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Optics Express

A Saturnian atom

Ernestine Lee, David Farrelly, T. Uzer

Published Sep 29, 1997• 17 citations
Publisher

Abstract

In Bohr's original planetary model of the atom the electron moves along orbits of special geometric simplicity. While wave mechanics precludes the idea that a physical path could be ascribed to the electron, a classical or planetary atom can still be envisaged in which the electronic wavepacket neither spreads nor disperses as its center moves along the Kepler orbit, and this orbit is conned to a single plane in space. We show theoretically how an electronic wavepacket may be localized in this fashion in a similar way to ion confinement in a Penning trap. Because external fields are needed to keep the packet confined, a more fitting analogy than a planetary orbit is the motion of a charged dust grain in one of the rings of a giant planet such as Saturn.

DOI
10.1364/oe.1.000221

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In Bohr's original planetary model of the atom the electron moves along orbits of special geometric simplicity. While wave mechanics precludes the idea that a physical path could be ascribed to the electron, a classical or planetary atom can still be envisaged in which the electronic wavepacket neither spreads nor disperses as its center moves along the Kepler orbit, and this orbit is conned to a single plane in space. We show theoretically how an electronic wavepacket may be localized in this fashion in a similar way to ion confinement in a Penning trap. Because external fields are needed to keep the packet confined, a more fitting analogy than a planetary orbit is the motion of a charged dust grain in one of the rings of a giant planet such as Saturn.
This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.
We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.
A model of the electronic internal structure has been developed, revealing the specific movement mode of electrons outside the nucleus. Building on this, the Bohr's planetary model of the hydrogen atom has been adapted into the Saturn model, suitable for describing multi-center and multi-electron bound systems. It has been discovered that the mathematical formalism of Bohr's old quantum theory and wave mechanics are compatible. A quantum chemistry method has been established to implement this compatibility (where the Saturn model and wave mechanics can complement each other), using this method, the energy eigenvalues of s electrons in atoms and the binding energies and bond lengths of four diatomic molecules such as hydrogen molecules have been successfully calculated. This provides new insights into material structure theory. The aforementioned compatibility could lead to the birth of local realism quantum mechanics.
The electronic transition energies from the electron clouds are the same as predicted by the Bohr model. The hydrogen atom, most probable radius of the first quantum mechanical electron cloud is identical to the radius of the first Bohr orbit. The quantum mechanical description goes much further, however. Not only does it predict a series of increasingly larger spherical electron clouds, but other electron cloud series as well. Because of their three dimensional shapes, these electron clouds sometimes are said to describe space states. The analogy to planetary orbits ends when we grasp the fact that quantum mechanical electron clouds are three-dimensional, where a Bohr orbit would be a circle lying entirely in a plane. Quantum mechanics also predicts the ionization energy of the hydrogen atom.