Complementarity Relation In Asymmetric Mach-zehnder Interferometer

The microscopic particle has wave-particle duality,and a experiment could show the particle-like property or wave-like property of microscopic particle,how-ever,both of them can’t appear at the same time.The quantification of wave-particle duality is mainly based on symmetric Mach-Zehnder interferometer(both beam splitters are symmetric).The article studys the wave-particle duality in asymmetric Mach-Zehnder interferometer(the first beam splitter is symmetric,the second beam splitter is asymmetric).For judging the particle’s path,the path detector is put in one of the paths.We use fringe visibility to quantify wave-like property.The people have used the distinguishability,the which-path information and the correlation to quantify particle-like property in asymmetric Mach-Zehnder interferometer and we distinguish two quantum states of detector through unam-biguous discrimination and use the maximum success probability of unambiguous discrimination to quantify particle-like property.The specific study is:1,We study fringe visibility V in asymmetric Mach-Zehnder interferometer and find the initial states of particle(ρ=1/2(Sxσx+Syσy+Szσz))and detector,the second asymmetric beam splitter(the reflection coefficient and transmission coefficient of the second beam splitter are expressed as sin2β/2 and cos2β/2)and unitary operator U which perform on detector influence fringe visibility.We find the condition of fringe visibility getting maximum value is the particle’s initial state is pure state and Sx=cosβ.2,After the particle interacting with the detector,the final state of the detec-tor can be expressed as ρfD=ωbρinD+ωaρoutD among ρinD=|r><r|,ρoutD=U|r><r|U+=|s><s| and(r|s)=C.When the amount relationship of(?)and C changes,we get different maximum success probability and different complementarity re-lation:when(?)or(?)the complementarity relation is 2Dopt/(1+P)+V2/V02≤1,when(?),the complementarity relation is Dopt+V≤1.