Duality relations in a two-path interferometer with an asymmetric beam splitter

摘要

We investigate quantitatively the wave-particle duality in a generalMach-Zehnder interferometer setup with an asymmetric beam splitter. Theasymmetric beam splitter introduces additional a priori which-path knowledge,which is different for a particle detected at one output port of theinterferometer and a particle detected at the other. Accordingly, the fringevisibilities of the interference patterns emerging at the two output ports arealso different. Hence, in sharp contrast with the symmetric case, here weshould concentrate on one output port and distinguish two possible paths takenby the particles detected at that port among four paths. It turns out that twononorthogonal unsharp observables are measured jointly in this setup. We applythe condition for joint measurability of these unsharp observables to obtain atrade-off relation between the fringe visibility of the interference patternand the which-path distinguishability.