Quantum limit for measurement of a weak classical force coupled to a noisy quantum-mechanical oscillator

TL;DR

This paper establishes the fundamental quantum limit for measuring weak classical forces on noisy quantum oscillators, providing optimal initial states and measurement strategies to guide ultra-sensitive force detection experiments.

Contribution

It derives the quantum limit for force estimation on noisy oscillators and identifies optimal states and measurements for achieving this limit.

Findings

Derived the quantum limit for force measurement accuracy.

Identified optimal initial states for the oscillator.

Provided measurement strategies to reach the quantum limit.

Abstract

Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the unavoidable influence of noise. Here we obtain a quantum limit for the uncertainty in the estimation of a resonant classical force acting on a noisy quantum-mechanical oscillator. We determine the best initial state of the oscillator and the best measurement procedure, thus getting a rigorous and useful benchmark for experiments aiming to detect extremely small forces.