A Quick Orientation

The electric current quantity in the ampere is extracted from the amount of charge in coulombs flowing past a given point in one second.

Since May 20, 2019, it's defined by the fixing of the numerical value of the elementary charge:

e = 1.602176634 × 10⁻⊃1;⁹ C

It is a measure of charge flow.

This redefinition fixes the ampere at an invariant constant of nature and paves the way for quantum-accurate current standards.

Why the Definition Changed

The old ampere definition relied on an imaginary force between infinite wires nice on paper, clumsy in a lab.

Modern atomic and quantum metrology relies on definitions:

  • Connected with fundamental constants

  • Realizable with simple, stable devices

Fixing e does just that:

If you can count electrons  or map current to other constants through quantum effects, then you can have the ampere any time, any place.

Two Quantum Journeys to the Ampere

  1. The Detour Method: Current from Quantum Voltage & Resistance

Two quantum effects make for rock-solid electrical standards:

Josephson Effect
A Josephson junction (JJ) establishes a precise link between voltage and frequency.

V = n f / K_J, K_J = 2 e / h

Use a microwave frequency f to precisely measure voltage.

Quantum Hall Effect
When subjected to a strong magnetic field, resistance becomes fixed at distinct plateau levels.

R = R_K / i, R_K = h / e⊃2;

Plug them together with Ohm’s law:

I = V / R

A current standard referenced to quantum effects, directly traceable to e and h.

Accurate currents at microamp–milliamp level already available. Basis of most calibration laboratories.

  1. The Direct Path: Single-Electron Pumps (“Electron Turnstiles”)

A single-electron pump transfers one electron per cycle.

Driven at frequency f:

I = e f

Current via counting electrons — no intermediates.

Modern pumps:

  • Provide pA to nA currents

  • Operate at cryogenic temperatures

  • Types: GaAs tunable-barrier pumps, silicon MOS pumps, graphene pumps

Main Error Sources:

  • Random electron tunneling

  • Hot electrons (thermal activation)

  • Non-adiabatic transitions (device too fast)

Countermeasures:

  • Optimized gate waveforms

  • Better device geometries

  • Reduced operating temperatures

  • On-chip charge sensing

  • Good EMI shielding

The Quantum Metrological Triangle (QMT)

The QMT closes the loop between three standards:

  • Josephson voltage: V(f)

  • Quantum Hall resistance: R(i)

  • Single-electron current: I = e f

Goal: Verify that

V / R = e f

  • Provides deep consistency check of electrical metrology, linking e and h

  • Over the last decade, uncertainties have been significantly reduced

How National Labs Measure Minuscule Currents

Creating picoamp currents and measuring them with part-in-10⁷ accuracy is difficult.

Typical setup:

  • Cryogenic single-electron pump (<1>

  • Cryogenic current comparator (CCC)

  • Josephson voltage arrays + Quantum Hall resistors

  • Heavy shielding to reduce noise

  • On-chip detectors to spot rare pumping errors

Precision:

  • < 10>

  • < 10>

State of the Art:

  • Best quantum accuracy in pA–nA region

  • Indirect standards (Josephson + QHE) less restrictive, but require cryogenics

What’s Next

More current without loss of accuracy:

  • Parallel pump arrays scaling from nA → μA

  • Requires phase-locked drives and error detection

Integrated, user-friendly packages:

  • Cryogen-free refrigerators + compact microwave electronics

  • Automatic calibration for industrial labs

Better error accounting:

  • On-chip sensors allow error-counted mode

  • Every mis-pump flagged → improved user confidence

Broader calibration use:

  • DC standards for picoammeter ranges, low-current electrometers

  • Quantum tech biasing, semiconductor leakage measurements, material science

Why This Matters Beyond Metrology

  • Universality: Based on constants of nature

  • Stable: No drift or aging issues

  • Traceability: Direct link to e and h

  • Innovation enabler: Enables ultra-low-noise currents for:

    • Nanotech

    • Cryo-CMOS

    • Quantum computing

    • Ultra-sensitive detectors

    • Precision biophysics

Practical Takeaways

  • Need micro- to milliamp with traceability? → Use Josephson + QHE with I = V/R

  • Need picoamp–nanoamp with cleanest link to e? → Use single-electron pumps + error detection/CCC

  • For systematic consistency → Cross-reference all three via the QMT

A Brief Glossary

  • Elementary charge (e): Charge of an electron (defined constant)

  • Planck constant (h): Relates frequency to energy

  • Josephson effect: Voltage-frequency relation in superconducting junction

  • Quantum Hall effect: Produces quantized resistance values in a two-dimensional electron gas

  • Single-electron pump: Device pushing one electron per cycle

  • CCC (Cryogenic Current Comparator): Sensitive superconducting current bridge

 

By defining the ampere in terms of e, and realizing it with Josephson junctions, quantum Hall devices, and single-electron pumps, current measurement is entering an era where counting electrons isn’t just a metaphor—it is the measurement.