{"id":4429,"date":"2024-09-22T17:47:02","date_gmt":"2024-09-22T17:47:02","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4429"},"modified":"2024-09-22T17:47:03","modified_gmt":"2024-09-22T17:47:03","slug":"two-slit-interference-with-single-electrons","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/two-slit-interference-with-single-electrons\/","title":{"rendered":"TWO-SLIT INTERFERENCE WITH SINGLE ELECTRONS"},"content":{"rendered":"\n

De Broglie\u2019s critics argued that the results from electron-diffraction experiments may indicate an undulating interaction between electrons, so these experiments didn\u2019t decisively prove that electrons are<\/em> waves when studied by diffraction. Definitive proof would still have to wait until technology advanced to make it possible to conduct the double-slit experiment with individual electrons. In one of his famous lectures, Feynman explained the ultimate significance of observing single-electron interference:<\/p>\n\n\n\n

We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.<\/p>\n\n\n\n

The first double-slit experiment with single electrons was performed by Italian physicists Pier Giorgio Merli, GianFranco Missiroli, and Giulio Pozzi25<\/sup> in Bologna in 1974. However, their electron source (a thermionic emitter) wasn\u2019t sufficiently stable to absolutely ensure that only single electrons would arrive at the detector at the same time. However, in 1989, a group at Hitachi Labs led by Japanese physicist Akira Tonomura developed a double-slit system that allowed them to observe the build-up of the fringe pattern with a very weak electron source.26<\/sup><\/p>\n\n\n\n

Figure 97\u00a0shows a schematic representation of the modifications that Tonomura made to a transmission electron microscope (TEM) to develop his experimental setup. Electrons are emitted from a very sharp tungsten tip when a potential difference of 3\u20135 kV is applied between the tip and a first anode ring; this effect is known as \u201cfield emission.\u201d These electrons are then accelerated to the second anode potential of 50 kV (the de Broglie wavelength for the accelerated electrons is \u03bb = 0.0055 nm). Assorted \u201celectron optics\u201d within the modified electron microscope attenuate and focus the electron beam so that a current of barely 1.60 \u00d7 10\u221216<\/sup>\u00a0A (that is only 1,000 electrons\/s) is beamed toward the double slit.<\/p>\n\n\n\n

\"\"<\/p>\n\n\n\n

The double slit is actually an extremely fine wire filament (1-\u03bcm diameter) placed between two conductive plates set 1 cm apart. The wire is biased at a positive voltage of 10 V relative to the plates. This arrangement is known as an\u00a0electron biprism<\/em>. Despite its complicated name, you should find this familiar: it is the electron equivalent of the interference experiment we conducted using a thin hair (Figure 4c).<\/p>\n\n\n\n

Obviously, any electrons that make it past the biprism must have gone either through one or the other side of the fine wire. The discussion of the interference pattern generated by the electron biprism is beyond the scope of this book, but suffice it to say that if electrons act as waves, they should produce fringes with a spacing of 700 nm for the de Broglie wavelength in this setup.<\/p>\n\n\n\n

Two electron lenses then magnify the interference pattern 2,000 times and project it onto a fluorescent screen. Each 50-keV electron hitting the screen produces about 500 photons that generate photoelectrons inside an intensified position detector. This device works in a manner similar to an image intensifier, the only difference being that it produces an\u00a0x,y<\/em>\u00a0coordinate for each hit, which can be read directly by a computer. The computer then integrates the hits to produce a final image of the electron interference pattern as shown in the inset of\u00a0Figure 97. Through which slit did each of the electrons go? The answer is the same as before: somehow each electron behaves as if it is going through both slits at the same time!<\/p>\n","protected":false},"excerpt":{"rendered":"

De Broglie\u2019s critics argued that the results from electron-diffraction experiments may indicate an undulating interaction between electrons, so these experiments didn\u2019t decisively prove that electrons are waves when studied by diffraction. Definitive proof would still have to wait until technology advanced to make it possible to conduct the double-slit experiment with individual electrons. In one of his […]<\/p>\n","protected":false},"author":1,"featured_media":4186,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[515],"tags":[],"class_list":["post-4429","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wave-particle-duality"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/evaporation.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4429","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4429"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4429\/revisions"}],"predecessor-version":[{"id":4430,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4429\/revisions\/4430"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4186"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4429"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4429"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4429"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}