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Proceedings of the Royal Society of London A Mathematical and Physical Sciences

Theory of modulation of light in a double resonance experiment

John N. Dodd, George William Series

Published Sep 19, 1961• 106 citations
Publisher

Abstract

Abstract A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (63P1 — 6 1S0), A2537 A, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, w0, is predicted, and resonant effects at static magnetic fields, 0, 1/2, 1, 3/2, 2 and 3 times H0, the field for which w0 is the Larm or frequency. Resonances at fields other than H0 are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A ‘frequency diagram’ is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states mJ = 0, ± 1, of 3P1. The resonances at fields other than H0 may be associated with intersections of frequency levels belonging to different mJ.

DOI
10.1098/rspa.1961.0165

Related papers

The modulation of light in a double resonance experiment

John N. Dodd, George William Series, Martin John Taylor

Abstract This work is an experimental study of the modulation which has been found in resonance radiation when the fluorescing vapour is subjected to static and radio-frequency magnetic fields, as in the double resonance experiment of Brossel & Bitter. The particular example chosen for study in this work also was the resonance line λ 2537 Å of mercury. The experimental observations are compared with the predictions of a theoretical treatment which has already been published. The phenomenon was studied under a variety of geometrical configurations. When the polarization of the exciting light allowed excitation to only one excited state (a component of a Zeeman multiplet), the depth of modulation was found to depend on the closeness to resonance of the frequency, ω0, of the radio-frequency field to the Larmor precessional frequency, ω = γH , in the static field H. When the polarization of the exciting light allowed excitation to more than one component of the multiplet, resonance effects were found in the depth of modulation and in the mean intensity of the fluorescent light at fields where the applied frequency was equal, not to the Larmor frequency alone, but to combinations of the Larmor frequency with the nutational frequency. From a quantum-mechanical point of view, these new phenomena are related to the interference effects which are found in resonance fluorescence when there is degeneracy between excited states: in the present case the degeneracy is induced by the radio-frequency field. The ease with which the geometrical conditions could be altered allowed the theory to be tested in considerable detail without quantitative assessment of the resonance line contours: nevertheless, a quantitative study was made of one particular feature. The predictions of the theory were confirmed at all points where they were tested.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Apr 23, 1963•34 citations

Theory of frequency and polarization modulation in resonance fluorescence

George William Series

A treatment of resonance fluorescence is given in which the properties of the incident and scattered light are expressed in terms of coherency matrices. Calculations are made for two successive scattering processes corresponding to the experiments described in an accompanying paper. For the first process the scattering atoms are subjected to a magnetic field consisting of parallel static and oscillating components. The fluorescent light is frequency-modulated and may also be polarization-modulated. This light excites fluorescence in a second cell in which the atoms are subjected to a static magnetic field. The equations show under what conditions the second fluorescence is intensity-modulated and describe the resonances in the amplitude of modulation which occur when the modulation frequency matches a Zeeman interval of the excited atoms.

Journal of Physics B Atomic and Molecular Physics•Jan 1, 1970•10 citations

Frequency- and polarization-modulated light in double resonance experiments on mercury vapour

G. D. Chapman, George William Series

Frequency-modulated light was generated by the application of a magnetic field oscillating at frequencies in the range 1-10 MHz to mercury vapour undergoing resonance fluorescence. The characteristics of the fluorescent light have been studied. When the primary illumination in the plane perpendicular to the field is anisotropic the sigma components are coherently excited. The light emitted along the field is then polarization-modulated. It becomes intensity-modulated if it is passed through a linear analyser. The light emitted obliquely to the magnetic field is intensity-modulated without passing through an analyser. The amplitudes of these modulations show resonance behaviour under the application of an additional static field parallel to the oscillating field. The polarization-modulated light was used to excite resonance fluorescence in a second cell of mercury vapour. The fluorescent light is intensity-modulated. The amplitude of modulation shows resonance behaviour when harmonics of the driving frequency coincide with Zeeman intervals in the excited atoms. These resonances have been explored in detail. They are satisfactorily interpreted by a theory given in an accompanying paper.

Journal of Physics B Atomic and Molecular Physics•Jan 1, 1970•11 citations

Density matrix formalism applied to light beat experiments

J. P. BARRATt

Recent experiments (Dodd, Fox, Series & Taylor, I959; Colegrove, Franken, Lewis & Sands, i959) have shown that coherence effects can be observed between the Zeeman components of an optical line provided some coherence exists in the excited state. This coherence may be due to a radio-frequency field inducing transitions between the Zeeman sublevels of this excited state, or to the excitation process itself or to both. These effects are actually more or less a generalization of the well-known Hanle's experiments on the polarization of resonance radiation.: In the case of 'double resonance' experiments (Dodd et al. I959), they appear as a modulation of the intensity of the fluorescence radiation at one of the harmonics of the r.f. field; they can be interpreted as interference between the radiations of different frequencies emitted by the atoms which are submitted to the 'double resonance' ('light beat'). These coherence effects are related to those observed in the trapping of resonance radiation. In this paper, the methods used in former papers (Barrat I959 a, b and c, hereafter referred to as I, II, III) for the problem of light trapping are applied to the light beats experiments, using a density matrix formalism. The expression for the density matrix representing the states of the atoms just after the excitation will first be derived; then the intensity of the re-emitted light will be calculated. It will be shown finally how this method can be applied to practical problems. Notation unexplained in this paper is the same as in papers on coherence in light trapping (papers I, II and III).

•Jan 1, 2016•0 citations

Proposal for Measuring Lamb Shifts by the Study of Modulated, Fluorescent Light

George William Series

A method is proposed for measuring the interval between two atomic energy levels of different parity. The method is related to optical radio-frequency double resonance and level-crossing experiments in that the behavior of atoms in excited states is deduced from observations of the fluorescent light. In contrast with the oscillating electric field ordinarily used to stimulate transitions between states of opposite parity, a small, static electric field is required. The rate at which atoms are excited is required to be modulated; consequently, the fluorescent light will be modulated. The amplitude of modulation will depend on the parameters. A general expression is derived. Two cases are of particular interest: (1) A resonance effect is predicted if the frequency of modulation matches the interval between the perturbed levels. This effect could best be studied for frequencies much greater than the combined natural widths of the levels. (2) For frequencies smaller than the natural width, a level-crossing effect is predicted whose peak occurs at the point of intersection of the unperturbed levels. The method might be applied to measure intervals between the $2s$ and $2p$ levels in hydrogen. Estimates are given of the required fields and frequencies.

Physical Review•Nov 2, 1964•44 citations

Magnetic resonance at nutational frequencies

Alan Corney, George William Series

An optical radio-frequency double resonance experiment on the level 5 3 P 1 of cadmium is described. Atoms in a static magnetic field and a field oscillating at about 2 Mc/s are excited by light modulated at 462 kc/s. Resonance effects in the fluorescent light are found when the modulation frequency is near the nutational frequency γ[( H - H 0 ) 2 + H 1 2 ] 1/2 .

Proceedings of the Physical Society•Feb 1, 1964•12 citations
Abstract A theory is formulated to describe the modulation which has been observed in fluorescent light from atoms subjected simultaneously to optical and radio-frequency radiation. The optical field stimulates one or more of a set of excited states of the atom, between which the radio-frequency field establishes coherence. This coherence is manifest in the fluorescent radiation. Interference between radiations of different frequency leads to modulation. General expressions are given for the intensity of the fluorescent light as a function of time. The Zeeman structure of the transition (63P1 — 6 1S0), A2537 A, in mercury is studied in detail. Modulation at frequencies, 1, 2, 3 and 4 times that of the radio-frequency field, w0, is predicted, and resonant effects at static magnetic fields, 0, 1/2, 1, 3/2, 2 and 3 times H0, the field for which w0 is the Larm or frequency. Resonances at fields other than H0 are due to excitation with light of mixed polarization. Most of the predicted effects have been found experimentally. A ‘frequency diagram’ is introduced and discussed, to represent the combined effects of static and radio-frequency magnetic fields. To each excited state belong a set of r frequencies, where r is the number of states linked by the radio-frequency perturbation. The 9 levels are drawn, as functions of H, for the states mJ = 0, ± 1, of 3P1. The resonances at fields other than H0 may be associated with intersections of frequency levels belonging to different mJ.
Abstract This work is an experimental study of the modulation which has been found in resonance radiation when the fluorescing vapour is subjected to static and radio-frequency magnetic fields, as in the double resonance experiment of Brossel & Bitter. The particular example chosen for study in this work also was the resonance line λ 2537 Å of mercury. The experimental observations are compared with the predictions of a theoretical treatment which has already been published. The phenomenon was studied under a variety of geometrical configurations. When the polarization of the exciting light allowed excitation to only one excited state (a component of a Zeeman multiplet), the depth of modulation was found to depend on the closeness to resonance of the frequency, ω0, of the radio-frequency field to the Larmor precessional frequency, ω = γH , in the static field H. When the polarization of the exciting light allowed excitation to more than one component of the multiplet, resonance effects were found in the depth of modulation and in the mean intensity of the fluorescent light at fields where the applied frequency was equal, not to the Larmor frequency alone, but to combinations of the Larmor frequency with the nutational frequency. From a quantum-mechanical point of view, these new phenomena are related to the interference effects which are found in resonance fluorescence when there is degeneracy between excited states: in the present case the degeneracy is induced by the radio-frequency field. The ease with which the geometrical conditions could be altered allowed the theory to be tested in considerable detail without quantitative assessment of the resonance line contours: nevertheless, a quantitative study was made of one particular feature. The predictions of the theory were confirmed at all points where they were tested.
A treatment of resonance fluorescence is given in which the properties of the incident and scattered light are expressed in terms of coherency matrices. Calculations are made for two successive scattering processes corresponding to the experiments described in an accompanying paper. For the first process the scattering atoms are subjected to a magnetic field consisting of parallel static and oscillating components. The fluorescent light is frequency-modulated and may also be polarization-modulated. This light excites fluorescence in a second cell in which the atoms are subjected to a static magnetic field. The equations show under what conditions the second fluorescence is intensity-modulated and describe the resonances in the amplitude of modulation which occur when the modulation frequency matches a Zeeman interval of the excited atoms.
Frequency-modulated light was generated by the application of a magnetic field oscillating at frequencies in the range 1-10 MHz to mercury vapour undergoing resonance fluorescence. The characteristics of the fluorescent light have been studied. When the primary illumination in the plane perpendicular to the field is anisotropic the sigma components are coherently excited. The light emitted along the field is then polarization-modulated. It becomes intensity-modulated if it is passed through a linear analyser. The light emitted obliquely to the magnetic field is intensity-modulated without passing through an analyser. The amplitudes of these modulations show resonance behaviour under the application of an additional static field parallel to the oscillating field. The polarization-modulated light was used to excite resonance fluorescence in a second cell of mercury vapour. The fluorescent light is intensity-modulated. The amplitude of modulation shows resonance behaviour when harmonics of the driving frequency coincide with Zeeman intervals in the excited atoms. These resonances have been explored in detail. They are satisfactorily interpreted by a theory given in an accompanying paper.
Recent experiments (Dodd, Fox, Series & Taylor, I959; Colegrove, Franken, Lewis & Sands, i959) have shown that coherence effects can be observed between the Zeeman components of an optical line provided some coherence exists in the excited state. This coherence may be due to a radio-frequency field inducing transitions between the Zeeman sublevels of this excited state, or to the excitation process itself or to both. These effects are actually more or less a generalization of the well-known Hanle's experiments on the polarization of resonance radiation.: In the case of 'double resonance' experiments (Dodd et al. I959), they appear as a modulation of the intensity of the fluorescence radiation at one of the harmonics of the r.f. field; they can be interpreted as interference between the radiations of different frequencies emitted by the atoms which are submitted to the 'double resonance' ('light beat'). These coherence effects are related to those observed in the trapping of resonance radiation. In this paper, the methods used in former papers (Barrat I959 a, b and c, hereafter referred to as I, II, III) for the problem of light trapping are applied to the light beats experiments, using a density matrix formalism. The expression for the density matrix representing the states of the atoms just after the excitation will first be derived; then the intensity of the re-emitted light will be calculated. It will be shown finally how this method can be applied to practical problems. Notation unexplained in this paper is the same as in papers on coherence in light trapping (papers I, II and III).
A method is proposed for measuring the interval between two atomic energy levels of different parity. The method is related to optical radio-frequency double resonance and level-crossing experiments in that the behavior of atoms in excited states is deduced from observations of the fluorescent light. In contrast with the oscillating electric field ordinarily used to stimulate transitions between states of opposite parity, a small, static electric field is required. The rate at which atoms are excited is required to be modulated; consequently, the fluorescent light will be modulated. The amplitude of modulation will depend on the parameters. A general expression is derived. Two cases are of particular interest: (1) A resonance effect is predicted if the frequency of modulation matches the interval between the perturbed levels. This effect could best be studied for frequencies much greater than the combined natural widths of the levels. (2) For frequencies smaller than the natural width, a level-crossing effect is predicted whose peak occurs at the point of intersection of the unperturbed levels. The method might be applied to measure intervals between the 2s2s2s and 2p2p2p levels in hydrogen. Estimates are given of the required fields and frequencies.