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arXiv:quant-ph/0106061 · Europhysics Letters (EPL)

Four-path interference and uncertainty principle in photodetachment microscopy

Tobias Kramer, Christian Bracher, M. Kleber

Published Nov 1, 2001• 36 citations
arXivHTMLPDF

Abstract

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.

DOI
10.1209/epl/i2001-00543-x

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We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.
We examine the dynamics of electrons photodetached from the H– ion in time-dependent electric and magnetic fields for the first time. The photodetachment microscopy patterns caused by a time-dependent gradient electric field and magnetic field have been analyzed in great detail based on the semiclassical theory. The interplay of the gradient electric field and magnetic field forces causes an intricate shape of the electron wave and multiple electron trajectories generated by a fixed energy point source can arrive at a given point on the microchannel-plate detector. The interference effects between these electron trajectories cause the oscillatory structures of the electron probability density and electron current distribution, and a set of concentric interference fringes are found at the detector. Our calculation results suggest that the photodetachment microscopy interference pattern on the detector can be adjusted by the electron energy, magnetic field strength, and position of the detector plane. Under certain conditions, the interference pattern in the electron current distribution might be seen on the detector plane localized at a macroscopic distance from the photodetachment source, which can be observed in an actual photodetachment microscopy experiment. Therefore, we make predictions that our work should serve as a guide for future photodetachment microscopy experiments in time-dependent electric and magnetic fields.
Negative ions undergoing near-threshold photodetachment in a weak laser field provide an almost pointlike, isotropic source of low-energy electrons. External fields exert forces on the emitted coherent electron wave and direct its motion. Here, we examine the spatial distribution of photodetached electrons in uniform, parallel electric and magnetic fields. The interplay of the electric and magnetic forces leads to a surprising intricate shape of the refracted electron wave, and multiple interfering trajectories generate complex fringe patterns in the matter wave. The exact quantum solution is best understood in terms of the classical electron motion.
During photodetachment in external electric and magnetic fields, the detached electron wave propagated from the negative ion in different directions may intersect again at a large distance from the negative ion, thus creating an interference pattern in the detached electron’s current density distributions on a detector plane placed at a certain distance from the negative ion. In this work, we calculate the photodetached electron’s current density distributions in perpendicular electric and magnetic fields on the basis of the semi-classical theory. Our results suggest that the electron current density distributions on the detector plane are not only related to the electric and magnetic fields’ strength, but also related to the electron energy. Under certain conditions, the interference pattern could reach macroscopic dimensions and could be observed in a direct photodetachment microscopy experiment. Our studies may guide the future researches in the wave propagation theory and the photodetachment microscopy of negative ion in the presence of external fields.
Investigation of electronic waves with high coherence in photodetachment of a negative ion gives a physical basis to develop the holographic electronic microscopy with high resolution. The interference pattern is considered in the framework of steady-state wave approach. In semiclassical approximation, an outgoing wave is described by the amplitude slowly varying along a trajectory. Quantum description of electron photodetachment from negative ion is formulated with the help of the inhomogeneous Schrödinger equation. Its asymptotic solution is expressed in terms of the Green function that has exact expression for the homogeneous electric field and the Coulomb field. It is demonstrated that repulsive Coulomb field is effective for magnification of the interference pattern at a short distance from an ion. For the first time, as shown for this case, the interference pattern in asymptotic area can be calculated by means of global semiclassical approximation or, a little more roughly, by simple uniform field approximation. New proposals and possible parameters for experimental measurement scheme for the effect are discussed.
Unlike other physical theories, Aetherometry claims that the wave interference phenomena of massbound particles is caused by the diffraction of the electric waves of their kinetic energy, and not by a much misunderstood particle-wave duality. The new analytical treatment proposes that kinetic energy is captured field energy adapted to the inertial and magnetic constraints of massbound charges. The coincidence of two independent, nonclassical and nonrelativistic analyses - one inertial and the other electric - in the determination of the experimentally observed de Broglie wavelengths and momenta of electrons and massbound charges highlights the central contention that the paths of the accelerated charges in a beam are electric functions of its kinetic energy, and reflect in part the more fundamental interference properties of the underlying flux of a massfree electric field. Conversely, the interference properties of photons only directly reflect the interference properties of moving but decelerating charges. Written as an antidote to Richard Feynman's famous lecture, the present communication suggests that there is a method, after all, to count how many electrons pass through a slit, in a double-slit experiment.
The Aharonov–Bohm (AB) effect in the photodetachment microscopy of the H− ions in an electric field has been studied on the basis of the semiclassical theory. After the H− ion is irradiated by a laser light, they provide a coherent electron source. When the detached electron is accelerated by a uniform electric field, two trajectories of a detached electron which run from the source to the same point on the detector, will interfere with each other and lead to an interference pattern in the photodetachment microscopy. After the solenoid is electrified beside the H− ion, even though no Lorentz force acts on the electron outside the solenoid, the photodetachment microscopy interference pattern on the detector is changed with the variation in the magnetic flux enclosed by the solenoid. This is caused by the AB effect. Under certain conditions, the interference pattern reaches the macroscopic dimensions and could be observed in a direct AB effect experiment. Our study can provide some predictions for the future experimental study of the AB effect in the photodetachment microscopy of negative ions.