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arXiv:1805.05093 · Physical Review A

Multifold paths of neutrons in the three-beam interferometer detected by a tiny energy kick

Hermann Geppert-Kleinrath, Tobias Denkmayr, Stephan Sponar, Hartmut Lemmel, Tobias Jenke, Yuji Hasegawa

Published May 10, 2018• 30 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.97.052111

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Comment on "Multifold paths of neutrons in the three-beam interferometer detected by a tiny energy kick"

Lev Vaidman A

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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.
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.
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.
The statistical properties of the detection events constituting the interference fringes at the output of an interferometer are well-known. Nevertheless, there is still no unified view of what is happening to a quantum system inside an interferometer. Strong measurements of path operators destroy the interference effect. In weak measurements, an observable is weakly coupled to a pointer system and the resulting weak values quantify the observable by minimally disturbing the system. Previous which-way experiments with weak measurements could extract either the real or imaginary part of a single weak value with each ensemble. Here, we present the simultaneous full complex quantification of two path weak values with a single ensemble in a Mach-Zehnder neutron interferometer. Magnetic fields, oscillating with different frequencies, change the energy state in each interferometer path. The time-dependent phase between the energy states distinctly marks each path. The resulting beating intensity modulation at the interferometer output gives both path weak values. For the present experiment, the weak values' absolute value and phase directly describe the observed amplitude and phase of the intensity modulation.
Abstract Although our every-day experience rejects it, the quantum Cheshire Cat suggests a potential spatial separation between different properties of a single particle in an interferometer. The first experiment with neutrons confirmed the quantum Cheshire Cat effect by using the path and spin degrees of freedom. The locations of each property are determined qualitatively through reactions to locally applied perturbations. Yet, no consensus on the interpretation has been reached. To clarify the origin of the effect, in the present experiment the energy degree of freedom is used as the third property; the three properties of neutrons appear to be separated in different paths in the interferometer. The analysis of the experiment suggests the strong involvement of the inner product between the state vectors, one evolved from the initial state through the perturbation and the other being the final state. The inner product results in amplitudes from two sub-beams which contribute to the intensity. The cross-term between amplitudes gives rise to the quantum Cheshire Cat.
Quantum theory provides us with the best account of microscopic components of matter as well as of radiation. It was introduced in the twentieth century and has experienced a wide range of success. Although the theory’s probabilistic predictions of final experimental outcomes is found to be correct with high precision, there is no general consensus regarding what is actually going on with a quantum system “en route”, or rather the perceivable intermediate behavior of a quantum system, e.g., the particle’s behavior in the double-slit experiment. Neutron interferometry using single silicon perfect crystals is established as a versatile tool to test fundamental phenomena in quantum mechanics, where an incident neutron beam is coherently split in two or three beam paths with macroscopic separation of several centimeters. Here, we present quantum optical experiments with these matter-wave interferometers, studying the effect of the quantum Cheshire Cat in some variants, the neutron’s presence in the paths of the interferometer as well as the direct test of a commutation relation. To reduce disturbances induced by the measurement, the interaction strength is lessened and so-called weak interactions are exploited by employing pre- and post-selection procedures. All results of the experiments confirm the predictions of quantum theory; the observed behaviors of the neutron between the pre- and post-selection in space and time emphasize striking and counter-intuitive aspects of quantum theory.
A two-loop perfect-crystal neutron interferometer was used for the quantitative determination of which-way (WW) information and the verification of the duality relation between predictability and visibility. Our interferometer has two remarkable features, it allows the absorption-free tuning of WW information and it enables the simultaneous measurement of the duality relation without changing the interferometer setup. In addition, the duality relation of three interfering beams is a good demonstration that WW information should not be misused as particle property because one interferometer beam remains in a coherent superposition of two path alternatives, which is not consistent with the particle picture. The coherent WW tuning was performed without changing the neutron's momentum and without dephasing.