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Physical Review A

Complementarity in which-path resonant Auger scattering

Ji‐Cai Liu, Faris Gel’mukhanov, Sergey P. Polyutov, Pavel O. Krasnov, Victor Kimberg

Published Feb 20, 2024• 1 citation
Publisher

Abstract

Different types of Young's double-slit experiments contain a significant amount of both particle and wave information running from full-particle to full-wave knowledge depending on the experimental conditions. We study the Young's double-slit interference in resonant Auger scattering from homonuclear diatomic molecules where opposite Doppler shifts for the dissociating atomic slits provide path information. Different quantitative formulation of Bohr's complementarity principle—path information vs interference—is applied to two types of resonant Auger scattering experiments, with fixed-in-space and randomly oriented molecules. Special attention is paid to the orientational dephasing in conventional Auger experiments with randomly oriented molecules. Our quantitative formulation of the complementarity is compared with the formulation made earlier by Greenberger and Yasin [D. M. Greenberger and A. Yasin, ].

DOI
10.1103/physreva.109.023116

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Different types of Young's double-slit experiments contain a significant amount of both particle and wave information running from full-particle to full-wave knowledge depending on the experimental conditions. We study the Young's double-slit interference in resonant Auger scattering from homonuclear diatomic molecules where opposite Doppler shifts for the dissociating atomic slits provide path information. Different quantitative formulation of Bohr's complementarity principle—path information vs interference—is applied to two types of resonant Auger scattering experiments, with fixed-in-space and randomly oriented molecules. Special attention is paid to the orientational dephasing in conventional Auger experiments with randomly oriented molecules. Our quantitative formulation of the complementarity is compared with the formulation made earlier by Greenberger and Yasin [D. M. Greenberger and A. Yasin, ].
The quantitative formulation of Bohr's complementarity proposed by Greenberger and Yasin is applied to some physical situations for which analytical expressions are available. This includes a variety of conventional double-slit experiments, but also particle oscillations, as in the case of the neutral-kaon system, and Mott scattering of identical nuclei. For all these cases, a unified description can be achieved including a new parameter $\ensuremath{\nu},$ which quantifies the effective number of fringes one can observe in each specific interferometric setup.
A detailed analysis of Einstein's version of the double-slit experiment, in which one tries to observe both wave and particle properties of light, is performed. Quantum nonseparability appears in the derivation of the interference pattern, which proves to be surprisingly sharp even when the trajectories of the photons have been determined with fairly high accuracy. An information-theoretic approach to this problem leads to a quantitative formulation of Bohr's complementarity principle for the case of the double-slit experiment. A practically realizable version of this experiment, to which the above analysis applies, is proposed.
Young's double slit experiment has often been used to illustrate the concept of complementarity in quantum mechanics. If information can in principle be obtained about the path of the photon, then the visibility of the interference fringes is reduced or even destroyed. This Gedanken experiment discussed by Bohr and Einstein can be realized when the slit is replaced by individual atoms sensitive to the transferred recoil momentum of a photon which "passes through the slit". Early pioneering experiments were done with trapped ions and atom pairs created via photo-dissociation. Recently, it became possible to perform interference experiments with single neutral atoms cooled to the absolute ground state of a harmonic oscillator potential. The slits are now single atoms representing a two-level system, and the excitation in the harmonic oscillator potential is the which-way marker. In this note, we analyze and generalize two recent experiments performed with single atoms and emphasize the different ways they record which-way information.
For the last 50 years, there has been considerable interest in the possibility of observing the equivalence of a Young's double-slit wave interference at the quantum level for diatomic molecules. For electron-impact ionization of diatomic molecules, indirect evidence for this type of interference has been found by changing the energy (wavelength) of the ejected electron while keeping the incident projectile scattering angle fixed. The present work represents an experimental and theoretical collaboration to better understand the physics of this type of interference. In addition to examining the effect of changing the ejected electron energy for a fixed scattered projectile angle, we have also examined the effect of keeping the ejected electron energy fixed while varying the projectile scattering angle. Model calculations are performed for three different types of possible two-center interference effects, and it is found that the most important one is diffraction of the projectile off two scattering centers.
Young’s double-slit experiment played a crucial role in establishing the wave nature of light. In this chapter, the shocking result that incident electrons yield a similar interference pattern as that formed by light waves is described. It is shown that the only way the experimental results could be explained is via a wave function description of electrons. It is also shown that, in the same experiment, the interference fringes disappear if the which-path information becomes available. This is the essence of wave–particle duality. The first of the Einstein–Bohr debates on wave-particle duality and Bohr’s principle of complementarity in the double-slit experiment is also discussed. Also presented are the counterintuitive notions of delayed choice and quantum eraser effects showing how the availability or erasure of information generated in the future can affect how the data in the present can be interpreted.
Young’s one-dimension-double-slit experiment represents the basic mystery of quantum world and was extended to which-way-1D-double-slit experiment. To explore the mystery, 2D-cross-double-slit apparatuses have been proposed, which consists of more than one double-slits intersecting to each other. In this article, we report which-way-2D-cross-double-slit experiments by detecting which slit of a double-slit of 2D-cross-double-slit apparatus a photon would pass through. The experimental results show that photons passing through the detected double-slit behave as particle, while photons passing through other undetected double-slit(s) distribute as wave in the same experiment with the same apparatus. Namely the particle nature and wave distribution coexist, which violates Bohr’s complementarity principle. We suggest that photon’s “particle nature” is intrinsic, while the term “wave nature” represents a wave-like distribution, which is a consequence of movement of photon as particle. It is a challenge to interpret mathematically those observations consistently.