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

Abstract

We investigate quantitatively the wave-particle duality in a general Mach-Zehnder interferometer setup with an asymmetric beam splitter. The asymmetric beam splitter introduces additional a priori which-path knowledge, and the additional knowledge is different for particles detected at one or the other output port. Accordingly, the interference patterns appearing at the two output ports are also different. Hence, in sharp contrast with the symmetric case, in the present case we should treat the two output ports separately. It turns out that two nonorthogonal unsharp observables are measured jointly in this setup. We apply the condition for joint measurability of these unsharp observables to obtain a trade-off relation between the fringe visibility of the interference pattern and the which-path distinguishability. © 2012 American Physical Society.