Optimal Estimation of a Classical Force with a Damped Oscillator in the non-Markovian Bath

TL;DR

This paper derives the exact quantum limit for estimating a classical force using a damped oscillator, revealing how non-Markovian bath memory effects can enhance sensitivity compared to Markovian baths.

Contribution

It provides an exact solution for the quantum limit of force estimation with a damped oscillator considering non-Markovian bath effects, highlighting the impact of bath memory.

Findings

Optimal force sensitivity approaches zero in non-Markovian baths.

In Markovian baths, sensitivity approaches a finite non-zero value at high energy.

Memory effects of the thermal bath significantly influence estimation precision.

Abstract

We solve the optimal quantum limit of probing a classical force exactly by a damped oscillator initially prepared in the factorized squeezed state. The memory effects of the thermal bath on the oscillator evolution are investigated. We show that the optimal force sensitivity obtained by the quantum estimation theory approaches to zero for the non-Markovian bath, whereas approaches to a finite non-zero value for the Markovian bath as the energy of the damped oscillator goes to infinity.