Simultaneous determination of two path weak-values with time-dependent phase manipulation in neutron interferometry

Abstract Weak values are found to play an important role in the study of many fundamental concepts of quantum mechanics. We present a method to simultaneously extract the imaginary part of the weak value of both path operators in a two-path Mach–Zehnder neutron interferometer using time-dependent phases. The measurement does not require spin manipulation, e.g. spin rotation and analysis. The methodology can be extended to an arbitrary number of paths and the working principles are transferable to any other kind of interferometer experiment in which alike time-dependent phases are feasible. Furthermore, we demonstrate a relation among components of path weak values relative to different post-selected states. This relation allows the additional extraction of the real part of both path weak values using the same setup, assuming the relative phase between the states after the different post-selections to be known.