Quantum parameter-estimation of frequency and damping of a harmonic-oscillator

Abstract

We determine the quantum Cramér-Rao bound for the precision with which the oscillator frequency and damping constant of a damped quantum harmonic oscillator in an arbitrary Gaussian state can be estimated. This goes beyond standard quantum parameter estimation of a single mode Gaussian state for which typically a mode of fixed frequency is assumed. We present a scheme through which the frequency estimation can nevertheless be based on the known results for single-mode quantum parameter estimation with Gaussian states. Based on these results, we investigate the optimal measurement time. For measuring the oscillator frequency, our results unify previously known partial results and constitute an explicit solution for a general single-mode Gaussian state. Furthermore, we show that with existing carbon nanotube resonators (see J. Chaste et al.~Nature Nanotechnology 7, 301 (2012)) it should be possible to achieve a mass sensitivity of the order of an electron mass ${\text{Hz}}^{-1/2}$.

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• Time-local optimal control for parameter estimation in the Gaussian regime
• Restoring metrological quantum advantage of measurement precision in noisy scenario
• Enhanced frequency and temperature estimation by a $\mathcal{P}\mathcal{T}$-symmetric quantum oscillator
• Enhancing precision of atomic clocks by tuning disorder in accessories
• Quantum sensing of even- versus odd-body interactions
• Enhanced frequency estimation by non-Gaussianity of Fock states
• Spectral analysis of the Koopman operator as a framework for recovering Hamiltonian parameters in open quantum systems
• Impact of the Unruh effect on the estimation precision of Gaussian channel parameters
• Gaussian quantum metrology in a dissipative environment