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Controlled Double-Slit Electron Diffraction

Roger Bach, Damian T. Pope, S. H. Liou, Herman Batelaan

Published Jan 1, 2012• 122 citations
OpenAlex

Abstract

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.

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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.

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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

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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.

Physical Review Letters•Jan 3, 2014•15 citations
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.
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
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.
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.
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.
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.