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Quantum Estimation of Kerr Nonlinearity in Driven-Dissipative Systems

Dong Xie,Chunling Xu,A. Wang

Published 2022 in Social Science Research Network

ABSTRACT

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

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