Quantum mechanical current-to-voltage conversion with quantum Hall resistance array

Abstract

Accurate measurement of the electric current requires a stable and calculable resistor for an ideal current-to-voltage conversion. However, the temporal resistance drift of a physical resistor is unavoidable, unlike the quantum Hall resistance directly linked to the Planck constant h and the elementary charge e. Lack of an invariant high-resistance leads to a challenge in making small-current measurements below 1 μA with an uncertainty better than one part in 10 6 . In this work, we demonstrate a current-to-voltage conversion in the range from a few nano amps to one microamp with an invariant quantized Hall array resistance. The converted voltage is directly compared with the Josephson voltage reference in the framework of Ohm's law.Markedly distinct from the classical conversion, which relies on an artifact resistance reference, this current-to-voltage conversion does not demand timely resistance calibrations. It improves the precision of current measurement down to 8×10 -8 at 1 μA.Keywords: quantum Hall effect, quantum Hall resistance array, current-to-voltage conversion of the measured Hall voltage to the array resistance, we have determined a ratio for the currentto-voltage conversion. Here, we measured the converted Hall voltage through direct comparison with the programmable Josephson voltage standard. Two current values coincide with each other within the measurement uncertainty in the investigated range from 5 nA to 1 μA. This indicates that a high-value quantized Hall array resistance can be utilized for a currentto-voltage conversion, which is quantum mechanically enhanced by the quantum Hall effect, without timely resistance calibrations. It is conspicuously distinguishable from the conventional current-to-voltage conversion. Additionally, the precision of current measurement based on this current-to-voltage conversion is achieved down to 8×10 -8 at 1 μA. Moreover, the demonstrated precision, as well as the value of realized quantum Hall resistance array, is not the fundamental limit.

Perspectives of the generation and measurement of small electric currents

“…Another approach was realized by the Korea Research Institute of Standards and Science (KRISS) and the NMIJ/AIST using a quantum Hall 'array' resistance standard (QHARS) [23,59,60] of 1 MΩ and a 2 V PJVS [17]. With this setup, they succeeded in the generation of 1 µA with 0.12 µA A −1 relative uncertainty, as evaluated by ULCA.…”

“…Open squares □: ULCA at PTB [22]. Down-pointing open triangles ▽: current-to-voltage conversion with a 1 MΩ QHARS by KRISS-AIST [23]. Square with vertical cross ⊞: current comparison between LNE and PTB [24].…”

Accurate graphene quantum Hall arrays for the new International System of Units

“…Furthermore, if QHE devices with arbitrary resistance and high I C could be implemented, they could be combined with existing programmable Josephson array voltage standards to realize the quantum ampere over ranges far beyond current pumps 14 , and without as high external amplification 15 , 16 . Due to their stability, QHAs are also desired for precision measurements of current in general 17 . Moreover, QHA devices with different resistances are also useful for practical resistance metrology and will reduce uncertainties in calibrations of a wide range of resistance values since they allow for direct comparison measurement between primary quantum standards and secondary standards, shortening the calibration chain.…”

Improvements of the programmable quantum current generator for better traceability of electrical current measurements

“…For currents above 1 nA, more recently different groups also proposed developments based on Ohm's law involving quantum electrical standards, either to improve current measurement uncertainty in the µA range below 10 −7 by current-to-voltage conversion with a quantum Hall resistance array [9] or to improve the stability of an externally referenced current source down to 1 nA/A at 50 mA with a PJVS [10]. On the other hand, National Metrology Institutes apply Ohm's law to secondary voltage and resistance standards, traceable to the Josephson and quantum Hall effects, respectively.…”