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Physical Review A

Neutrons and photons inside a nested Mach-Zehnder interferometer

Lev Vaidman A

Published May 26, 2020• 10 citations
Publisher

Abstract

Recent experiments with identically tuned nested Mach-Zehnder interferometers which attempted to observe the location of particles inside these interferometers are analyzed. In spite of claims to the contrary, it is argued that all experiments support the same surprising picture according to which the location of the particles inside the interferometers is not described by continuous trajectories.

DOI
10.1103/physreva.101.052119

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Response to the comment on “Paradox of photons disconnected trajectories being located by means of ‘weak measurements’ in the nested Mach–Zehnder interferometer” (JETP Letters 105, 152 (2017))

G. N. Nikolaev

The author of the comment on my work [1] states that the proposed modification of the scheme of the experiment reported in [2] is improper and that the experiment faithfully demonstrates a discontinuous trace of photons.It is difficult to agree with this statement because of the absence of clear and well-founded (see below).In [1], I discussed the recent experiment [2] with a nested Mach-Zehnder interferometer.The authors treated the experiment so that the past of photons is not described by continuous trajectories because photons are detected inside the inner Mach-Zehnder interferometer and are not detected outside it.The idea of a small modification of the scheme of the experiment [2] has been proposed just to detect photons at the input of the inner Mach-Zehnder interferometer.Instead of the vibration of the mirror, the direction of polarization of light is modulated in this scheme.Further, in one of the arms of the inner Mach-Zehnder interferometer, this modulation is converted into a shift of the light beam of orthogonal polarization, which is then transformed to the original polarization.The realization of the idea is as follows.A birefringent plate, a phase compensator, and two polarizers that oriented at the angle of 45° and in parallel to the initial polarization are placed in one of the arms of the inner Mach-Zehnder interferometer.The same polarizers are placed in the other two arms of the nested Mach-Zehnder interferometer.The author of the comment states that such a modification is improper because it "violates the faithfulness of the experiment because it causes different transformations of the polarization record at E into a signal at the detector, depending on the path the beam takes."The author of the comment also claims that "the signal at the detector does not present a faithful indication of the trace inside the interferometer" in the absence of con-

arXiv:1705.08721•Journal of Experimental and Theoretical Physics Letters•Apr 1, 2017•7 citations
Recent experiments with identically tuned nested Mach-Zehnder interferometers which attempted to observe the location of particles inside these interferometers are analyzed. In spite of claims to the contrary, it is argued that all experiments support the same surprising picture according to which the location of the particles inside the interferometers is not described by continuous trajectories.
In a paper titled ``Asking photons where they have been? Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors and by a discontinuous path. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The picture of interfering multiple trajectories provide a satisfactory explanation of the experimental findings and the absence of footprints.
Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87 , 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111 , 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111 , 240402 (2013)] is unnecessary.
In a paper titled "Asking photons where they have been?" \cite{LV} Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors. They argue that the experiment supports Aharonov-Vaidman's formulation of quantum mechanics \cite{AharonovVaidman} where post-selected particles are assigned disconnected trajectories. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The standard view of interfering trajectories accounts for the experimental findings.
The author of the comment on my work [1] states that the proposed modification of the scheme of the experiment reported in [2] is improper and that the experiment faithfully demonstrates a discontinuous trace of photons.It is difficult to agree with this statement because of the absence of clear and well-founded (see below).In [1], I discussed the recent experiment [2] with a nested Mach-Zehnder interferometer.The authors treated the experiment so that the past of photons is not described by continuous trajectories because photons are detected inside the inner Mach-Zehnder interferometer and are not detected outside it.The idea of a small modification of the scheme of the experiment [2] has been proposed just to detect photons at the input of the inner Mach-Zehnder interferometer.Instead of the vibration of the mirror, the direction of polarization of light is modulated in this scheme.Further, in one of the arms of the inner Mach-Zehnder interferometer, this modulation is converted into a shift of the light beam of orthogonal polarization, which is then transformed to the original polarization.The realization of the idea is as follows.A birefringent plate, a phase compensator, and two polarizers that oriented at the angle of 45° and in parallel to the initial polarization are placed in one of the arms of the inner Mach-Zehnder interferometer.The same polarizers are placed in the other two arms of the nested Mach-Zehnder interferometer.The author of the comment states that such a modification is improper because it "violates the faithfulness of the experiment because it causes different transformations of the polarization record at E into a signal at the detector, depending on the path the beam takes."The author of the comment also claims that "the signal at the detector does not present a faithful indication of the trace inside the interferometer" in the absence of con-