, the SI units for electricity can be linked directly to the values of fundamental physical constants through so-called quantum standards. The quantum standard for voltage is based on the Josephson effect, which arises in a structure that consists of two superconductors coupled by a weak link. This can be used to realise voltage in terms of the elementary charge, e, and Planck’s constant, h, with a relative uncertainty of around 10-10. The unit for resistance, the ohm, can be linked to the values of e and h based on the quantum Hall effect observed in a 2-dimensional electron gas.
A separate, conceptually simple quantum standard is being developed for electric current, based on pumping individual electrons through a nanostructure at a certain frequency.
Groundbreaking work in the field
VTT and the Centre for Metrology and Accreditation (MIKES) have been pioneers in the field and have remained at the cutting edge of the international development of quantum standards since the 1970s. At that time, Heikki Seppä and his partners developed the Nordic countries’ first Josephson standard for DC voltage.
In recent years, MIKES has been especially active in the development of a quantum standard for electric current, based on single-electron phenomena in nanostructures . The solution of MIKES is the so-called SINIS turnstile that was invented in what was then the Helsinki University of Technology’s Low Temperature Laboratory in 2007 .
The structure of the SINIS turnstile is similar to that of a hybrid single-electron transistor. It consists of a nanoscale normal metal island connected to superconducting electrodes by tunnel junctions. Electrons can be pumped through the transistor one at a time, in a controlled manner. The maximum frequency for precise electron pumping is around 100 MHz, which corresponds to a current of I = ef ≈ 16 pA, but the current can be increased by connecting several SINIS turnstiles in parallel.
At the moment, MIKES is developing a quantum current source based on 10 SINIS turnstiles in parallel, with the intention of achieving a current of 100 pA with a relative uncertainty of under one part per million.
Research led to Microphoton project
As a by-product of the SINIS turnstile research, together with the O.V. Lounasmaa laboratory of Aalto University and the National Metrology Institute of Germany (PTB), MIKES has demonstrated that nanostructures of this kind, made of a superconductor and normal metal, are highly sensitive to thermal radiation that can penetrate in cryogenic measurement environments. Even individual microwave photons can shift a component from its correct operating point, but most of these problems can be eliminated through careful filtering and shielding .
As a result of the research, MIKES was accepted as the coordinator of the MICROPHOTON project , which belongs to the European Metrology Research Programme (EMRP). The project’s main goal is the development of generators and detectors of single microwave photons in a frequency range of around 10 GHz – 300 GHz.
The anticipated long-term application is quantum information processing and communication (QIPC) based on superconducting quantum bits (qubits) and microwave photons. Three other leading European national metrology institutes and three universities are taking part in the project, in addition to MIKES.
MIKES’ individual contribution to the project includes investigating the suitability of SINIS nanostructures for the detection of single microwave photons and understanding and minimising the detrimental effects caused to quantum and nanocomponents by thermal radiation.
Quantum Hall effect and graphene
Since 1993, the Finnish national standard of resistance has been based on the quantum Hall effect observed on the interface of GaAs/AlGaAs heterostructure. Operation of a resistance quantum standard of this kind requires that it must be cooled down to about 1.5 K in a magnetic field of around 10 T. However, graphene, which was discovered in 2004, is revolutionising resistance metrology, since the quantum Hall effect can be observed in this material at a far higher temperature and in a far weaker magnetic field than in GaAs structures.
MIKES is also at the forefront of international research in this field. The epitaxial growth of graphene on silicon carbide was developed in collaboration with Aalto University’s Department of Micro- and Nanosciences. With graphene devices, MIKES has succeeded in obtaining a correct value for quantum Hall resistance with a relative uncertainty below one part per million in a magnetic field of only 3T – i.e. weaker than ever before .
The PTB of Germany recently used graphene devices produced and tested by Aalto University and MIKES in the world’s first, highly promising precision AC measurements of the quantum Hall resistance in graphene .
Volt is realised by the Josephson effect
The oldest quantum standard is the voltage standard based on the Josephson effect. It has served as Finland’s national standard of DC voltage since the early 1980s. An AC voltage standard based on the Josephson effect is now under development.
Around 15 years ago, VTT and MIKES had already noted that in AC voltage standard it would be beneficial to use the Josephson device to generate a quantized square wave and to compare the wave’s fundamental frequency component to the voltage of a controllable sine wave generator using a lock-in amplifier . Thus far, the generation of a 1 V sine wave has been demonstrated with an uncertainty level of 1.5 parts per million at frequencies of 62.5 Hz and 1 kHz.
The method has also been used to realize AC resistance and impedance bridges based on two Josephson voltage standards . One problem has been the lack of a commercially available, stable and precisely controllable sine wave generator – MIKES had to design and build one itself . This device, the two-channel precision sine wave generator DualDAC, has been commercialised via VTT’s spin-off company Aivon Oy and is already being used by several national metrology institutes around the world.
Research will continue
Using quantum standards, the units of DC voltage and resistance can be linked to fundamental physical constants with a relative uncertainty below one part per billion. However, according to the present definitions of the SI system, the volt and ohm are based on the ampere which is defined using electromagnetic forces, and have an uncertainty two or three times greater.
On the other hand, it has been internationally agreed that minimum uncertainties in voltage and resistance calibrations based on Josephson and quantum Hall effects can be smaller than the measurement uncertainties set by the SI system. This means that the most accurate calibrations of electric quantities are, in a sense, performed outside the SI system. This inconsistency will be eliminated when the ampere is defined using a fixed value for the elementary charge in the “new SI system”.
In any case, development of the quantum standards will continue and special focuses of research and development in MIKES are as follows: an electric current quantum standard based on single-electron phenomena, a quantum Hall resistance/impedance standard based on graphene and the use of the Josephson voltage standard in AC applications.
The long-term aim is to close the so-called quantum metrology triangle to demonstrate the consistency between quantum standards for voltage, current and resistance at uncertainty level below 0.1 parts per million. Another vision is a “universal quantum standard for all electric quantities” which would be based on Josephson standards and a graphene-based quantum Hall standard in the same cryostat. With such a system, the units of both voltage, resistance, electric current, capacitance and inductance could be realized in accordance with the new SI definitions.
In research on quantum standards, MIKES’ key research partners have been other research groups from VTT, Aalto University and other national metrology institutes in Europe. Much of this research has been done in the framework of the European Metrology Research Programme (EMRP) that is jointly funded by the EMRP participating countries within EURAMET and the EU. Key Finnish funders have included the Academy of Finland and the Technology Industries of Finland Centennial Foundation.
Figure 2. The Hall resistance RH of quantum Hall components made of graphene (red curve) and a GaAs/AlGaAs heterostructure (blue curve) as a function of a magnetic field at a temperature of 1.5 K. In graphene components, a quantum Hall resistance plateau of 12.9 kΩ suitable for metrological use can be obtained in a magnetic field of just 2 T, whereas a magnetic field of over 8 T is needed in the GaAs structure for this purpose.
Dr. Antti Manninen is a Senior Principal Scientist in MIKES, VTT’s Centre for Metrology. Dr Manninen’s key research interests include the application of cryoelectronic micro and nanodevices to electrical metrology, particularly as quantum standards.
Alexandre Satrapinski (left), Pekka Immonen, Antti Kemppinen, Antti Manninen, Emma Mykkänen, Jaani Nissilä and Janne Lehtinen study, develop and use quantum standards for electricity at MIKES.
 A. Manninen, Uusi SI-järjestelmä toteuttaa Maxwellin unelman, Arkhimedes 2/2012, pp. 10 - 20.
 J.P. Pekola, O.-P. Saira, V.F. Maisi, A. Kemppinen, M. Möttönen, Yu.A. Pashkin, and D.V. Averin, Single-electron current sources: towards a refined definition of ampere, Rev. Mod. Phys. 85 (2013) 1421 - 1472.
 J.P. Pekola, J.J. Vartiainen, M. Möttönen, O.-P. Saira, M. Meschke, and D.V. Averin, Hybrid single-electron transistor as a source of quantized electric current, Nature Phys. 4 (2008) 120 - 124.
 A. Kemppinen, S.V. Lotkhov, O.-P. Saira, A.B. Zorin, J.P. Pekola, and A.J. Manninen, Long hold times in a two-junction electron trap, Appl. Phys. Lett. 99 (2011) 142106.
 A. Satrapinski, S. Novikov, and N. Lebedeva, Precision quantum Hall resistance measurement on epitaxial graphene device in low magnetic field, Appl. Phys. Lett. 103 (2013) 173509.
 C.-C Kalmbach, J. Schurr, F. J. Ahlers, A. Muller, S. Novikov, N. Lebedeva, and A. Satrapinski, Towards a graphene-based quantum impedance standard, Appl. Phys. Lett. 105 (2014) 073511.
 J. Nissilä, A. Kemppinen, K. Ojasalo, A. Manninen, J. Hassel, P. Helistö, and H. Seppä, Realization of a square-wave voltage with externally-shunted SIS Josephson junction arrays for a sub-ppm quantum AC voltage standard, IEEE Trans. Instrum. Meas. 54 (2005) 636 - 640.
 J. Lee, J. Schurr, J. Nissilä, L. Palafox, and R. Behr, The Josephson two-terminal-pair impedance bridge, Metrologia 47 (2010) 453 - 459.
J. Nissilä, K. Ojasalo, M. Kampik, J. Kaasalainen, V. Maisi, M. Casserly, F. Overney, A. Christensen, L.Callegaro, V. D’Elia, N.T.M. Tran, F. Pourdanesh, M. Ortolano, D.B. Kim, J. Penttilä, and L. Roschier, A precise two-channel digitally synthesized AC voltage source for impedance metrology, CPEM 2014 Digest, Rio de Janeiro, 24 - 29 August, 2014, pp. 768 - 769.