Optimal phase estimation with photon-number difference measurement using twin-Fock states of light

J H Xu(徐佳慧)^{1}, J Z Wang(王建中)^{1}, A X Chen(陈爱喜)^{1}, Y Li(李勇)^{2}, G R Jin(金光日)^{1}

1 Key Laboratory of Optical Field Manipulation of Zhejiang Province and Physics Department of Zhejiang Sci-Tech University, Hangzhou 310018, China; 2 Beijing Computational Science Research Center, Beijing 100193, China

Abstract Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach-Zehnder interferometer (i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér-Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference (i.e., the Ĵ_{z} measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the Ĵ_{z} measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91636108, 11775190, and 11774024), Science Foundation of Zhejiang Sci-Tech University, China (Grant No. 18062145-Y), Open Foundation of Key Laboratory of Optical Field Manipulation of Zhejiang Province, China (Grant No. ZJOFM-2019-002), and Science Challenge Project, China (Grant No. TZ2018003).

Corresponding Authors:
G R Jin
E-mail: grjin@zstu.edu.cn

Cite this article:

J H Xu(徐佳慧), J Z Wang(王建中), A X Chen(陈爱喜), Y Li(李勇), G R Jin(金光日) Optimal phase estimation with photon-number difference measurement using twin-Fock states of light 2019 Chin. Phys. B 28 120303

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