Quantum Phase Slip Nanowires for Current Standards

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The Volt is currently defined with accuracy of one part in ten-thousand trillion using the Josephson junction. The Ohm is currently defined with accuracy of one part in ten billion using the quantum Hall effect. The weakest link in the metrological triangle of electrical S. I. units is the Ampre. This is currently defined by means of Coulomb blockade effects in a single-electron pump. The accuracy here however is worse than one part in a hundred million, i.e. more than eight orders of magnitude worse than the Josephson voltage standard. The aim of this proposal is to conduct feasibility studies on the use of quantum phase-slip (QPS) nanowires as a fundamental current standard with accuracy potentially exceeding one part in a hundred million.The quantum phase-slip (QPS) nanowire was proposed by Mooij and colleagues initially for experiments in quantum computation. It was subsequently shown that a voltage-biased QPS nanowire is the precise dual of the current-biased Josephson junction. The Josephson voltage standard is based upon measurement of Shapiro steps - i.e. steps at constant voltage in the current-voltage characteristics when the microwaves at (typically) 70 GHz are coupled to the junction. Making appropriate transformations one would expect that steps at constant current would appear in the current-voltage characteristics of a QPS nanowire when microwaves are coupled to it. If the microwave frequency is f then the steps appear at equally-spaced currents i = 2nef, where e is the electronic charge and n an integer. Hence the current-frequency relationship depends only upon the quantum number e, and measurements anywhere in this universe should therefore yield a current standard which is ultimately limited only by the accuracy of the measurement of the microwave frequency.The above discussion necessarily pre-supposes the existence of quantum phase slips in superconducting nanowires. While their existence seems plausible, as yet there has been no compelling experimental evidence for this. Most of the published experiments on superconducting nanowires to date focus on the measurement of a resistance below the bulk transition temperature of the superconductor, this resistance being larger than that predicted by the standard LAMH model of thermally-activated phase slips. The interpretation of these data has however been called into question by Rogachev et al. who showed that this enhanced resistance could also be accounted for by thermal activation simply by using a modified LAMH model. Since resistance measurements alone are open to this ambiguity of interpretation, in our experiments we will attempt to experimentally address the fundamental physics question at the heart of the QPS nanowire: Is there a sinusoidal voltage-charge relationship? (This is the dual of the first Josephson equation which states that there is a sinusoidal current-phase relationship in a Josephson junction.) We will do this by a series of experiments on QPS devices of increasing complexity, culminating at the end of the three-year programme in attempts to measure microwave-induced constant-current steps in QPS nanowires.