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Applied Physics Letters

Experimental realization of the Ehrenberg-Siday thought experiment

Giulio Pozzi, Chris Boothroyd, Amir Hossein Tavabi, Emrah Yücelen, Rafal E. Dunin‐Borkowski, Stefano Frabboni, Gian Carlo Gazzadi

Published Feb 22, 2016• 10 citations
Publisher

Abstract

In 1949, at the end of a paper dedicated to the concept of the refractive index in electron optics, Ehrenberg and Siday noted that wave-optical effects will arise from an isolated magnetic field even when the rays themselves travel in magnetic-field-free space. They proposed a two-slit experiment, in which a magnetic flux is enclosed between interfering electron beams. Now, through access to modern nanotechnology tools, we used a focused ion beam to open two nanosized slits in a gold-coated silicon nitride membrane and focused electron beam induced deposition to fabricate a thin magnetic bar between the two slits. We then performed Fraunhofer experiments in a transmission electron microscope equipped with a field emission gun and a Lorentz lens. By tilting the specimen in the objective lens field of the electron microscope, the magnetization of the bar could be reversed and the corresponding change in the phase of the electron wave observed directly in the form of a shift in the interference fringe pattern.

DOI
10.1063/1.4942462

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In 1949, at the end of a paper dedicated to the concept of the refractive index in electron optics, Ehrenberg and Siday noted that wave-optical effects will arise from an isolated magnetic field even when the rays themselves travel in magnetic-field-free space. They proposed a two-slit experiment, in which a magnetic flux is enclosed between interfering electron beams. Now, through access to modern nanotechnology tools, we used a focused ion beam to open two nanosized slits in a gold-coated silicon nitride membrane and focused electron beam induced deposition to fabricate a thin magnetic bar between the two slits. We then performed Fraunhofer experiments in a transmission electron microscope equipped with a field emission gun and a Lorentz lens. By tilting the specimen in the objective lens field of the electron microscope, the magnetization of the bar could be reversed and the corresponding change in the phase of the electron wave observed directly in the form of a shift in the interference fringe pattern.
Two nanosized slits are opened by focused ion beam milling in a membrane to observe, with a transmission electron microscope, electron interference fringes. Then, on the same sample, one of the slits is closed by focused ion beam induced deposition and the corresponding transmitted intensity is recorded. The comparison between the two measurements provides an impressive experimental evidence of the probability amplitude of quantum mechanics following step by step the original idea proposed by Feynman [The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1966), Vol. 3, Chap. 1].
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.
In a "thought experiment," now a classic in physics pedagogy, Feynman visualizes Young's double-slit interference experiment with electrons in magnetic field. He shows that the addition of an Aharonov-Bohm phase is equivalent to shifting the zero-field wave interference pattern by an angle expected from the Lorentz force calculation for classical particles. We have performed this experiment with one slit, instead of two, where ballistic electrons within two-dimensional electron gas diffract through a small orifice formed by a quantum point contact (QPC). As the QPC width is comparable to the electron wavelength, the observed intensity profile is further modulated by the transverse waveguide modes present at the injector QPC. Our experiments open the way to realizing diffraction-based ideas in mesoscopic physics.
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.