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Chinese Optics Letters

Photons can hide where they have been

Qi-Zhang Yuan, Xun‐Li Feng

Published Dec 18, 2020• 5 citations
Publisher

Abstract

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.

DOI
10.3788/col202119.012701

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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.
The history of photons in a nested Mach-Zehnder interferometer with an inserted Dove prism is analyzed. It is argued that the Dove prism does not change the past of the photon. Alonso and Jordan correctly point out that an experiment by Danan et al. demonstrating the past of the photon in a nested interferometer will show different results when the Dove prism is inserted. The reason, however, is not that the past is changed, but that the experimental demonstration becomes incorrect. The explanation of a signal from the place in which the photon was (almost) not present is given. Bohmian trajectory of the photon is specified.
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.
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.
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.
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 an recent work with the title ``Asking Photons Where They Have Been,'' Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013)]. In their words: ``The photons tell us that they have been in the parts of the interferometer through which they could not pass.'' They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.