Quantum force estimation in arbitrary non-Markovian Gaussian bath

TL;DR

This paper analyzes quantum force estimation in non-Markovian Gaussian baths, revealing how non-Markovian effects can enhance quantum Fisher information and affect measurement strategies in quantum metrology.

Contribution

It provides a general solution for quantum metrology in arbitrary non-Markovian Gaussian environments without specific assumptions on bath spectrum or coupling.

Findings

Quantum Fisher information can be increased by non-Markovian effects.

Measurement below bath correlation time activates non-Markovian advantages.

Quantum Fisher information can become unbounded with increasing initial energy.

Abstract

The force estimation problem in quantum metrology with an arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. Studying the short time behavior and comparing to regular Markovian dynamics we observe an increase of quantum Fisher information. We emphasize that this phenomenon is due to the ability to perform measurements below the correlation time of the bath, activating non-Markovian effects. This brings huge consequences for the sequential preparation-and- measurement scenario as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow bands.