Powering an autonomous clock with quantum electromechanics

TL;DR

This paper presents a theoretical analysis of an autonomous nanoelectromechanical clock driven by electron tunnelling, revealing complex statistical properties and correlations that influence its accuracy and precision over time.

Contribution

It introduces a theoretical model of a nanoscale autonomous clock with self-oscillations, analyzing its tick statistics and temporal correlations to understand its accuracy and thermodynamics.

Findings

Tick distribution shows a tradeoff between accuracy, resolution, and dissipation.

Non-monotonic Allan variance indicates temporal correlations affect clock precision.

Correlations between ticks can enhance timekeeping precision over certain timescales.

Abstract

We theoretically analyse an autonomous clock comprising a nanoelectromechanical system, which undergoes self-oscillations driven by electron tunnelling. The periodic mechanical motion behaves as the clockwork, similar to the swinging of a pendulum, while induced oscillations in the electrical current can be used to read out the ticks. We simulate the dynamics of the system in the quasi-adiabatic limit of slow mechanical motion, allowing us to infer statistical properties of the clock's ticks from the current auto-correlation function. The distribution of individual ticks exhibits a tradeoff between accuracy, resolution, and dissipation, as expected from previous literature. Going beyond the distribution of individual ticks, we investigate how clock accuracy varies over different integration times by computing the Allan variance. We observe non-monotonic features in the Allan variance as a function of time and applied voltage, which can be explained by the presence of temporal correlations between ticks. These correlations are shown to yield a precision advantage for timekeeping over the timescales that the correlations persist. Our results illustrate the non-trivial features of the tick series produced by nanoscale clocks, and pave the way for experimental investigation of clock thermodynamics using nanoelectromechanical systems.