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Journal of Physics Conference Series

Asking Neutrons where they have been

St. Sponar, Hermann Geppert, Tobias Denkmayr, Hartmut Lemmel, Yuji Hasegawa

Published Oct 1, 2019• 9 citations
Publisher

Abstract

Abstract Based on the results of Vaidman’s photonic three-path interferometer experiment with weak path marking [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] the authors claim that the photons have discontinuous particle trajectories. Here, we present a neutron optical version of the experiment by Danan et al., where in various beam paths of the interferometer the energy of the neutrons is slightly shifted. This is achieved by using resonance-frequency spin-rotators (SR) operating at different frequencies. The which-way information is derived from the time-dependent intensity, which is considered to result from the interfering cross terms between the stationary main component and the energy-shifted which-way signals. Our statements are based on a simple theoretical model, following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics and reveals the multifold presence of the neutron’s wave function in the interferometer.

DOI
10.1088/1742-6596/1316/1/012002

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Abstract Based on the results of Vaidman’s photonic three-path interferometer experiment with weak path marking [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] the authors claim that the photons have discontinuous particle trajectories. Here, we present a neutron optical version of the experiment by Danan et al., where in various beam paths of the interferometer the energy of the neutrons is slightly shifted. This is achieved by using resonance-frequency spin-rotators (SR) operating at different frequencies. The which-way information is derived from the time-dependent intensity, which is considered to result from the interfering cross terms between the stationary main component and the energy-shifted which-way signals. Our statements are based on a simple theoretical model, following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics and reveals the multifold presence of the neutron’s wave function in the interferometer.
A neutron optical experiment is presented to investigate the paths taken by neutrons in a three-beam interferometer. In various beam paths of the interferometer, the energy of the neutrons is partially shifted so that the faint traces are left along the beam path. By ascertaining an operational meaning to ``the particle's path,'' which-path information is extracted from these faint traces with minimal perturbations. Theory is derived by simply following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics. Which-way information is derived from the intensity, sinusoidally oscillating in time at different frequencies, which is considered to result from the interfering cross terms between stationary main component and the energy-shifted which-way signals. Final results give experimental evidence that the (partial) wave functions of the neutrons in each beam path are superimposed and present in multiple locations in the interferometer.
An experiment with nested Mach-Zehnder interferometer [Phys. Rev. Lett. 111, 240402 (2013)] has been recently implemented with neutrons [Phys. Rev. A 97, 052111 (2018)]. Which-path information has been extracted from faint traces the neutrons left, providing operational meaning to "the particle's path". The authors of the neutron interference experiment criticised the conclusions obtained by the authors of the optical experiment. I refute the criticism and argue that the results of the neutron interference experiment actually support the surprising picture of the past of the particle in the nested Mach-Zehnder interferometer.
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 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.
We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.
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.