Quantum estimation of coupling strengths in driven-dissipative optomechanics

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.