Ultimate quantum bounds on mass measurements with a nano-mechanical oscillator

TL;DR

This paper derives the fundamental quantum limit for mass measurement sensitivity using nano-mechanical oscillators, identifying optimal quantum states to maximize detection precision within quantum mechanical constraints.

Contribution

It establishes the ultimate quantum bounds on mass measurement precision with nano-mechanical resonators and identifies quantum states that optimize sensitivity.

Findings

Quantum Cramér-Rao bound sets the lower limit for mass measurement accuracy.

Optimal quantum states for maximum sensitivity are characterized.

Fundamental limits are determined by quantum mechanics, independent of technical noise.

Abstract

Nano-mechanical resonators have a large potential as sensors of very small adsorbed masses, down to the atomic level and beyond. Here I establish the fundamental lower bound on the mass that can be measured with a nano-mechanical oscillator in a given quantum state based on the quantum Cram\'er--Rao bound, limited only by the laws of quantum mechanics, and identify the quantum states which will allow the largest sensitivity for a given maximum energy.