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))

TL;DR

This paper defends the classical wave theory explanation for the paradoxical results in a photon trajectory experiment, arguing that the proposed modifications resolve perceived discontinuities and that criticisms against this approach are unfounded.

Contribution

It clarifies that the paradoxical results are due to detection methods, not actual discontinuous photon trajectories, and defends the original classical wave explanation against recent criticisms.

Findings

The experiment's paradoxical results are explained by detection methods.

Proposed modifications eliminate the perceived discontinuity.

Criticisms against the classical wave explanation are unfounded.

Abstract

In [JETP Lett. 105(3), 152 (2017)], a clear and comprehensive analysis of the paradoxical results of experiment [Phys. Rev. Lett. 111, 240402 (2013)] was carried out on the basis of the classical wave theory of light, which presupposes the continuity of possible of light paths. It was shown that the paradoxical results of the experiment are due not to the discontinuity of the trajectories of light, as claimed in [Phys. Rev. Lett. 111, 240402 (2013)], but to the used way of detecting the path of photons. The experiment modification proposed in [JETP Lett. 105(3), 152 (2017)] allows us to eliminate the seeming discontinuity of the light trajectories. In Comment [arXiv:1705.02137 (2017)] to the article such modification is declared unreasonable. This Response to the Comment shows that this statement is not based on clear and logical arguments. Instead, it is only asserted that the proposed modification "violates the faithfulness indication of the trace" of photons. Therefore, the Comment's criticism can not be considered as well-founded. Consequently, the conclusion of [JETP Lett. 105(3), 152 (2017)] that a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111, 240402 (2013)] is unnecessary, remains valid.

Full text

The author of the comment arXiv:quant-ph/1705.02137 on my work JETP.Lett.105.475 states that the proposed modification of the scheme of the experiment reported in Phys.Rev.Lett.111.240402 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 reasons (see below).

In JETP.Lett.105.475 , I discussed the recent experiment Phys.Rev.Lett.111.240402 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 Phys.Rev.Lett.111.240402 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 $\mathrm{45^{o}}$ and in parallel to the initial polarization are placed in one of the arms of the inner Mach-Zehnder interferometer. The exact 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 since 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 conditions that “the shift of the direction in the region of the local coupling is translated to the shift of the output beam in the same way for all possible paths of the beam toward the detector”. It is not explained what is the “faithfulness” of the experiment and indication and how it is logically related to the cited conditions. The necessity of these conditions was not justified either in Phys.Rev.Lett.111.240402 or in subsequent works of these authors Phys.Rev.A87.052104 ; Phys.Rev.A89.024102 ; fphy.2015.00048 ; Phys.Rev.A93.17801 ; Phys.Rev.A93.036103 ; arXiv:quant-ph/1610.04781 ; arXiv:quant-ph/1610.07734 ; Chin.Phys.Lett.34.020301 .

The authors’ treatment of the two-state vector formalism is attractively simple but is not justified and, thereby, can provide false conclusions and is limited. This concerns the interpretation of the results of the experiment as the manifestation of the “discontinuous trace” of photons by the authors of Phys.Rev.Lett.111.240402 . This same treatment does not explain the absence of any signals when the beam of light in the lower arm of the outer Mach-Zehnder interferometer is blocked. At the same time, this absence is clearly explained by the traditional theories of light and quantum mechanics. Therefore, it is unnecessary to introduce a new concept of discontinuity of possible paths of photons.