### Wide range quantum-accurate current source

e-SI-Amp partner Laboratoire national de métrologie et d’essais (LNE) have been developing a wide range, quantum-accurate current generator which uses a combination of Josephson and Quantum Hall devices.

Unlike single-electron based hardware developed within the e-SI-Amp project, which only operates at very low currents, the Programmable Quantum Current Generator (PQCG) has an operating range from a few mA down to 1 µA. Such a quantum-accurate current source is possible with due to the use of quantum voltage standards and quantum resistance standards in combination with a highly accurate cryogenic current amplifier. This technology can be used to perform calibrations of electrical equipment for end-users, for instance of the ammeter input range of popular metrology-grade instruments like the HP3458 or the Fluke 8508A.

### Measurement system performance

The measurement system (see picture) is composed of three main elements, the quantum Hall resistance, the Josephson voltage source and the cryogenic amplifier. In this implementation, each is placed in a separate cryostat.

A particular feature of this system is that it overcomes the problem of the leads resistance between the two quantum standards by using a topological property of the quantum Hall effect. It also resolves the usual problem of gain stability of the amplifiers by using a special type of dc transformer known as a cryogenic current comparator, made of superconducting windings surrounded by a superconducting shield.

The expected calibration performance is summarised below

Range | Relative Uncertainty |
---|---|

1 µA - 10 mA | 10^{-8} |

100 nA | 10^{-7} |

10 nA | 10^{-6} |

### Relationship with electron pumping and the metrology triangle

One remarkable aspect of the proposed SI redefinition, upon which the PQCG relies, is that numerically fixing the value of the elementary charge is actually compatible with TWO different methods of realisation of the ampere. One is via electron pumping (‘clocking’ electrons one at a time through a circuit), the other is to use the Josephson and Quantum Hall effects in combination, as in the PQCG. To understand how this is possible requires some understanding of the circuit elements pictured above.

- The AC Josephson effect involves two weakly coupled superconductors being exposed to applied microwave field, giving a quantised DC
*voltage*. - The Quantum Hall effect arises when electrons are confined to one-dimensional edge channels by a large magnetic field, creating a quantised Hall
*resistance*.

Something expected theoretically, and observed with increasing accuracy over many years, is that the voltages from with the AC Josephson effect, and measured quantum Hall resistances depend *solely upon the values of the Planck constant h and the elementary charge e. *

The effective electrical current (via Ohm’s law) created by a known ratio of these quantities is expected to be EXACTLY the same as an electron pump realisation, giving TWO routes to a quantum current standard. Which one chosen is then a matter of convenience (with an electron pump realisation being more suited to smaller current levels).

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