# Steady-State Force Sensing with Single Trapped Ion

## TL;DR

This paper introduces a steady-state quantum sensing scheme using a single trapped ion to detect weak, time-varying forces with high sensitivity, leveraging critical spin-boson coupling and phonon squeezing.

## Contribution

It presents a novel steady-state force sensing method with a single trapped ion, utilizing critical coupling and phonon squeezing to enhance sensitivity beyond previous approaches.

## Key findings

- Force sensitivity diverges near critical coupling
- Quadrature measurement saturates the Cramer-Rao bound
- Phonon squeezing improves minimal detectable force to xN level

## Abstract

We propose a scheme for detecting time-varying weak forces using quantum probe consisting of single spin and quantum oscillator under the effect of collective dissipation. We study the force estimation in the steady-state regime where the information of the force is extracted by measuring observable of the oscillator such as quadrature and mean phonon excitation. We quantify the force sensitivity in terms of quantum Fisher information and show that it diverges approaching the critical spin-boson coupling making the system sensitive to very small force perturbation. We show that close to the critical coupling the measurement of the oscillator quadrature is optimal in a sense that saturates the fundamental Cramer-Rao bound. Furthermore, we study the force estimation in the presence of phonon squeezing and show that it can significantly improve the sensitivity reaching minimal detectable force of order of xN (1${\rm xN=10^{-27}{\rm N}}$).