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Annales de la fondation Louis de Broglie/Annales de la Fondation Louis de Broglie

Electron interferometry: Interferences between two electrons and a precision method of measuring decoherence

FRANZ HASSELBACH, Harald Kiesel, Peter Sonnentag

Published Jan 1, 2004• 3 citations
OpenAlex

Abstract

Louis de Broglie's discovery of the wave nature of matter 80 years ago and the subsequent development of quantum mechanics by Erwin Schrodinger, Werner Heisenberg and Paul Dirac solved many riddles of those days and determined physics of the whole 20th century. Yet, after this long time, matter wave interferometry is as up to date as it was in 1927 when Louis de Broglie's hypothesis was verified, e.g., by Davisson and Germer. Atom interferometry, ion interferometry and Bose-Einstein condensates are today's fascinating applications based on de Broglie's discovery. The focus of the present contribution are Hanbury Brown-Twiss anti-correlations (i.e. interferences between two fermions (electrons)) and the quantitative observation of decoherence by electron biprism interferometry.

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Louis de Broglie's discovery of the wave nature of matter 80 years ago and the subsequent development of quantum mechanics by Erwin Schrodinger, Werner Heisenberg and Paul Dirac solved many riddles of those days and determined physics of the whole 20th century. Yet, after this long time, matter wave interferometry is as up to date as it was in 1927 when Louis de Broglie's hypothesis was verified, e.g., by Davisson and Germer. Atom interferometry, ion interferometry and Bose-Einstein condensates are today's fascinating applications based on de Broglie's discovery. The focus of the present contribution are Hanbury Brown-Twiss anti-correlations (i.e. interferences between two fermions (electrons)) and the quantitative observation of decoherence by electron biprism interferometry.
Since the beginning of the 20th century, physicists have known that light must be considered as both a wave and a particle. Some properties of light – such as diffraction – can only be explained by treating it as waves, while others – like the photoelectric effect – can only be explained by treating it as particles. In the 1920s Louis de Broglie suggested that this wave–particle duality, which lies at the heart of the counterintuitive laws of quantum mechanics, could be extended to massive particles. In other words, electrons, atoms and molecules should diffract and interfere just like light does.
Summary. — This chapter reviews recent experiments on matter wave interferometry with large molecules. Starting from an elementary introduction to matter wave physics we discuss far-field diffraction and near-field interferometry with thermally excited many-body systems. We describe the constraints imposed by decoherence and dephasing effects, and present an outlook to the future challenges in macromolecule and cluster interferometry. PACS 03.75.-b – Matter waves. 1. – Historical introduction and overview The year 1923 is generally considered as the year of birth of matter wave physics. It is the year when Louis de Broglie proposed the idea that each material particle is accompanied by an oscillatory phenomenon [1]. De Broglie based his hypothesis on two discoveries: the energy-frequency equivalence for photons, E = ¯hω, and the energy-mass equivalence for matter, E = mc 2. While the first relation had already been central to Planck’s explanation of the black body spectrum [2] and to Einstein’s analysis of the photo effect [3], the latter was a consequence of Einstein’s theory of special relativity.
De Broglie proposed the matter wave in 1924. The de Broglie wave is neither a mechanical wave nor an electromagnetic wave and has a very short wavelength. The Davisson-Germer electron diffraction experiment performed in 1925 involved bombarding the surface of a nickel crystal with a narrow beam of electrons. When the accelerating voltage V was maintained at 54 V, the wavelength of the incident electron was λ=h/ 2 m e V = 0.167 nm [Y. S. Chen and Z. Z. Li, College Physics (Tianjin University, Tianjin, 1999)] demonstrating the existence of the matter wave. We introduce a type of electron wave with a very long wavelength in this study that is different from the matter wave. For example, the wavelength of the electron wave can reach 0.43 mm in the double-slit interference of electrons. Experiments demonstrate that this long-wavelength electron wave can produce both double-slit interference and electron diffraction. A comparative analysis of matter and electron waves reveals the physical natures of these waves and wave‐particle duality.
Arguments about particles or waves gave way to a recognized need for both particles and waves in the description of radiation. The confusion over particle versus wave properties was resolved by Louis de Broglie. He postulated that since light has a dual wave–particle nature, matter also has this nature. The idea was to perform a diffraction experiment with electrons. An interference pattern was demonstrated not only with electrons, but also with many kinds of material particles like protons and neutrons. However, any attempt to observe an interference pattern with neutral atoms was found difficult by the fact that atoms carried no charge as electrons do and could not penetrate through condensate matter like neutrons. The de Broglie wavelength of an electron in the smallest orbit turns out to be exactly equal to the circumference of the orbit predicted by Bohr. The interpretation of the interference phenomenon becomes more subtle when the light beams are replaced by individual photons or particles.
A longstanding goal of Akira Tonomura was to observe Hanbury Brown--Twiss anti-correlations between electrons in a field-emission free electron beam. The experimental results were reported in his 2011 paper with Tetsuji Kodama and Nobuyuki Osakabe [Phys. Rev. A 83, 063616 (2011)]. An open issue in such a measurement is whether the observed anti-correlations arise from quantum statistics, or are simply produced by Coulomb repulsion between electrons. In this paper we describe a simple classical model of Coulomb effects to estimate their effects in electron beam interferometry experiments, and conclude that the experiment did indeed observe quantum correlations in the electron arrrival times.
Davisson and Germer performed an experiment, in which electrons were reflected from parallel layers of atoms in a crystal. The electrons showed interference, thus demonstrating the wave nature of the electron. Louis de Broglie postulated a wave model of the electron, in which an electron orbit was represented by a group of in-phase waves. The model predicted that the angular momentum of an electron could take on only a limited number of values, a concept that Neils Bohr had introduced some years earlier as an ad hoc assumption. In an electron microscope, electrons stream off a hot filament and are accelerated to high velocity by passing between two electrically charged plates. The electrons' wavelength is related to their velocity and it is easy to obtain electrons with wavelengths near 0.1 nm, which suggests the possibility of obtaining resolution of about the same magnitude.