Fringe visibility and distinguishability in two-path interferometer with an asymmetric beam splitter

摘要

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 =(Sx,Sy,Sz) 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 cosβ =-Sx.The fringe visibility obtain the maximum only if Sx =0 andβ =π/2 when the input particle is initially in a mixed state.The complementary relationship V2 + D2 ≤ 1 is proved in a general Mach-Zehnder interferometer with an asymmetric beam splitter,and the conditions for the equality are also presented.