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Applied Physics Express

Electron interference experiment with optically zero propagation distance for V-shaped double slit

Ken Harada, Tetsuya Akashi, Yoshio Takahashi, Tetsuji Kodama, Keiko Shimada, Yoshimasa A. Ono, Shigeo Mori

Published Jan 6, 2021• 8 citations
Publisher

Abstract

Abstract In an electron double-slit experiment, an optically zero propagation distance condition (infocus imaging condition), in which the double-slit position was imaged just on the detector plane (image plane), was realized in a 1.2 MV field-emission transmission electron microscope. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we observed the interference features under the pre-interference condition, interference condition and post-interference condition of electron waves. We conclude that it is possible to observe the interference fringes only when the path information of the individual electrons is not available.

DOI
10.35848/1882-0786/abd91e

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Abstract In an electron double-slit experiment, an optically zero propagation distance condition (infocus imaging condition), in which the double-slit position was imaged just on the detector plane (image plane), was realized in a 1.2 MV field-emission transmission electron microscope. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we observed the interference features under the pre-interference condition, interference condition and post-interference condition of electron waves. We conclude that it is possible to observe the interference fringes only when the path information of the individual electrons is not available.
Electron double-slit experiments, the essence of quantum mechanical “wave/particle duality,” have been extensively and continuously studied because their unrealistic interpretations have attracted many researchers. Here, we discuss recent sophisticated V-shaped double-slit experiments to elucidate electron-path information, i.e., which slit electrons pass through, which path they pursue, and where they arrive and interfere on the image plane. In a transmission electron microscope, an optically zero-propagation distance condition was realized, where the double-slit position was imaged just on the detector plane. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we confirmed that it is possible to observe interference fringes only when the path information of individual electrons is not available. Furthermore, we studied how the interference fringes would shift their detected positions when electron wave phases were modulated before illumination to the double slit. Phase shifts were generated by tilting electron beams. We confirmed that each single electron as a wave changed its phase even when it traveled alone inside the microscope.
Electron double-slit experiments, the essence of quantum mechanical “wave/particle duality”, have been extensively and continuously studied because their unrealistic interpretations have attracted many researchers. Here, we discuss recent sophisticated V-shaped double-slit experiments to elucidate electron-path information, i.e., which slit electrons pass through, which path they pursue, and where they arrive and interfere on the image plane. In a transmission electron microscope, an optically zero-propagation distance condition was realized, where the double-slit position was imaged just on the detector plane. Interference fringes composed of dot images were controlled by using two electron biprisms. Using a V-shaped double slit, we confirmed that it is possible to observe interference fringes only when the path information of individual electrons is not available. Furthermore, we studied how the interference fringes would shift their detected positions when electron wave phases were modulated before illumination to the double slit. Phase shifts were generated by tilting electron beams. We confirmed that each single electron as a wave changed its phase even when it traveled alone inside the microscope.
Advanced electron microscopy technologies have made it possible to perform precise double-slit interference experiments. We used a 1.2-MV field emission electron microscope providing coherent electron waves and a direct detection camera system enabling single-electron detections at a sub-second exposure time. We developed a method to perform the interference experiment by using an asymmetric double-slit fabricated by a focused ion beam instrument and by operating the microscope under a "pre-Fraunhofer" condition, different from the Fraunhofer condition of conventional double-slit experiments. Here, pre-Fraunhofer condition means that each single-slit observation was performed under the Fraunhofer condition, while the double-slit observations were performed under the Fresnel condition. The interference experiments with each single slit and with the asymmetric double slit were carried out under two different electron dose conditions: high-dose for calculation of electron probability distribution and low-dose for each single electron distribution. Finally, we exemplified the distribution of single electrons by color-coding according to the above three types of experiments as a composite image.
The key features of quantum mechanics are vividly illustrated by the Young-Feynman two-slit thought experiment, whose second part discusses the recording of an electron distribution with one of the two slits partially or totally closed by an aperture. Here, we realize the original Feynman proposal in a modern electron microscope equipped with a high brightness gun and two biprisms, with one of the biprisms used as a mask. By exciting the microscope lenses to conjugate the biprism plane with the slit plane, observations are carried out in the Fraunhofer plane with nearly ideal control of the covering of one of the slits. A second, new experiment is also presented, in which interference phenomena due to partial overlap of the slits are observed in the image plane. This condition is obtained by inserting the second biprism between the two slits and the first biprism and by biasing it in order to overlap their images.
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.
Current nanotechnology techniques make possible the preparation of slits in the submicrometer range so that electron interference and diffraction experiments can be done even with a conventional electron microscope. If the instrument is also equipped with a field emission source, it is possible to follow almost in real time the transition from the image of the slits to their Fraunhofer pattern through the intermediate Fresnel diffraction images. We discuss our results for the two-slit experiment and illustrate them for the three-slit case.