Quantum force estimation in arbitrary non-Markovian Gaussian bath

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.

6 pages of main text and 12 pages of Appendix

References in corpus (5)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Ultrasensitive force and displacement detection using trapped ions
• The ultimate precision limits for noisy frequency estimation
• Quantum Metrological Limits via a Variational Approach
• Optimal Estimation of a Classical Force with a Damped Oscillator in the non-Markovian Bath

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