Quantum estimation of coupling strengths in driven-dissipative optomechanics
Kamila Sala, Tabitha Doicin, A. D. Armour, Tommaso Tufarelli
Abstract
We exploit local quantum estimation theory to investigate the measurement of linear $({g}_{1})$ and quadratic $({g}_{2})$ coupling strengths in a driven-dissipative optomechanical system in the red-sideband regime. We consider model parameters inspired by recent experiments, in the regime ${g}_{2}<{g}_{1}$. We find that (i) ${g}_{1}$ is easier to estimate than ${g}_{2}$ at lower driving strengths, while (ii) strong enough driving allows the two parameters to be estimated with similar relative precision. Our analysis also reveals that the majority of information about ${g}_{1}$ and ${g}_{2}$ is encoded in the reduced state of the mechanical element, and that the best estimation strategy for both coupling parameters is well approximated by a direct measurement of the mechanical position quadrature. Interestingly, we also show that temperature does not always have a detrimental effect on the estimation precision.