Quantum estimation of Kerr nonlinearity in driven-dissipative 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.

8pages,5figures

References in corpus (11)

• High-sensitivity diamond magnetometer with nanoscale resolution
• Confining the state of light to a quantum manifold by engineered two-photon loss
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor
• Quantum sensing with arbitrary frequency resolution
• Quantum Metrology: Dynamics vs. Entanglement
• General optimality of the Heisenberg limit for quantum metrology
• Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions
• Polaritonic Feshbach Resonance
• Exact solutions of interacting dissipative systems via weak symmetries
• Achieving optimal quantum acceleration of frequency estimation using adaptive coherent control

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