The Ampere

Along with the ohm and the volt, the ampere is one of the three base units in the field of electricity. It was adopted as a base unit in the International System of Units (SI) back in 1948, and its definition stood the test of time for 70 years. But all of that changed in November 2018, when the ampere was redefined based on a fundamental constant in nature: the elementary charge, denoted by e.

Profile of the ampere

Official definition (1948, 9th CGPM)

Symbol: A

Quantity: intensity of an electric current

Units derived from the ampere: coulomb, volt, ohm, farad, henry, tesla

Since 1948, the ampere – the base unit of electric current intensity – has been defined on the basis of the mechanical force between two wires one meter apart that carry an electrical current. In practice, however, this definition is difficult to realize with the requisite measurement uncertainty. Moreover, it does not convey the fundamental notion of an electric current, i.e., the flow of elementary charges per unit of time. Hence the idea of redefining the ampere by fixing the value of the elementary charge, e. With that goal in mind, researchers at the LNE developed a standard that tangibly realizes that new definition with a record relative uncertainty of 10^{-8}.

Definition of the ampere

The ampere, the SI unit of electric current, is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10^{−19} when expressed in the unit C, which is equal to A·s, where the second is defined in terms of ΔνCs.

In practice, metrology laboratories create an electrical current standard using two voltage and resistance standards. The units for those standards – the volt and the ohm – can be realized to approximately 10-9 thanks to two quantum effects (the Josephson effect and the quantum Hall effect) that depend solely on e and the Planck constant. The ampere is then realized by applying Ohm’s law, which connects voltage, current and resistance. In concrete terms, however, Ohm’s law is applied to physical mechanisms that, although they are calibrated from quantum standards, deviate over time. As a result, the relative uncertainty for an ampere is typically 10^{-6}.

To improve on that, scientists at the LNE developed a quantum circuit that can be used to apply Ohm’s law directly to the quantum voltage and resistance standards. In practice, they had to find a means of ignoring parasitic resistance from the electrical connections linking the two standards, which was leading to errors in the reference quantum circuit. But how? Using the properties of the quantum Hall effect, additional connections can be added between the two standards; the electric current in those connections will diminish as the number of connections increases. The result: the parasite potential drop resulting from those connections becomes negligible and the reference current remains fully quantified.

Using that information, a precise, ultra-sensitive amplifier identifies the reference current by adding all of the component circuits, then amplifies it using a servo-controlled amplifier with an external power source. This quantum current generator offers an initial example of a combination of two quantum standards. It generates currents across a wide range of values between 1 µA and 10 mA, accurate to within 10^{-8}. In addition, it realizes the future definition of the ampere since, using the quantum Hall and Josephson effects, it delivers a current that is proportional to the elementary charge.

As currently configured, the system is formidable: it requires no fewer than three cryogenic systems to cool the quantum voltage and resistance standards along with the amplifier to a temperature approaching absolute zero. But the LNE’s researchers have shown that it is possible to obtain the quantum Hall effect in graphene under a weaker magnetic field, and at a less restrictive temperature, than in a gallium arsenide sample of the kind currently used. Eventually, only one cryostat will be needed to realize our standard. Moreover, that cryostat is already ready to use for the redefinition in the International System of Units.