Can a Dove prism change the past of a single photon?

Abstract

We reexamine the thought experiment and real experiment of Vaidman et al., by placing Dove prisms in the nested Mach-Zehnder interferometer arms. In those previous works, the criterion of whether a single photon was present, or not, was the presence of a "weak trace", indicating the presence of a nonzero weak value. This was verified by slightly varying the mirror angle at a given frequency, which was then detected on a position sensitive detector at the oscillation frequency. We show the presence of the Dove prisms gives identical weak values everywhere to the previous configuration because the prisms change neither the path difference, nor the mode profile in the aligned case. Nevertheless, the same slight variations of the interferometer mirrors now give a signal at the first mirror of the nested interferometer. We can interpret this result as a misaligned optical interferometer, whose detailed response depends on the stability of the elements, or as the detector coupling to a nonzero effective weak value.