Abstract

Nonlinear phase measurement plays an important role in many dynamic processes. In this paper, we propose a single-mode measurement scheme for second-order nonlinear phase shifts that utilizes coherent states and homodyne measurement. The sensitivity at operating point $\varphi = 0$ is $1/4{N^{3/2}}$ with $N$ photons on average and approaches the quantum Cramér–Rao bound. In addition, sensitivity with a small value of $\varphi$ is discussed. For practical purposes, we analyze the effects of photon losses, thermal photon noise, and phase diffusion on sensitivities with $\varphi = 0$ as well as a small value of $\varphi$. The sensitivity still scales as $1/{N^{3/2}}$ in the presence of photon losses and thermal photon noise but degrades to the scaling of $1/N$ with phase diffusion.

© 2021 Optical Society of America

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