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arXiv:1503.01076 · Optics and Spectroscopy

Trapping of classical particles by an electromagnetic potential well deepening over time

A. Ch. Izmailov

Published Nov 1, 2015• 3 citations
arXivHTMLPDF

Abstract

On the basis of fundamental relations of classical mechanics, we established a mechanism of trapping and localization of sufficiently slow particles by an electromagnetic potential well that becomes deeper over time (up to a certain limit). It is assumed that these particles are contained in high vacuum, and acting upon them forces are not dissipative. Such potential wells can be created by means of an electromagnetic field (nonresonance radiation, in particular) with fixed spatial distribution and nondecreasing over time electric field strength. Trapping and localization of particles in such electromagnetic traps, which takes place due to gradient forces, is analyzed for laser beams with typical intensity distribution. The obtained results can be used in high-resolution spectroscopy of different particles, including, in some cases, atoms and molecules.

DOI
10.1134/s0030400x15110107

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On the basis of fundamental relations of classical mechanics, we established a mechanism of trapping and localization of sufficiently slow particles by an electromagnetic potential well that becomes deeper over time (up to a certain limit). It is assumed that these particles are contained in high vacuum, and acting upon them forces are not dissipative. Such potential wells can be created by means of an electromagnetic field (nonresonance radiation, in particular) with fixed spatial distribution and nondecreasing over time electric field strength. Trapping and localization of particles in such electromagnetic traps, which takes place due to gradient forces, is analyzed for laser beams with typical intensity distribution. The obtained results can be used in high-resolution spectroscopy of different particles, including, in some cases, atoms and molecules.
We analyze possible motion control of microparticles by means of external electromagnetic fields which induce potential wells having fixed spatial distribution but deepening over time up to some limit. It is assumed that given particles are under conditions of the high vacuum and forces acting on these particles are not dissipative. We have established slowdown of comparatively fast particles as a result of their transit through considered potential wells. This process is demonstrated on example of the nonresonance laser beam with the intensity amplifying over time. More detailed research of particle slowdown in such electromagnetic fields is carried out on the basis of simple analytical relationships obtained from basic equations of classical mechanics for the model of the one-dimensional rectangular potential well deepening over time. Method for cooling of particles, demonstrated in the present work, may be applied for essential increase of spectroscopy resolution of various microparticles, including in definite cases also atoms and molecules in the ground quantum state.
The possibility of controlling the motion of microparticles by means of external electromagnetic fields (nonresonance laser radiation, in particular) that induce potential wells for such particles, which are characterized by fixed spatial distribution but deepen over time to a certain level, are analyzed. It is assumed that the particles are located in high vacuum and are affected by nondissipative external forces. Slowing down of relatively fast particles when they pass through the discussed potential wells is shown. Such slowing down of particles is demonstrated using a nonresonance laser beam with intensity increasing over time as an example. Specific features of particle dynamics in the electromagnetic fields under consideration in the case of a one-dimensional rectangular potential well are studied in detail based on simple analytical relations derived from the fundamental equations of classical mechanics. The methods of particle cooling and localization demonstrated in the present work can substantially increase spectroscopy resolution of various microparticles, including, under certain conditions, atoms and molecules.
The possibility of a significant slowdown of particles by removing them from a localized state in an electromagnetic potential well with a fixed spatial distribution is shown with a sufficiently slow decrease in the depth of this well with time. It is believed that the considered particles are in high vacuum conditions and forces acting on them are not dissipative, i.e. these particles move without friction. Depending on whether the particles have an electric (magnetic) dipole moment, a controlled electric (magnetic) field or nonresonant laser radiation can be used to slow them down in this way. A detailed analysis of the features and efficiency of the established particle deceleration mechanism was carried out on the example of the one-dimensional rectangular potential well based on simple mathematical relationships. The obtained results can be used in the mechanics of micro- and nanoparticles in high vacuum, and under certain conditions also in ultra-high resolution spectroscopy of atoms and molecules "cooled" by the proposed method.
Author suggests and analyzes new universal trapping method of comparatively slow-speed particles of a rarefied gas medium in the potential well induced by the nonhomogeneous electromagnetic field increasing with time (up to some moment). Given method is especially effective at inelastic collisions of particles with walls of the gas cell when necessary preliminary slowdown of particles is possible for their following capture even to a highly shallow potential depth. Corresponding sufficiently compact and simple electromagnetic traps may be used for capture and accumulation not only slow-speed micro- and nano-particles in the high vacuum but also atoms and molecules of a rarefied gas in a cell.
The trapping of charged elementary particles and ions by various electromagnetic field configurations is a well established art. Last month (page 17) we told of a lone electron that was confined for almost a year in the vacuum of a Penning trap, yielding a superbly delicate observation of lowenergy relativistic hysteresis. But the trapping of electrically neutral particles—atoms in particular—is quite another matter. In the absence of the simple Lorentz force acting on a charged particle, one has to reach for a much weaker, second-order handle—the atom's magnetic or induced electric dipole moment. A variety of ingenious magnetic and laser traps have been proposed for atoms, but they all suffer a severe limitation: The weak dipole interaction with the trapping field yields only very shallow trapping potential wells, generally incapable of holding an atom moving much faster than a man can run—about 10 meters/second.