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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Interference with electrons: from thought to real experiments

Gioṙgio Matteucci

Published Nov 18, 2013• 5 citations
Publisher

Abstract

The two-slit interference experiment is usually adopted to discuss the superposition principle applied to radiation and to show the peculiar wave behaviour of material particles. Diffraction and interference of electrons have been demonstrated using, as interferometry devices, a hole, a slit, double hole, two-slits, an electrostatic biprism etc. A number of books, short movies and lectures on the web try to popularize the mysterious behaviour of electrons on the basis of Feynman thought experiment which consists of a Young two-hole interferometer equipped with a detector to reveal single electrons. A short review is reported regarding, i) the pioneering attempts carried out to demonstrate that interference patterns could be obtained with single electrons through an interferometer and, ii) recent experiments, which can be considered as the realization of the thought electron interference experiments adopted by Einstein-Bohr and subsequently by Feynman to discuss key features of quantum physics.

DOI
10.1117/12.2025383

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The two-slit interference experiment is usually adopted to discuss the superposition principle applied to radiation and to show the peculiar wave behaviour of material particles. Diffraction and interference of electrons have been demonstrated using, as interferometry devices, a hole, a slit, double hole, two-slits, an electrostatic biprism etc. A number of books, short movies and lectures on the web try to popularize the mysterious behaviour of electrons on the basis of Feynman thought experiment which consists of a Young two-hole interferometer equipped with a detector to reveal single electrons. A short review is reported regarding, i) the pioneering attempts carried out to demonstrate that interference patterns could be obtained with single electrons through an interferometer and, ii) recent experiments, which can be considered as the realization of the thought electron interference experiments adopted by Einstein-Bohr and subsequently by Feynman to discuss key features of quantum physics.
The Young-Feynman two-hole interferometer is widely used to present the electron wave-particle duality and in particular the buildup of interference fringes with single electrons. The teaching approach consists of two steps: i) electrons come through only one hole but diffraction effects are disregarded; ii) electrons come through both holes and interference fringes are described. Therefore, a student might believe that wave phenomena are not revealable in case i) but they arise only by the combined effect of electrons from the two holes. To avoid misunderstanding regarding the distribution of electrons passing through one hole, Fresnel and Fraunhofer diffraction patterns are discussed. In particular, an original experiment, realized with a standard electron microscope and a sample with round holes is presented to introduce the wave nature of electrons. The experimental results clearly show that a careful discussion of electron diffraction phenomena from one hole provides students with the evidence that the interference experiment from both holes is not strictly required to show the superposition of electron waves.
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.
Quantum mechanics has fundamentally changed the way scientists think about the world. Quantum mechanical theory has found it's way into our everyday lives through advances in technology. In this dissertation a fundamental quantum mechanical demonstration and the technological development of a new quantum mechanical device are presented. Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. Here we demonstrate the full realization of Richard Feynman's famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individuals slits. Probability distributions for single- and double-slit arrangements were observed. Additionally, by recording single electron detection events diffracting through a double-slit,a diffraction pattern was built up from individual events. Additionally, a demonstration of a three grating Talbot-Lau interferometer for electrons is presented. As a proof of principle the interferometer is used to measure magnetic fields. The possibility to extend this work to build a scaled-up electron interferometer for sensitive magnetic field sensing is discussed. A theoretical model is presented to simulate the two experiments. This model is developed from Richard Feynman's path integral formalism, where a wave function is propagated through the elements of the system. The theoretical simulations reproduce the experimental data well, except for a large discrepancy of a factor of 5.5 between the experimental and theoretical sensitivity of the Talbot-Lau interferometer. The origin of the discrepancy is currently unknown. These experiments were built off of previous work done here at the University of Nebraska-Lincoln, and improvements to the preexisting system are discussed. While these experiments likely did not demonstrate anything contrary to conventional quantum mechanics, it is important to continually probe these types of experiments to test the fundamental principles of quantum mechanics and explore it's technical applications. Advisor: Herman Batelaan
We construct proper microscopic propositions to consistently explain the interference patterns obtained for electrons and photons in well-defined one- and two-slit experiments. Our propositions are also made explicit on the basis of quantum mechanics with proper quantitative analysis to support the correctness of the physical mechanisms proposed herein, which obey the wave-particle duality. In particular, our propositions and theoretical analysis demonstrate that for single-photon detection (after time integration), we cannot produce interference pattern if the usual diffraction slits are replaced with slit holes such that the non-transparent slit material does not permit photons to transmit, reflect internally or refract. However, the said non-transparent slit material with slit holes can produce the usual interference pattern with electromagnetic waves.
Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.
Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.