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Applied Physics Letters

Ion and electron beam nanofabrication of the which-way double-slit experiment in a transmission electron microscope

Stefano Frabboni, Gian Carlo Gazzadi, Giulio Pozzi

Published Dec 27, 2010• 15 citations
Publisher

Abstract

We have realized a which-way experiment closely resembling the original Feynman’s proposal exploiting focused ion beam milling to prepare two nanoslits and electron beam induced deposition to grow, selectively over one of them, electron transparent layers of low atomic number amorphous material to realize a which-way detector for high energy electrons. By carrying out the experiment in an electron microscope equipped with an energy filter, we show that the inelastic scattering of electron transmitted through amorphous layers of different thicknesses provides the control of the dissipative interaction process responsible for the localization phenomena which cancels out the interference effects.

DOI
10.1063/1.3529947

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We have realized a which-way experiment closely resembling the original Feynman’s proposal exploiting focused ion beam milling to prepare two nanoslits and electron beam induced deposition to grow, selectively over one of them, electron transparent layers of low atomic number amorphous material to realize a which-way detector for high energy electrons. By carrying out the experiment in an electron microscope equipped with an energy filter, we show that the inelastic scattering of electron transmitted through amorphous layers of different thicknesses provides the control of the dissipative interaction process responsible for the localization phenomena which cancels out the interference effects.
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].
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.
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 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.
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.
The Young-Feynman two-slit experiment for single electrons was carried out by inserting two nanometric slits and a fast recording system, capable of detecting the electron arrival-time, in a conventional transmission electron microscope. The sensor, designed for experiments at future high energy colliders, is based on a custom 4096 Monolithic Active Pixels CMOS chip, is equipped with a fast readout chain and can manage up to 10^6 frames per second, allowing the collection of high statistic samples of single electron events within a time interval compatible with the stability of the experimental setup and the coherence conditions of the illumination. For the first time in a single electron two-slit experiment, the time distribution of electron arrivals was obtained.