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C R C Critical Reviews in Analytical Chemistry

Coherent Forward Scattering Spectroscopy (Cfs): Present Status and Future Perspectives

Gerd M. Hermann, Kay Niemax

Published Jan 1, 1988• 6 citations
Publisher

Abstract

I. INTRODUCTION A. Level-Crossing Phenomena and the Effect of Coherent Forward Scattering Coherent forward.scattering (CFS—used for the physical effect as well as for the approach of coherent forward scattering spectroscopy) has been investigated first in connection with atomic resonance radiation phenomena like double resonance and level-crossing effects.1 The very early level crossing has been measured in lateral fluorescence in a weak magnetic field.2 This “zero-field level crossing” in lateral detected resonance fluorescence is called “Hanle effect”3 and can be classically described by the model of an atomic oscillator, emitting during its Larmor precession with respect to the applied magnetic field (Figure 1).

DOI
10.1080/10408348808542814

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The forward scattering of resonance radiation, with special reference to double resonance and level-crossing experiments

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Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations

INTRODUCTORY PAPER ON HANLE EFFECT, LEVEL CROSSING AND DOUBLE RESONANCE EXPERIMENTS

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The author reviews experimental techniques which use the properties of the scattering of light by free atoms in the neighborhood of a resonant frequency for investigation of excited atomic energy levels : - Hanle effect and its recent developments : (Hanle effect in an electrostatic field, molecular Hanle effect, Hanle effect of stepwise excited levels, sensitized fluorescence Hanle effect). - Double resonance experiments and its variations (« light beats »), excitation with modulated light...). - Level crossings and anticrossings (including of the study Stark effect by level crossings).

Le Journal de Physique Colloques•Jan 1, 1969•1 citation

Coherence Effects in Resonance Fluorescence

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The crossed-level method of atomic spectroscopy is discussed and the angular distribution formula for both the incoherent and coherent resonance scattering is derived. The form of this distribution function, as given here, explicity displays the geometric factors depending on radiation propagation vectors. With the application to hydrogen in mind, the distribution function is expressed explicitly for single electron transitions with external fields possessing axial symmetry. The properties of the distribution function are discussed with emphasis on the case of unpolarized radiation. For the case of hydrogen there are two possible applications of major interest. The first concerns the possibility of a precision measurement of the $2p$ fine structure splitting and, hence, a determination of the fine structure constant. Explicit results for the shape and other properties of the resonance line with a uniform magnetic field obtained. The other application is concerned with the possibility of measuring the $2s\ensuremath{-}2p$ Lamb splitting. This requires an electric field parallel to the magnetic field. Unfortunately, the level crossings which are sensitive to the Lamb splitting cannot radiate sufficiently rapidly while those which do radiate appreciably occur at field strengths which are extremely insensitive to the Lamb splitting.

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The Hanle effect

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The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.

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"Anticrossing" Signals in Resonance Fluorescence

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Physical Review•Jan 5, 1967•125 citations

Oriented atoms in weak magnetic fields

Peter Hannaford

This article reviews the early investigations of Series on the resonance absorption and fluorescence of light by samples of oriented atoms dagger subjected to static and oscillatory magnetic fields. These investigations include experiments on optical-radiofrequency double resonance, light beats in double resonance, circulation of coherence in optical pumping, and time-biasing in level-crossing spectroscopy. It then describes some selected laser spectroscopy experiments involving the interaction of optically oriented atoms with static magnetic fields that were stimulated by the earlier work of Series, including experiments on hyperfine structure quantum beats, cascade quantum beats, ground-state quantum beats in transmission, and optogalvanic detection of atomic coherences. Finally, it describes some current work which uses static magnetic fields to manipulate the external variables (momentum and position) of laser-cooled oriented atoms, with applications in the rapidly developing field of atom optics and atom interferometry.

Physica Scripta•Jan 1, 1997•6 citations
I. INTRODUCTION A. Level-Crossing Phenomena and the Effect of Coherent Forward Scattering Coherent forward.scattering (CFS—used for the physical effect as well as for the approach of coherent forward scattering spectroscopy) has been investigated first in connection with atomic resonance radiation phenomena like double resonance and level-crossing effects.1 The very early level crossing has been measured in lateral fluorescence in a weak magnetic field.2 This “zero-field level crossing” in lateral detected resonance fluorescence is called “Hanle effect”3 and can be classically described by the model of an atomic oscillator, emitting during its Larmor precession with respect to the applied magnetic field (Figure 1).
Abstract A theoretical and experimental study has been made of the intensity of forward scattered light in conditions of radio-frequency double resonance and level-crossing. The main conclusions are (i) that the magnetic resonance and level-crossing effects which are familiar in the laterally scattered light are to be found also in the forward scattered light, but (ii) that the resonance curves are Doppler-broadened, and the strength of the oscillatory field necessary to generate them is correspondingly increased, and (iii) that coherence narrowing is much more pronounced in forward than in lateral scattering. The differences derive from the coherence between the radiation from different atoms which is present in forward, but not in lateral scattering, and which is implicitly recognized in the classical theory of the propagation of light in polarizable media. The equations of electromagnetism form the basis of the present analysis. In the presence of the oscillatory magnetic field the polarization tensor is complex and time-dependent. The time dependence leads to the result that the number of eigenwaves necessary to describe propagated waves in the medium is four, as against the usual two. An arbitrary wave is resolved into a superposition of the four eigenwaves, all of which have different propagation constants. The analysis is very general, and is applicable to experiments with lasers. The components of the polarization tensor are derived by finding first the polarizability of individual atoms from a semi-classical theory of their interaction with light and magnetic fields. The macroscopic polarization, obtained by summing over individual atoms, is then given by folding the individual polarizabilities with the Doppler distribution of resonance frequencies. In the particular case studied in detail (the inter-combination resonance line, 2537 A, in mercury), the Doppler width is much greater than the radiation width, and the imaginary (absorptive) part of the polarizability is Gaussian. Expressions are derived in a ‘weak scattering’ approximation for the intensity of the forward scattered light. They are magnetic resonance functions which are found to be the Doppler-broadened equivalents of the familiar functions, based on Lorentzians, characteristic of scattering by a single atom. In the case of double resonance the forward scattered light is strongly modulated, as is the laterally scattered light. To investigate coherence narrowing, the zero-field level-crossing has been studied with the restriction of ‘weak scattering’ removed. The result is obtained that the width of levelcrossing curves is inversely proportional to the vapour density for magnetic fields such that the Zeeman splitting is small in relation to the Doppler width. This analytical result has been verified experimentally.
The author reviews experimental techniques which use the properties of the scattering of light by free atoms in the neighborhood of a resonant frequency for investigation of excited atomic energy levels : - Hanle effect and its recent developments : (Hanle effect in an electrostatic field, molecular Hanle effect, Hanle effect of stepwise excited levels, sensitized fluorescence Hanle effect). - Double resonance experiments and its variations (« light beats »), excitation with modulated light...). - Level crossings and anticrossings (including of the study Stark effect by level crossings).
The crossed-level method of atomic spectroscopy is discussed and the angular distribution formula for both the incoherent and coherent resonance scattering is derived. The form of this distribution function, as given here, explicity displays the geometric factors depending on radiation propagation vectors. With the application to hydrogen in mind, the distribution function is expressed explicitly for single electron transitions with external fields possessing axial symmetry. The properties of the distribution function are discussed with emphasis on the case of unpolarized radiation. For the case of hydrogen there are two possible applications of major interest. The first concerns the possibility of a precision measurement of the 2p2p2p fine structure splitting and, hence, a determination of the fine structure constant. Explicit results for the shape and other properties of the resonance line with a uniform magnetic field obtained. The other application is concerned with the possibility of measuring the $2s\ensuremath{-}2p$ Lamb splitting. This requires an electric field parallel to the magnetic field. Unfortunately, the level crossings which are sensitive to the Lamb splitting cannot radiate sufficiently rapidly while those which do radiate appreciably occur at field strengths which are extremely insensitive to the Lamb splitting.
The history of the discovery, study, and explanation of the effect discovered fifty years ago by the German physicist Hanle and its development and generalization by the French school of physicists led by Kastler are described. The effect is observed optically in an increase in the degree of depolarization of the resonance fluorescence. It is studied in the range of magnetic fields in which the Zeeman splitting of the atomic magnetic sublevels does not exceed the level widths determined by thermal relaxation mechanisms and electromagnetic interaction. It is a direct optical manifestation of interference of degenerate atomic states and is intimately connected with the conservation law for the angular momentum of the photon-atom system. In the review, different applications of the effect to the measurement of mean lifetimes, linewidths, and Stark splitting constants of atoms in excited states are given. The resonance scattering of light by atoms in the ground state in a weak magnetic field is considered in detail—in particular, in the presence of radio-frequency magnetic fields oriented in different ways. The different possible types of parametric resonances in one or two radio-frequency fields for arbitrary orientation of the constant magnetic field are interpreted as the effect of crossing of the levels of an atom that is dressed by the radio-frequency field. Applications of the effect in the quantum magnetometry of ultraweak fields (down to 10-10 Oe) are examined.
The level-crossing technique of atomic spectroscopy utilizes the spatial interference in the scattering of resonance radiation which can occur when two Zeeman levels of an atom are brought into coincidence ("crossed") by the application of an external magnetic field. "Anticrossing" refers to the case where the two levels involved are coupled by a small static interaction. In this paper the general expression for an anticrossing signal is given and its predictions compared with signals observed in the 22P2 ^{2}P22P term of Li. It is shown that anticrossings produce signals in many experimental situations for which there would be no signal from a normal level crossing.
This article reviews the early investigations of Series on the resonance absorption and fluorescence of light by samples of oriented atoms dagger subjected to static and oscillatory magnetic fields. These investigations include experiments on optical-radiofrequency double resonance, light beats in double resonance, circulation of coherence in optical pumping, and time-biasing in level-crossing spectroscopy. It then describes some selected laser spectroscopy experiments involving the interaction of optically oriented atoms with static magnetic fields that were stimulated by the earlier work of Series, including experiments on hyperfine structure quantum beats, cascade quantum beats, ground-state quantum beats in transmission, and optogalvanic detection of atomic coherences. Finally, it describes some current work which uses static magnetic fields to manipulate the external variables (momentum and position) of laser-cooled oriented atoms, with applications in the rapidly developing field of atom optics and atom interferometry.