Quantum estimation of Kerr nonlinearity in driven-dissipative systems

• URL: http://arxiv.org/abs/2204.05577v1
• Date: Tue, 12 Apr 2022 07:16:49 GMT
• Title: Quantum estimation of Kerr nonlinearity in driven-dissipative systems
• Authors: Dong Xie, Chunling Xu, An Min Wang
• Abstract summary: We investigate the quantum measurement of Kerr nonlinearity in a driven-dissipative system. In the steady state, the "super-Heisenberg scaling" $1/N3/2$ can only be achieved when the nonlinearity parameter is close to 0.
• Score: 1.430924337853801
• License: http://creativecommons.org/licenses/by/4.0/
• 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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