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Physical Review A

Billiard-ball echo model

Raymond John Beach, Sven R. Hartmann, Richard M. Friedberg

Published May 1, 1982• 27 citations
Publisher

Abstract

Photon echoes in gaseous media are explained with the use of a simple heuristic model in which the atoms behave like composite billiard balls. The laser providing the excitation pulses becomes an atom smasher which "splits" the atoms and then by judicious programming puts them back together again. The most general photon-echo reordering process is explained without recourse to formal analysis so that an intuitive feeling is obtained which works equally well for the ordinary two-pulse photon echo, the Raman echo, the trilevel echo, the grating echo, etc. A formal analysis of the billiard-ball echo model is presented in its support.

DOI
10.1103/physreva.25.2658

Related papers

Elliptical billiard-ball echo model

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The billiard-ball echo model is expanded to include the effects of using sub-Doppler-linewidth lasers in photon-echo experiments. The simple heuristic model which emerges explains such echo phenomena in gases as the echo time width and the degradation of echo intensity with angling of the excitation pulses. We derive simple results in the small-pulsearea limit and give formal expressions for excitation pulses of arbitrary area.

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Echoes in gaseous media: A generalized theory of rephasing phenomena

THOMAS W. MOSSBERG, Ravinder Kachru, Sven R. Hartmann +1 more

The primary objective of this paper is to provide a formalism to predict and characterize the echoes which may be produced in a gaseous sample by an arbitrary sequence of one- or two-frequency laser excitation pulses which successively transfer atomic population between two or more atomic energy levels. The resulting echoes can occur at times which depend on the relative frequencies of the excitation pulses as well as on the times at which the pulses were applied. Using an idealized model of the excitation pulses and the atoms, the authors derive a simple transformation equation which provides the density matrix of a single atom after a general excitation sequence. Equations are derived which utilize the single-atom density matrix to predict the properties of the echoes (if any) which result. The means by which the sample of atoms "remembers" the information necessary to produce different types of echoes is discussed, and it is then shown how a study of the echo can provide information concerning the atomic relaxation processes which tend to destroy this information. It is observed that trilevel echoes can be used to determine the relaxation characteristics of superposition states between energy levels coupled by two-photon transitions. In the case of certain other echoes (such as the three-excitation-pulse stimulated echo) the authors discuss the heretofore unappreciated fact that the sample remembers the "echo information" via a nonthermal velocity distribution of the atoms in one specific atomic state. In these cases a study of the echo behavior can provide information pertaining to the relaxation processes affecting only the one atomic state. The formalism developed is used to predict the properties of several echo effects. First, to provide a connection with previous work, the well-known photon echo is briefly discussed. Then important new properties of the three-excitation-pulse-stimulated echo are described. Finally, three different types of trilevel echo are analyzed. Each of the trilevel echoes discussed has widespread applicability in the study of relaxation processes.

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A simple diagrammatic approach to the description of laser-induced macroscopic ordering processes in gases is developed. We derive a set of simple rules which can be used to construct diagrams---each of which represents the macroscopic properties of a gaseous sample after it has been excited by a particular sequence of short, resonant, laser-excitation pulses. The features of the diagrams which signify various forms of laser-induced macroscopic ordering, e.g., photon echoes, grating echoes, stimulated echoes, standing-wave echoes, trilevel echoes, nonthermal velocity distributions, etc., are discussed. Important differences between the actions of traveling-wave and standing-wave excitation pulses are pointed out. The diagrammatic technique presented here for gases can easily be generalized to describe laser-induced macroscopic ordering in solids as well.

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Photon Echo in Gaseous Media

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Optical echos in gaseous media are investigated in order to determine the conditions under which an echo would be expected. The results are similar to those for a solid, except that the time between exciting pulses is limited when the two pulses do not travel in the same direction. With increasing pulse separation collisions reduce the echo intensity in a way which is characteristic of the type of collision process.

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Billiard balls and matter-wave interferometry

Richard M. Friedberg, Sven R. Hartmann

The billiard-ball model (BBM) is redeveloped to allow quantitative diagrammatic evaluation of signal parameters associated with optical coherent transient experiments. It is expanded to include the action of external forces and fields as well as to include atomic-beam-type experiments. Matter-wave interferometric experiments are examined in the context of the BBM and their relationship to photon-echo experiments is explored.

Physical Review A•Aug 1, 1993•29 citations
Photon echoes in gaseous media are explained with the use of a simple heuristic model in which the atoms behave like composite billiard balls. The laser providing the excitation pulses becomes an atom smasher which "splits" the atoms and then by judicious programming puts them back together again. The most general photon-echo reordering process is explained without recourse to formal analysis so that an intuitive feeling is obtained which works equally well for the ordinary two-pulse photon echo, the Raman echo, the trilevel echo, the grating echo, etc. A formal analysis of the billiard-ball echo model is presented in its support.
The primary objective of this paper is to provide a formalism to predict and characterize the echoes which may be produced in a gaseous sample by an arbitrary sequence of one- or two-frequency laser excitation pulses which successively transfer atomic population between two or more atomic energy levels. The resulting echoes can occur at times which depend on the relative frequencies of the excitation pulses as well as on the times at which the pulses were applied. Using an idealized model of the excitation pulses and the atoms, the authors derive a simple transformation equation which provides the density matrix of a single atom after a general excitation sequence. Equations are derived which utilize the single-atom density matrix to predict the properties of the echoes (if any) which result. The means by which the sample of atoms "remembers" the information necessary to produce different types of echoes is discussed, and it is then shown how a study of the echo can provide information concerning the atomic relaxation processes which tend to destroy this information. It is observed that trilevel echoes can be used to determine the relaxation characteristics of superposition states between energy levels coupled by two-photon transitions. In the case of certain other echoes (such as the three-excitation-pulse stimulated echo) the authors discuss the heretofore unappreciated fact that the sample remembers the "echo information" via a nonthermal velocity distribution of the atoms in one specific atomic state. In these cases a study of the echo behavior can provide information pertaining to the relaxation processes affecting only the one atomic state. The formalism developed is used to predict the properties of several echo effects. First, to provide a connection with previous work, the well-known photon echo is briefly discussed. Then important new properties of the three-excitation-pulse-stimulated echo are described. Finally, three different types of trilevel echo are analyzed. Each of the trilevel echoes discussed has widespread applicability in the study of relaxation processes.
A simple diagrammatic approach to the description of laser-induced macroscopic ordering processes in gases is developed. We derive a set of simple rules which can be used to construct diagrams---each of which represents the macroscopic properties of a gaseous sample after it has been excited by a particular sequence of short, resonant, laser-excitation pulses. The features of the diagrams which signify various forms of laser-induced macroscopic ordering, e.g., photon echoes, grating echoes, stimulated echoes, standing-wave echoes, trilevel echoes, nonthermal velocity distributions, etc., are discussed. Important differences between the actions of traveling-wave and standing-wave excitation pulses are pointed out. The diagrammatic technique presented here for gases can easily be generalized to describe laser-induced macroscopic ordering in solids as well.