Uncertainty-principle noise in vacuum-tunneling transducers

TL;DR

This paper analyzes the fundamental quantum noise limits in vacuum-tunneling transducers used for precise position measurements, highlighting the roles of shot noise and electron-induced momentum fluctuations.

Contribution

It demonstrates how the Heisenberg uncertainty principle constrains vacuum-tunneling transducers through specific noise sources and explores configurations to reach quantum measurement limits.

Findings

Shot noise and momentum fluctuations enforce the uncertainty principle.

Analysis of various potential barrier configurations.

Practical approaches to achieve quantum-limited measurements.

Abstract

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied.