Quantum Estimation of Kerr Nonlinearity in Driven-Dissipative Systems

We mainly investigate the quantum measurement of Kerr nonlinearity in driven-dissipative system. Without dissipation, precision parameter $\chi$ scales as "super-Heisenberg scaling" $1/N^2$ with $N$ being total average number particles (photons) due to nonlinear generator. Here, we find that $1/N^{3/2}$ can also be obtained by choosing a proper interrogation time. In steady state, only achieved when is close 0 case single-photon loss and one-photon driving or two-photon driving. The disappears increase strength nonlinearity. When system suffers from addition loss, optimal will not appear at $\chi=0$ Counterintuitively, it higher lower precision. It means improved some extent increasing loss.