Estimation of an Optomechanical Parameter via Weak Value Amplification

In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection, because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise the weak value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.