What is the Fastest Speed at which a Single Electron Can Be Detected?

TL;DR

This paper investigates the fundamental speed limit for detecting a single electron using electrometers, relating it to fundamental constants and the Rydberg frequency, independent of specific technology.

Contribution

It derives a fundamental speed limit for single-electron detection based on physical constants, linking it to the Rydberg frequency and semiconductor properties.

Findings

Speed limit related to Rydberg frequency.

Limit expressed in terms of fundamental constants.

Uncertainty whether Rydberg frequency is the absolute maximum.

Abstract

Electrometers measure electric charge, but there must be a fundamental speed limit to measuring one electric charge. Since there are no dimensional inputs to this question, the answer must be expressible in terms of the fundamental physical constants of Nature, e,h,m,c. In general the question should be posed without reference to any specific technology, but for definiteness, we analyze the field effect transistor, which is essentially an electrometer. In spite of selecting a specific technology, we find that the speed limit is related to a fundamental constant, the Rydberg frequency, or as appropriate, the semiconductor Rydberg frequency including the electron effective mass, and the relative dielectric constant. We do not know whether the Rydberg frequency represents the upper speed limit, but on dimensional grounds we claim that the final limit can only differ by some power of the fine-structure-constant.