The quantum electrical triangle

Abstract

The past 35 years have seen the development of an unexpected plethora of quantum electrical standards based on just two fundamental constants, e and h. First came a voltage standard based on the Josephson a.c. effect, in terms of which most maintained primary standards of voltage are defined. This was followed a decade later by the quantized Hall effect, based on the von Klitzing constant which allows the ohm to be maintained very precisely. It became clear 20 years ago that there is also a possible quantum current standard. This third standard has yet to play a full part in practical electrical metrology. However, recent developments suggest that there are many different possible manifestations in which such a current standard might be realized. The three quantum standards, taken together, define the quantum electrical triangle of standards which would allow the units to be realized in terms of different combinations of e and h. We summarize the very different physics behind the three standards, reviewing the present state of development in all three. Implications for the future are also considered, especially relating to ultra-low temperature, nanoscale and truly quantum mechanical versions of the standards.