Time uncertainty and fundamental sensitivity limits in quantum sensing: application to optomechanical gravimetry

TL;DR

This paper investigates how intrinsic quantum time uncertainty affects the sensitivity limits of quantum sensors, especially optomechanical gravimeters, revealing fundamental coupling effects and proposing optimal measurement conditions.

Contribution

It derives a two-parameter quantum Fisher information framework incorporating time as a nuisance parameter, revealing fundamental sensitivity limits and optimal decoupling strategies.

Findings

Time uncertainty degrades measurement sensitivity in quantum sensors.

Optimal decoupling conditions can mitigate effects of time uncertainty.

The framework applies broadly to various quantum sensing platforms.

Abstract

High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.