Ultimate accuracy of frequency to power conversion by single-electron injection

TL;DR

This paper provides a theoretical analysis of a frequency-to-power converter based on single-electron injection, assessing its potential for precise metrological applications and identifying key sources of systematic error.

Contribution

It introduces a detailed theoretical framework for analyzing errors in a frequency-to-power converter, highlighting how to minimize systematic errors for metrological accuracy.

Findings

Systematic errors can be reduced below 1% with proper system parameters.

Injection energy accuracy is critical for minimizing power conversion errors.

A simplified configuration suitable for metrology is proposed.

Abstract

We analyze theoretically the properties of the recently introduced and experimentally demonstrated converter of frequency to power. The system is composed of a hybrid single-electron box with normal island and superconducting lead, and the detector of the energy flow using a thermometer on a normal metal bolometer. Here we consider its potential for metrology. The errors in power arise mainly from inaccuracy of injecting electrons at the precise energy equal to the energy gap of the superconductor. We calculate the main systematic error in form of the excess average energy of the injected electrons and its cumulants, and due to sub-gap leakage. We demonstrate by analytic and numerical calculations that the systematic 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 we propose a simplified configuration for metrological purposes.