Ampere: SI Redefinition & Quantum Realizations

• Ampere is defined as the SI unit of electric current by fixing the elementary charge, making current a direct measure of electron flow per second.
• Quantum electrical standards, leveraging the Josephson and quantum Hall effects, provide a coherent framework for realizing voltage, resistance, and current.
• Advances in programmable quantum current generators and single-electron pumps offer improved accuracy and traceability for modern metrology.

Searching arXiv for recent and canonical sources on the ampere, its SI redefinition, and quantum realizations.

I’ll look up the cited arXiv records to ground the article in the relevant literature.

The ampere, symbol A, is the SI unit of electric current. Since 20 May 2019, it has been defined by taking the fixed numerical value of the elementary charge to be $e = 1.602\,176\,634\times10^{-19}\,\mathrm{C}$, with $1\,\mathrm{C}=1\,\mathrm{A\,s}$ and the second defined in terms of $\Delta\nu_{\mathrm{Cs}}$. In this formulation, current is explicitly charge flow per unit time: $I=\mathrm{d}Q/\mathrm{d}t$ with $Q=Ne$, so $1\,\mathrm{A}$ corresponds to the transport of approximately $6\,241\,509\,074\,460\,762\,608$ elementary charges per second. The revised SI therefore places the ampere on explicit quantum foundations and links its realization to fixed constants, notably $e$ and $h$, through the Josephson effect, the quantum Hall effect, and single-electron transport (Poirier et al., 2019, Li et al., 2020).

1. Definition and physical meaning

The formal SI definition states: “The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge $e$ to be $1\,\mathrm{C}=1\,\mathrm{A\,s}$0 when expressed in the unit coulomb, C, which is equal to A·s, where the second is defined in terms of $1\,\mathrm{C}=1\,\mathrm{A\,s}$1.” In symbols, $1\,\mathrm{C}=1\,\mathrm{A\,s}$2 is exact. Because $1\,\mathrm{C}=1\,\mathrm{A\,s}$3, the definition makes the physical meaning of current explicit as a rate of passage of elementary charges. In the revised SI, a current can therefore be realized by counting electrons, or more generally by forming $1\,\mathrm{C}=1\,\mathrm{A\,s}$4 for $1\,\mathrm{C}=1\,\mathrm{A\,s}$5 transported charges in time $1\,\mathrm{C}=1\,\mathrm{A\,s}$6 (Poirier et al., 2019, Li et al., 2020).

This charge-counting interpretation is a conceptual shift from earlier practice. It does not alter the operational equation $1\,\mathrm{C}=1\,\mathrm{A\,s}$7, but it makes the quantum of charge the defining invariant. A consequence is that quantum electrical standards, once traceable “representations” of SI units, become direct SI realizations when their governing constants are expressed in terms of fixed $1\,\mathrm{C}=1\,\mathrm{A\,s}$8 and $1\,\mathrm{C}=1\,\mathrm{A\,s}$9 (Li et al., 2020).

The 2019 revision also fixed $\Delta\nu_{\mathrm{Cs}}$0, while the second and metre continued to be realized from fixed atomic frequency and the speed of light, respectively. This establishes a coherent constant-based framework in which the ampere is no longer subordinate to an electromechanical force law, but to elementary charge transfer referenced to atomic time (Li et al., 2020).

2. From telegraphy and force laws to the revised SI

The historical emergence of the ampere is closely tied to nineteenth-century telegraphy. Telegraph networks relied on batteries, iron wires, earth return, and practical estimates of line resistance, yet the industry used a patchwork of standards: electromotive force was “for the most part measured in units of the predominant Daniell cell,” while resistance standards varied by company. As late as 1881 there were “12 different units of electromotive force, 10 different units of electric current and 15 different units of resistance” in use across countries. Daniell’s 1836 cell, with a typical open-circuit EMF of about $\Delta\nu_{\mathrm{Cs}}$1 in modern units, provided a stable de facto reference scale for practical voltage (Jayson, 2015).

The British Association for the Advancement of Science formed its Committee on Electrical Standards in 1862 and, by 1873, defined practical electrical units as decimal multiples of cgs emu units: $\Delta\nu_{\mathrm{Cs}}$2 abohm, $\Delta\nu_{\mathrm{Cs}}$3 abvolt, and consequently $\Delta\nu_{\mathrm{Cs}}$4 abampere. The International Electrical Congresses of 1881–1904 ratified and expanded this system, while Giovanni Giorgi’s 1901 MKSX proposal exploited the coincidence $\Delta\nu_{\mathrm{Cs}}$5 to show that a coherent MKS-based electromagnetic system could be obtained by adding one practical electrical unit as a fourth base unit. The International Electrotechnical Commission adopted MKSX in 1935, selected the ampere in 1950, and the 1960 SI incorporated Giorgi’s scheme (Jayson, 2015).

From 1948 until the 2019 revision, the ampere was defined through the force per unit length between “two straight parallel conductors of infinite length, of negligible circular cross-section, placed 1 m apart in vacuum.” The special case of equal currents fixed the force per unit length at $\Delta\nu_{\mathrm{Cs}}$6 for currents of $\Delta\nu_{\mathrm{Cs}}$7 in each conductor, and equivalently fixed the vacuum permeability at $\Delta\nu_{\mathrm{Cs}}$8 exactly. In practice, realizations based on ampere balances were limited to relative uncertainties of a few parts in $\Delta\nu_{\mathrm{Cs}}$9 or a few parts in $I=\mathrm{d}Q/\mathrm{d}t$0, chiefly because of geometric and mechanical measurement limitations (Poirier et al., 2019, Li et al., 2020, Davis, 2016).

The revised SI replaced this force-based definition because it tied electrical units to mechanical realizations and left quantum electrical standards outside SI proper. A further consequence of the revision is that $I=\mathrm{d}Q/\mathrm{d}t$1, $I=\mathrm{d}Q/\mathrm{d}t$2, and $I=\mathrm{d}Q/\mathrm{d}t$3 are no longer exact; they are derived from fixed $I=\mathrm{d}Q/\mathrm{d}t$4, $I=\mathrm{d}Q/\mathrm{d}t$5, and $I=\mathrm{d}Q/\mathrm{d}t$6 together with the measured fine-structure constant $I=\mathrm{d}Q/\mathrm{d}t$7, through

$I=\mathrm{d}Q/\mathrm{d}t$8

The uncertainty of these constants is therefore dominated by the uncertainty of $I=\mathrm{d}Q/\mathrm{d}t$9, cited as about $Q=Ne$0 in the 2018 CODATA adjustment (Li et al., 2020, Davis, 2016).

3. Quantum electrical realization through Josephson and Hall standards

The modern quantum realization of the ampere proceeds from exact voltage and resistance standards. In the revised SI, the Josephson constant and the von Klitzing constant are exact:

$Q=Ne$1

Under microwave irradiation of frequency $Q=Ne$2, the ac Josephson effect generates quantized voltage steps

$Q=Ne$3

while the integer quantum Hall effect yields quantized Hall resistance

$Q=Ne$4

with integer plateau index $Q=Ne$5 and longitudinal resistance approximately zero (Poirier et al., 2019, Li et al., 2020).

Applying Ohm’s law to these two standards gives a quantum-referenced current:

$Q=Ne$6

On the $Q=Ne$7 plateau this reduces to $Q=Ne$8, formally identical in structure to single-electron pumping, but realized with macroscopic quantum standards rather than by counting transferred electrons one by one (Poirier et al., 2019, Djordjevic et al., 2024).

This change removed the need for the 1990 conventional system, which had used exact conventional values $Q=Ne$9 and $1\,\mathrm{A}$0 to exploit the reproducibility of Josephson and quantum Hall devices before $1\,\mathrm{A}$1 and $1\,\mathrm{A}$2 were fixed. In the revised SI, the mise en pratique recommends truncated exact values with 15 significant digits for practical use: $1\,\mathrm{A}$3 and $1\,\mathrm{A}$4. Relative to the 1990 conventional values, the volt changes by $1\,\mathrm{A}$5 ppb and the ohm by $1\,\mathrm{A}$6 ppb (Poirier et al., 2019, Li et al., 2020).

Metrologically, these standards are already highly mature. Programmable Josephson voltage standards routinely deliver $1\,\mathrm{A}$7 outputs, with equivalence demonstrated at the few $1\,\mathrm{A}$8 level in international key comparisons, and interlaboratory quantum Hall comparisons routinely agree within a few parts in $1\,\mathrm{A}$9. Graphene-based quantum Hall devices extend operating ranges to lower magnetic fields, higher temperatures, and higher currents (Poirier et al., 2019, Li et al., 2020).

4. Programmable quantum current generators and current traceability

A practical realization of the ampere across everyday calibration ranges is provided by programmable quantum current generators. The 2016 programmable quantum current generator combined a programmable Josephson voltage standard, a quantum Hall resistance standard, and a cryogenic current comparator in a quantum electrical circuit. In that system, the servo loop yielded

$6\,241\,509\,074\,460\,762\,608$0

where $6\,241\,509\,074\,460\,762\,608$1 is the cryogenic current comparator gain ratio, $6\,241\,509\,074\,460\,762\,608$2 is the number of Josephson junctions, and $6\,241\,509\,074\,460\,762\,608$3 accounts for wire effects mitigated by multiple connections. The device demonstrated quantization to within $6\,241\,509\,074\,460\,762\,608$4 over $6\,241\,509\,074\,460\,762\,608$5, with relative standard deviation $6\,241\,509\,074\,460\,762\,608$6, and a combined relative uncertainty of $6\,241\,509\,074\,460\,762\,608$7 from $6\,241\,509\,074\,460\,762\,608$8 to $6\,241\,509\,074\,460\,762\,608$9 (Brun-Picard et al., 2016, Poirier et al., 2019).

Subsequent work improved the noise performance. Relocating the damping resistor in the cryogenic current comparator circuit to $e$0 reduced integrated flux noise between $e$1 and $e$2 from $e$3 to $e$4, enabling lower-uncertainty calibration of precision ammeters. In a direct comparison between the realizations of the ampere at PTB and LNE using a calibrated Ultrastable Low-Noise Current Amplifier, the two institutes agreed in the range $e$5 to $e$6 parts in $e$7 with a combined standard uncertainty of $e$8 parts in $e$9 (Djordjevic et al., 2021).

A further step was reported in 2024 with a new programmable quantum current generator based on a triple connection that suppresses cable corrections to $h$0. With full quantum instrumentation, this device generated currents in the microampere range at quantized values $h$1, with relative uncertainties less than $h$2 and no post-measurement error corrections. Demonstrated outputs included $h$3, $h$4, $h$5, and $h$6, with weighted mean deviations consistent with zero within a few parts in $h$7 (Djordjevic et al., 2024).

These developments substantially simplify current traceability. The revised SI also recognizes additional practical routes, including $h$8 with capacitance traced via calculable capacitors or QHE-based impedance bridges, but the Josephson-plus-Hall route is presently the most mature quantum realization for routine metrology over broad current ranges (Poirier et al., 2019, Li et al., 2020).

5. Direct realization by elementary charge transfer

The most literal realization of the revised definition is direct single-charge transport. Ideal single-electron pumps and related devices generate

$h$9

or $e$0 for one transferred electron per cycle. This route places the ampere directly on counted charge quanta and a clock frequency, but its practical difficulty is suppressing missed, extra, and thermally activated transfer events while maintaining useful current levels (Pekola et al., 2012, Li et al., 2020).

Several device classes have been pursued. Metallic multi-junction pumps achieved error rates as low as $e$1 per cycle in a 7-junction device, but currents are typically only a few picoamperes. Semiconductor tunable-barrier quantum-dot pumps have reached higher currents: GaAs devices achieved $e$2 at $e$3 with relative combined uncertainty $e$4 ($e$5), and an earlier GaAs pump generated $e$6 at $e$7 with $e$8 uncertainty; silicon MOS quantum-dot pumping at $e$9 reached $1\,\mathrm{C}=1\,\mathrm{A\,s}$00 ($1\,\mathrm{C}=1\,\mathrm{A\,s}$01) without magnetic field (Poirier et al., 2019, Giblin et al., 2012).

The 2012 waveform-engineered GaAs pump showed that specially designed gate-drive waveforms could restore accurate quantization at $1\,\mathrm{C}=1\,\mathrm{A\,s}$02 where sine-drive operation did not show a quantized plateau on the ppm scale, yielding $1\,\mathrm{C}=1\,\mathrm{A\,s}$03 and experimentally demonstrated accuracy better than $1\,\mathrm{C}=1\,\mathrm{A\,s}$04 ppm. Hybrid metal/semiconductor CMOS-integrated pumps demonstrated robust pumping at $1\,\mathrm{C}=1\,\mathrm{A\,s}$05 and $1\,\mathrm{C}=1\,\mathrm{A\,s}$06, with $1\,\mathrm{C}=1\,\mathrm{A\,s}$07 giving about $1\,\mathrm{C}=1\,\mathrm{A\,s}$08 and multi-charge pumping up to $1\,\mathrm{C}=1\,\mathrm{A\,s}$09 at $1\,\mathrm{C}=1\,\mathrm{A\,s}$10, corresponding to about $1\,\mathrm{C}=1\,\mathrm{A\,s}$11, albeit with measurement uncertainty at the $1\,\mathrm{C}=1\,\mathrm{A\,s}$12 level (Giblin et al., 2012, Jehl et al., 2013).

Because tunnelling is stochastic, validation architectures have also been developed. A self-referenced single-electron quantized-current source combined serial semiconductor pumps with on-chip detectors, demonstrating a reduction of total current uncertainty by more than one order of magnitude and, in one trace, determining that $1\,\mathrm{C}=1\,\mathrm{A\,s}$13 electrons had been transferred with probability $1\,\mathrm{C}=1\,\mathrm{A\,s}$14 over $1\,\mathrm{C}=1\,\mathrm{A\,s}$15, giving $1\,\mathrm{C}=1\,\mathrm{A\,s}$16 with uncertainty $1\,\mathrm{C}=1\,\mathrm{A\,s}$17 after accounting. A germanium single-hole pump extended tunable-barrier pumping to Ge/SiGe and showed quantized plateaux up to $1\,\mathrm{C}=1\,\mathrm{A\,s}$18 with $1\,\mathrm{C}=1\,\mathrm{A\,s}$19, corresponding to about $1\,\mathrm{C}=1\,\mathrm{A\,s}$20, though without a quantitative accuracy budget. A 2025 proof-of-concept using Skipper-CCDs demonstrated single-electron-resolution packet metrology, discrete current steps at $1\,\mathrm{C}=1\,\mathrm{A\,s}$21, nanoampere currents with a single sensor, and scaling analyses toward low-ppm realizations by parallelization (Fricke et al., 2013, Rossi et al., 2021, Gamero et al., 11 Feb 2025).

Despite this progress, the direct electron-counting route remains primarily a research path for the ampere’s mise en pratique. The best reported uncertainties are still generally larger than those of Ohm’s-law realizations based on Josephson and Hall standards in routine metrology (Poirier et al., 2019, Li et al., 2020).

6. Universality tests, electromagnetic constants, and emerging platforms

The internal consistency of quantum electrical metrology is commonly expressed by the quantum metrology triangle relation

$1\,\mathrm{C}=1\,\mathrm{A\,s}$22

This links the Josephson effect, the quantum Hall effect, and single-electron transport. Direct closures using metallic SET pumps reported relative uncertainties of $1\,\mathrm{C}=1\,\mathrm{A\,s}$23, $1\,\mathrm{C}=1\,\mathrm{A\,s}$24, and $1\,\mathrm{C}=1\,\mathrm{A\,s}$25; these confirmed consistency but were too imprecise for CODATA adjustments. Continued quantum metrology triangle experiments remain of fundamental interest, including searches for extremely small QED renormalization effects predicted at the $1\,\mathrm{C}=1\,\mathrm{A\,s}$26 level in very high magnetic fields (Poirier et al., 2019, Pekola et al., 2012).

Universality tests of the underlying standards are correspondingly stringent. Josephson universality across junction technologies was refined to about $1\,\mathrm{C}=1\,\mathrm{A\,s}$27 by Tsai et al. and, with similar junctions, to about $1\,\mathrm{C}=1\,\mathrm{A\,s}$28 by Jain et al. Quantum Hall universality across Si-MOSFET, GaAs/AlGaAs, InGaAs/InP, and graphene agrees to a few $1\,\mathrm{C}=1\,\mathrm{A\,s}$29, and graphene enabled a record universality test with relative uncertainty $1\,\mathrm{C}=1\,\mathrm{A\,s}$30 in the work of Ribeiro-Palau et al. Graphene quantum Hall devices have shown quantization at $1\,\mathrm{C}=1\,\mathrm{A\,s}$31 with uncertainties below $1\,\mathrm{C}=1\,\mathrm{A\,s}$32 at magnetic inductions from $1\,\mathrm{C}=1\,\mathrm{A\,s}$33 to $1\,\mathrm{C}=1\,\mathrm{A\,s}$34, temperatures up to $1\,\mathrm{C}=1\,\mathrm{A\,s}$35, and currents up to $1\,\mathrm{C}=1\,\mathrm{A\,s}$36 (Poirier et al., 2019).

A notable emerging platform is the quantum anomalous Hall effect. By directly coupling a quantum anomalous Hall resistor to a programmable Josephson voltage standard within one cryostat and zero magnetic field, a quantum current sensor realized the ampere in the range $1\,\mathrm{C}=1\,\mathrm{A\,s}$37 to $1\,\mathrm{C}=1\,\mathrm{A\,s}$38. The lowest Type A relative uncertainty was $1\,\mathrm{C}=1\,\mathrm{A\,s}$39 at $1\,\mathrm{C}=1\,\mathrm{A\,s}$40, while the lowest total root-sum-square combined relative uncertainty was $1\,\mathrm{C}=1\,\mathrm{A\,s}$41 at about $1\,\mathrm{C}=1\,\mathrm{A\,s}$42. This does not yet match cryogenic current-comparator-based realizations, but it demonstrates a zero-field route to a quantum ampere in the nanoampere regime (Rodenbach et al., 2023).

A common misconception is that the 2019 revision altered electromagnetic theory itself. The cited literature instead emphasizes that existing SI equations are unaffected; what changed is the definitional status of constants and the practical route by which electrical units are realized. The ampere is no longer defined by an idealized force experiment, but by fixed elementary charge, with voltage, resistance, and current realized coherently through quantum phenomena. This reorganization strengthens traceability, removes the conventional 1990 electrical system, and gives the ampere a direct interpretation as counted charge flow in time (Davis, 2016, Li et al., 2020).