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Physical Review Letters

Angular Momentum Sensitive Two-Center Interference

Markus Ilchen, Leif Glaser, Frank R. Scholz, Peter Walter, Sascha Deinert, André Rothkirch, Jörn Seltmann, Jens Viefhaus, Piero Decleva, B. Langer, André Knie, Arno Ehresmann, Omar Marzook Al-Dossary, Markus Braune, Gregor Hartmann, André Meißner, Lokesh C. Tribedi, M. AlKhaldi, U. Becker

Published Jan 15, 2014• 31 citations
Publisher

Abstract

In quantum mechanics the Young-type double-slit experiment can be performed with electrons either traveling through a double slit or being coherently emitted from two inversion symmetric molecular sites. In the latter one the valence photoionization cross sections of homonuclear diatomic molecules were predicted to oscillate over kinetic energy almost 50 years ago. Beyond the direct proof of the oscillatory behavior of these photoionization cross sections σ, we show that the angular distribution of the emitted electrons reveals hitherto unexplored information on the relative phase shift between the corresponding partial waves through two-center interference patterns.

DOI
10.1103/physrevlett.112.023001

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In quantum mechanics the Young-type double-slit experiment can be performed with electrons either traveling through a double slit or being coherently emitted from two inversion symmetric molecular sites. In the latter one the valence photoionization cross sections of homonuclear diatomic molecules were predicted to oscillate over kinetic energy almost 50 years ago. Beyond the direct proof of the oscillatory behavior of these photoionization cross sections σ, we show that the angular distribution of the emitted electrons reveals hitherto unexplored information on the relative phase shift between the corresponding partial waves through two-center interference patterns.
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.
The ion momentum distribution in the x-ray-induced dissociative photoionization of molecules is investigated, treating the ionization analytically under the Born-Oppenheimer approximation and simulating numerically the ion motion via the Schrödinger equation. The ion-photoelectron entanglement transfers information of the electronic interference to the ion dynamics. As a consequence, the ion momentum distributions of dissociative molecular photoionization present Young's double-slit interference when the photoelectron emission angle is fixed. We demonstrate that double-slit interference signatures persist in the ion longitudinal momentum shift even when the information of the correlated photoelectron is lost, which is the case for heteronuclear molecules when an additional photoelectron recoil momentum arises due to the different ion masses. For the case of sequential double ionization, we show that double-slit interference in the ion dynamics can be utilized for coherent control of the molecular dynamics.
Evidence is given for Young-type interferences caused by a single electron acting on a given double-center scatterer analogous to an atomic-size double-slit system. The electron is provided by autoionization of a doubly excited He atom following the capture of the electrons of H2 by a He2+ incoming ion. The autoionizing projectile is a single-electron source, independent of the interferometer provided by the two H+ centers of the fully ionized H2 molecule. This experiment resembles the famous thought experiment imagined by Feynman in 1963, in which the quantum nature of the electron is illustrated from a Young-like double-slit experiment. Well-defined oscillations are visible in the angular distribution of the scattered electrons, showing that each electron interferes with itself.
Interferences caused by a single electron impacting on an independent double-center scatterer, which plays the role of an atomic-size double-slit system, are experimentally evidenced for the first time. The electron originates from the autoionization of doubly excited 2 l n l ' (n ⩾ 2) configurations of He following a double charge exchange process by He 2+ ions impinging on H 2 molecules. Well-defined oscillations are visible in the angular distribution of the electrons emitted towards the receding H + protons. The presence of these oscillations demonstrates that a single electron interferes with itself. This is analogous to the famous "thought" experiment imagined and discussed by Feynman in 1963, in which the quantum nature of the electron was illustrated by making it traverse an atomic-size double-slit arrangement.
Young's classic double-slit experiment demonstrates the reality of interference when waves and particles travel simultaneously along two different spatial paths. Here, we propose a double-slit experiment in momentum space, realized in the free-space elastic scattering of vortex electrons. We show that this process proceeds along two paths in momentum space, which are well localized and well separated from each other. For such vortex beams, the (plane-wave) amplitudes along the two paths acquire adjustable phase shifts and produce interference fringes in the final angular distribution. We argue that this experiment can be realized with the present-day technology. We show that it gives experimental access to the Coulomb phase, a quantity which plays an important role in all charged particle scattering but which usual scattering experiments are insensitive to.
In this paper, we shed new light on the molecular photoionization of a diatomic molecule. We will elaborate the differences and analogy between a quantum optical and light–matter interaction approach in a study of K-shell photoionization of N 2 in which the photoelectron and the subsequently emitted Auger electron are both measured in coincidence in the body fixed frame of the molecule. The two electrons form an entangled state inside a double slit. By changing the photon energy we create different types of interference in the photoelectron and the Auger electron wave.