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

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).
Xu J H1, Wang J Z1, Chen A X1, Li Y2, Jin G R1, †
       

The CFI for the J^z measurement (thick solid line), the single-fringe detection (thin solid line), and the multi-fringe detection (red dashed line), obtained respectively, from Eqs. (2), (5), and (7), with {pμ(im)(θ)} . The dashed horizontal lines are the classical limit of the QFI FQ = N and the ideal result of the QFI with the twin-Fock input state FQ = N(N + 2)/2 for N = 6. The shaded area is a region where the CFI of the J^z measurement outperforms that of the single-fringe detection.