ampere

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The unit of electric current in SI, one of the base units. Symbol A. After 20 May 2019,

It 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.

Resolutions Adopted.
Resolution 1, appendix 3.
26 CGPM, Versailles 13-16 November 2018.
BIPM.

Here C is the symbol for the coulomb, the SI unit of charge. The definition amounts to saying that 1 ampere is a flow of 6,241,509,125,883,260,000 elementary charges per second. Means actually exist for counting individual electrons as they go by, but at present only for exceedingly weak currents (less than 10⁻⁹ A). The ampere is usually currently realized through Ohm's Law, amperes = volts/ohms, using a Josephson voltage standard and a quantum Hall effect standard of resistance, both quantum devices accurate to parts-per-billion. (See “the conventional ampere”, below.)

The redefinition of the ampere was part of a revolutionary revision of SI as a whole, with the aim of basing the system solely on fundamental constants given exact values by definition. The ampere's definition is based on two such constants:

Recommendation 1 of the 94th meeting of the CIPM (2005) anticipated the ampere would be redefined at the 24th CGPM in 2011. At that meeting (Paris, October 2011), the CGPM again only declared its intention, but gave fuller details. The value of the elementary charge e was to be made a matter of definition, rather than something to be determined experimentally. The new value was to be exactly 1.602 17X × 10⁻¹⁹ coulombs, where X stood for one or more yet to be determined digits. Additional years of experimentation, measuring e, enabled metrologists to increase the accuracy by 4 more decimal places by 2018.

The conventional ampere, ~1990 – 2019

From shortly before 1990 to 20 May 2019, in practice experimenters at the highest levels used an ampere that was not the SI ampere.

This divergence resulted from the appearance of radically new quantum voltage and resistance standards which reduced the uncertainty in measurements by orders of magnitude.

A volt standard from the Josephson effect

In 1962 Brian Josephson, a graduate student at Cambridge University, predicted a certain phenomenon on theoretical grounds.¹ The following year experimenters verified its existence,² and it has since been called the Josephson effect.

Imagine two superconductors separated by a very thin (say, ) layer of insulation. In a superconductor chilled below its critical temperature (say, 4 kelvin), pairs of electrons flow without any resistance. Josephson predicted that in such an arrangement these pairs would "tunnel" (a term of the art) through the insulator.

Now shine a beam of microwaves on the junction. But if a superconducting junction is exposed to electromagnetic radiation such as microwaves, then a “quantized” voltage develops across the junction that is proportional to the frequency of the radiation. That proportion is expressed by the Josephson constant KJ = 2e/h, where e is the elementary charge and h is the Planck constant. “Quantized” means that only specific values of voltage can exist, proportional to those constants, instead of a continuous range of values.

J said quant

V = n f/KJ 

voltage depends only on the second, and time is currently by far the most accurately measured dimension.

The first voltage standards using Josephson effect produced only 1 to 10 mV, which is awkwardly small for metrological purposes. To boost the voltage, junctions were wired in series, the way flashlight batteries are wired in series to get 6 volts from 4 1.5-volt batteries. This approach topped out at 20 junctions, because it required touchy regulation of each and every junction's bias current. In 1977, Levinson et al³ suggested a different circuit that eliminated that problem. In today's Josephson voltage standards, a single chip may contain tens of thousands of Josephson junctions.

extreme closeup of a josephson junction on a chip

A false color scanning electron microscope image of Josephson juntions on a chip. The blue and red elements are made of superconductors. The green material is an insulator, which extends beneath the blue layer, separating it from the red.

M. Malnou/NIST/JILA

Thousands of Josephson junctions on a single chip.

Courtesy NIST.

An ohm standard from the quantum Hall effect

In 1879 Edwin Hall reported an effect⁴ now called the ordinary Hall effect. Imagine a strip of conductor with an electric current flowing through it. When a magnetic field is applied perpendicular to the surface of the strip, an electric potential appears between the two areas next to the opposing edges of the strip, at right angles to the current. This potential is called the Hall voltage. The Hall resistance is the ratio of the Hall voltage to the current through the conductor (Ohm's law). In the ordinary Hall effect the Hall resistence can be varied continuously, for example, by changing the strength of the magnetic field.

schematic of Hall effect using graphene sheet

Courtesy NIST.

Fast forward a hundred years to a time of semiconductors, liquid helium and quantum mechanics. Klaus von Klitzing had been studying the Hall effect for a number of years. a specially prepared silicon MOSFET transistor a very thin film 4.2 kelvin the Hall resitene is found by dividing the Hall voltage by the current through the

Around 3 am on the morning of 5 February 1980,

(For readers familiar with MOSFET transistors, the Hall voltage is measured and the Hall resistance

as gate volatge increase, so does Hall whole number of depends only on h/e² This h/e2 is about 25 ohms. It has been named the vonKlitzing constant. (Later, a fractional quantised Hall effect was discovered, which won't be discussed here.)

Notice the way in which the quantized Hall effect reistance device resembles the Josephson voltage device: . to make the quantum effects observable, we need a very thin layer. Adbanved devices use graphene, a layer only that the 1 carbon atom thick. two-dimensional electron gas (2DEG).

semiconductor chip used by von Klitzing in discovery of the quantum Hall effect

Silicon chip on which Klaus von Klitzing discovered the quantum Hall effect.

Courtesy: Physikalisch-Technische Bundesanstalt www.ptb.de

Courtesy PTB.

⁵ original title was efree persuaded him to change it, as at that time fine structre to by The value of this effect to metrology was so obvious that the very next day von Klitzing was on the phone to the Physikalisch-Technische Bundesanstalt, Germany's National Metrology Institute.

In 1980, reported that a certain the resistance changed in discrete, precise steps (i.e., it was quantized). The steps turned out to be exactly the Plank constant divided by the square of the elementary carge times i, i being a whole number. h/e2 , 25,812.807 ohm became known as the von Klitzing constant   and the resistance by a quantized Hall resistance.

A graphene-based quantum Hall resistance standard

A sophisticated quantum Hall device made at NIST. The blue-gray rectangle in the center is the open face of the Hall bar. The locations of graphene components are outlined by white lines. Current is applied through the contacts at the left and right ends of the bar. The Hall voltage is measured through the triplets of contacts above and below the bar. Not shown are the required magnet and supercooling equipment, which are external to the device.

Courtesy NIST.

Josephson and von Klitzing discoveries embraced

Josephson and von Klitzing both received Nobel Prizes.

During the period 1963 – 1990, the various national metrological laboratories used slightly different values for the Josephson constant, and later for the von Klitizing constant. That complicated comparisons of results. To faciliate research, in 1988, at the request of the Comité Consultatif d'Electricité, the CIPM specified exact values of the constants effective 1 January 1990.⁶ Experimentalists proceeded to realize the ampere from “amperes equals volts divided by ohms.” In the literature, such work is often said to have been done in “conventional” units, an indication that SI units are not meant. The CIPM specified the symbol RK-90 for the conventional value of the von Klitzing constant and KJ−90 for the Josephson constant. Sometimes other symbols are given a subscript “90”, e.g., “V₉₀”, to indicate that the measurement was made with quantum device standards using the CIPM's exact values.

To illustrate the fixing of the constants: the CODATA report for 2014 gives a numerical value for the Josephson constant of “KJ [=] 483 597.8525(30) × 10⁹ Hz V⁻¹”, but for “the conventional value of Josephson constant KJ−90 483 597.9 GHz V⁻¹ exact”.

1. Brian D. Josephson.
Possible new effects in superconductive tunnelling.
Physics Letters, vol. 1, issue 7, pages 251-253 (1 July 1962).

2. Sidney Shapiro.
Josephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations.
Physical Review Letters, vol. 11, issue 2, pages 80- 15 July 1963 doi:10.1103/PhysRevLett.11.80

3. M.T. Levinsen, R.Y. Chiao, M.J. Feldman and B.A. Tucker
An inverse ac Josephson effect voltage standard.
Applied Physics Letter, vol. 31, issue 11, pages 776-778 (1 December 1977)
doi:10.1063/1.89520

4. E.H. Hall.
On a new action of the magnet on electric currents.
American Journal of Mathematics, vol. 2, no. 3, pages 287-292. (Sept. 1879)
doi:10.2307/2369245.

5. K. v. Klitzing, G. Dorda and M. Pepper.
New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance.
Physical Review Letters, vol. 45, issue 6, 494 – (11 August 1980)

6. T. J. Quinn.
News from the BIPM.
Metrologia, vol. 26, no. 1, page

The same issue contains "New international electrical reference standards based on the Josephson and quantum Hall effects," by B.N. Taylor and T.J. Witt, and other related articles.


engraving of Ampère

The ampere is named for André Marie Ampère (1775–1836).

The previous SI definition

The following definition was abrogated in resolution 1 of the 26th CGPM (2018). It was originally proposed by the CIPM in 1946 and adopted by the CGPM in 1948.

One ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in a vacuum, would produce between these conductors a force equal to 2 × 10⁻⁷ newtons per meter of length.

CIPM 1946 Resolution 2, approved by the Ninth CGPM in 1948.

Since the setup described is purely conceptual, the ampere must be realized through calculations based on results from an actual setup.

It may seem as if this old definition, unlike that in the post-2018 SI, does not involve specifying the value of a fundamental constant. But it does: it sets the magnetic constant μ0 = 4π∙10⁻⁷ Hm⁻¹ = 4π∙10⁻⁷ m∙kg∙s²∙A⁻². Under the new definition of the ampere, the magnetic constant must be determined experimentally.

Previous to the 1948 definition, the ampere had been realized in a variety of ways: with delicate balances able to compare electrical and mechanical forces (see, for example, Weber), by electroplating defined masses of metal, and so on. See history of the ampere.

resources

Wikipedia has comprehensive and necessarily technical entries on

Josephson voltage standard

Quantum Hall Effect

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