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Erasing the past of photons

Jinxian Guo, Qi-Zhang Yuan, Yuan Wu, Weiping Zhang

Published Sep 22, 2021• 0 citations
OpenAlex

Abstract

Photons have been proved to hide their past, especially in interferometers. Recently, several surprising results have been shown in nested Mach-Zehnder interferometer(NMZI), proving that the 'weak trace' of photons can be hidden. This paper rearranges the three path interference problem which gives the general result of its output and the conditions for eliminating the weak trace. Surprisingly, such conditions strongly depend on the detection method of the output photon, as well as the phase differences and splitting ratios in the NMZI. Further analysis gives a new weak trace elimination phenomenon which is independent of the position sensitive detector. Moreover, we setup an experiment to verify the weak trace elimination conditions and demonstrate the new weak trace elimination phenomenon.

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Hiding the which-path information of photons

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Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.

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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

Comment on “Past of a quantum particle”

Zheng-Hong Li, M. Al-Amri, Muhammad Suhail Zubairy

We present an analysis of a nested Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leaves a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results, contrary to some recent claims [Vaidman, Phys. Rev. A 87, 052104 (2013)], are in accordance with the usual quantum-mechanical expectations.

Physical Review A•Oct 29, 2013•65 citations
Photons have been proved to hide their past, especially in interferometers. Recently, several surprising results have been shown in nested Mach-Zehnder interferometer(NMZI), proving that the 'weak trace' of photons can be hidden. This paper rearranges the three path interference problem which gives the general result of its output and the conditions for eliminating the weak trace. Surprisingly, such conditions strongly depend on the detection method of the output photon, as well as the phase differences and splitting ratios in the NMZI. Further analysis gives a new weak trace elimination phenomenon which is independent of the position sensitive detector. Moreover, we setup an experiment to verify the weak trace elimination conditions and demonstrate the new weak trace elimination phenomenon.
Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.
Recently, the nested Mach-Zehnder interferometer [Phys.Rev. Lett.111, 240402 (2013)] was modified by adding Dove prisms in a paper [Quantum Stud.: Math.Found.2, 255 (2015)], and an interesting result is that, after the Dove prisms were inserted, a signal at the first mirror of the nested interferometer was obtained.But, according to the former original paper, the photons have never been present near that mirror.In this work, we interpret this result naturally by resorting to the three-path interference method.Moreover, we find that even though the photons have been somewhere, they can hide the trace of being there.
We present a three-path photon interferometer, theoretically investigate the behavior of the photon passing through it, and revisit the surprising experimental outcomes introduced by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)]. Our study shows that the ``discontinuous trajectory'' behavior of the photon results from the interference of the three propagation paths of the photon, which originate from the light source and end in the detector. If two of the three paths are adjusted in a destructive interference condition, there will be a zero probability domain in the overlap region of these two paths. However, these two paths can still individually interfere with the third path and contribute to the final output. In this condition, the discontinuous trajectory phenomenon appears. Our theory has a clear physical image and agrees with the experimental outcomes very well.
An ideal experiment is designed to determine the past of a particle in the nested Mach-Zehnder interferometer (MZI) by using standard quantum mechanics with quantum non-demolition measurements. We find that when the photon reaches the detector, it only follows one arm of the outer interferometer and leaves no trace in the inner MZI. When it goes through the inner MZI, it cannot reach the detector. Our result obtained from the standard quantum mechanics contradicts the statement based on two-state vector formulism, 'the photon did not enter the (inner) interferometer, the photon never left the interferometer, but it was there'. Therefore, the statement and also the overlapping claim are incorrect.
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-