A unified realization of electrical quantities from the quantum International System of Units

Abstract

In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm's law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here we report a unified realization of the volt, ohm, and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 $\mu$V/V. The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 $\mu \Omega$/$\Omega$. We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33 nA to 252 nA, and our lowest uncertainty is 4.3 $\mu$A/A at 83.9 nA. For other current values, a systematic error that ranges from -10 $\mu$A/A to -30 $\mu$A/A is present due to the imperfect isolation of the PJVS microwave bias.

16 pages, 4 figures, 15 pages of supplemental information

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