Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter
Yanjun Liu, Jing Lu, Zhihui Peng, Lan Zhou, Dongning Zheng · Chinese Physics B · 2019
We study the fringe visibility and the distinguishability of a general Mach–Zehnder interferometer with an asymmetric beam splitter. Both the fringe visibility V and the distinguishability D are affected by the input state of the particle characterized by the Bloch vector S = ( S x , S y , S z ) and the second asymmetric beam splitter characterized by the paramter β . For the total system is initially in a pure state, it is found that the fringe visibility reaches the upper bound and the distinguishability reaches the lower bound when cos β = − S x . The fringe visibility obtain the maximum only if S x = 0 and β = π /2 when the input particle is initially in a mixed state. The complementary relationship V 2 + D 2 ≤ 1 is proved in a general Mach–Zehnder interferometer with an asymmetric beam splitter, and the conditions for the equality are also presented.