Optimal estimation of optomechanical couplings

Abstract

We apply the formalism of quantum estimation theory to obtain information about the value of the optomechanical coupling in the simplest model of two harmonic oscillators. In particular, we discuss the minimum mean-square error estimator and a quantum Cram er-Rao inequality for the estimation and accuracy of the coupling's value. Our estimation strategy reveals some cases, where quantum statistical inference is inconclusive and only prior expectations on the coupling strength are reassured. We show that this situations involve also the highest expected information losses. It is demonstrated that interaction times in the order of one time period of mechanical oscillations are the most suitable for this type of estimation scenario. We also compare situations involving di erent initial photon and phonon excitations.