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arXiv:1304.7469

Asking photons where have they been

Danan, Ariel, Demitry Farfurnik, Shimshon Bar-Ad, Lev Vaidman A

Published Apr 28, 2013• 1 citation
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Abstract

Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.

DOI
10.48550/arxiv.1304.7469

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Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a ``common sense'' approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
We present surprising experimental evidence regarding the past of photons passing through an interferometer. The information about the positions through which the photons pass in the interferometer is retrieved from modulations of the detected signal at the vibration frequencies of mirrors the photons bounce off. From the analysis we conclude that the past of the photons is not represented by continuous trajectories, although a "common sense" analysis adopted in various welcher weg measurements, delayed-choice which-path experiments, and counterfactual communication demonstrations yields a single trajectory. The experimental results have a simple explanation in the framework of the two-state vector formalism of quantum theory.
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.
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.
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.
We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32 (2015) 050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111 (2013) 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions: (i) were the photons in A? (ii) were the photons in B? and (iii) were the photons in C? the proposed experiment measures a degenerate operator answering the questions: (i) were the photons in A? and (ii) were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre- and post-selected photon, but this evidence will be in agreement with the results of Danan et al.