Super-sensitive phase estimation with coherent boosted light using parity measurements**Project supported by the National Natural Science Foundation of China (Grant No. 11665010), the Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, China (Grant No. QSQC1414), and the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 17B055).

Abstract

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.