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

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 mu A 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 x 10(-8) at 1 mu A.