Quantum estimation of Kerr nonlinearity in driven-dissipative systems

TL;DR

This paper investigates quantum measurement precision of Kerr nonlinearity in driven-dissipative systems, revealing conditions for super-Heisenberg scaling and effects of different loss mechanisms on measurement accuracy.

Contribution

It demonstrates how to achieve super-Heisenberg scaling in measurement precision and explores the impact of various dissipation and driving conditions on this scaling.

Findings

Super-Heisenberg scaling of 1/N^{3/2} can be achieved with proper interrogation time.

Optimal measurement precision occurs near zero nonlinearity under certain conditions.

Two-photon loss can improve measurement precision in two-photon driven systems.

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.