Ultimate Accuracy of Frequency to Power Conversion by Single-Electron Injection

We analyze theoretically the properties of the recently introduced and experimentally demonstratedconverter of frequency to power. The system is composed of a hybrid single-electron box with normalisland and superconducting lead, and the detector of the energy flow using a thermometer on a normalmetal bolometer. Here, we consider its potential for metrology. The errors in power arise mainly frominaccuracy of injecting electrons at the precise energy equal to the energy gap of the superconductor. Wecalculate the main systematic error in the form of the excess average energy of the injected electrons and itscumulants, and that due to subgap leakage. We demonstrate by analytic and numerical calculations that thesystematic error in detection can, in principle, be made much smaller than the injection errors, which also,with proper choice of system parameters, can be very small,<1%, at low enough temperature. Finally, wepropose a simplified configuration for metrological purposes.

Automated summary

This theoretical analysis of a system for converting frequency to power reveals that the main errors come from the inaccuracy of injecting electrons and subgap leakage. The study shows that systematic errors in detection can be significantly reduced compared to injection errors, and with proper system parameters, injection errors can be very small at low temperatures.