Instrumentation & Measurement Magazine 24-3 - 6

To see more clearly how
this link comes about in
the Kibble balance, I need
to delve somewhat into
the history and physics
of the quantum electrical
standards.

The Electrical
Units
The electrical units were introduced in the SI in 1948
[5] with the definition of
the ampere as that constant
current which, if maintained
in two straight parallel conductors of infinite length, of
negligible circular cross-section, and placed 1 metre apart
in vacuum, would produce
between these conductors a
Fig. 1. Measurements of official copies of the kilogram in terms of the IPK since 1889. Source: Michael Stock, BIPM [2],
Open Access, Creative Commons Attribution 3.0 licence.
force equal to 2 × 10−7 newton
per metre of length. Before
the development of quanThe second method involves the use of a Kibble balance (or tum electrical standards, the electrical units were maintained
watt balance) [4] to link the kilogram to the Planck constant. by stable artifacts whose values were determined through
This is the technique that was adopted by the National Research various electro-mechanical experiments such as the current
Council of Canada (NRC), as well as other NMIs, including the balance [6], the voltage balance [7], the calculable inductor [8]
National Institute of Standards and Technology (NIST) in the US, and the calculable capacitor [9]. These were extremely difficult
the Laboratoire National de Métrologie et d'Essais (LNE) in France, experiments which were limited by challenging dimensional
the National Physical Laboratory (NPL) in the UK and the Na- and mechanical demands, but remarkably, by 1990, the SI electional Institute of Metrology (NIM) in China, the last one being a trical units achieved uncertainties below 4 parts in 107.
On the other hand, the level of precision of electrical stanvariation called the Joule balance.
The Kibble balance (or watt balance) compares the weight dards improved by about three orders of magnitude with
of a mass with an electromagnetic force which can be deter- the development and wide-spread adoption of Josephson efmined with extreme accuracy by measurements of voltage, fect voltage standards and quantum Hall effect resistance
resistance and velocity. In the next few sections, I discuss standards.
how the electromagnetic force is linked to the Planck constant
The Josephson Effect
through the use of quantum electrical standards.
The Planck constant has units of joule-second (kg m2 s−1) Tunneling is the quantum-mechanical phenomenon that aland hence, given the definitions of the meter and the second, it lows a particle to escape a potential barrier, even though it does
is clear, from a theoretical point of view, that fixing the numer- not have enough energy to do so. In a tunnel junction a current
ical value of h does indeed define the kilogram. However, this can be established between two metallic electrodes separated
definition is not as easy to visualize as the old one based on the by a thin insulator by electrons tunneling through the insulatIPK. One will begin to understand this link by noting that there ing barrier (Fig. 2a). For small voltages and currents, the I-V
are various different forms of energy in nature (e.g., gravita- characteristics are approximately linear and resemble a resistional, kinetic, electromagnetic, nuclear, etc.), and that energy tive characteristic (dotted line on Fig. 2b).
can be converted from one form to another. And, while mass
When the electrodes in a tunnel junction are superconductcan be related to gravitational energy, the Planck constant is ing, the I-V characteristics become very rich with a range of
related to the energy of an electromagnetic field. Specifically, effects that were first theoretically predicted by Brian Josephaccording to quantum mechanics, an electrically charged par- son in 1962 [10]. He was later awarded with a Nobel Prize in
ticle can exchange energy with an electromagnetic field only physics after his predictions were confirmed experimentally
in discrete (quantized) amounts given by E = hf, where f is the by a number of researchers.
frequency of the radiation. This is often conceptualized by
One of the main characteristics of the superconducting state
thinking of the electromagnetic field as being composed of dis- is that conduction electrons can bind to other electrons and
crete particles (photons), each having an energy, hf.
form stable pairs, known as Cooper pairs. In low-temperature
6

IEEE Instrumentation & Measurement Magazine

May 2021

Instrumentation & Measurement Magazine 24-3

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