Optimal estimation of gravitation with Kerr nonlinearity in an optomechanical system

We present a high precision scheme of a gravitational accelerometer which consists of an optomechanical system embedding a Kerr nonlinear medium. The quantum Cramér–Rao bound and the quantum Fisher information (QFI) are well-known tools to depict the ultimate precision limit in quantum parameter estimation. In our scheme, the analytical expression of time-dependent QFI is obtained with the absence of noise, which shows that the precision has been improved due to the existence of Kerr nonlinearity. At the light-matter decoupling time, the theoretical bound for the relative sensitivity is g/g≈ 6.36× 10^-13 .