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

Further studies of modulated light in a double resonance experiment

B P Kibble, George William Series

Published Jul 23, 1963• 15 citations
Publisher

Abstract

Abstract This is an investigation, at low frequencies, of the modulation of fluorescent light which has already been found a t higher frequencies in a double resonance experiment. In the earlier work, in which the frequency of magnetic resonance was of order 10 Mc/s, the Zeeman levels of the excited atom s were well separated compared with their natural width (1 M c/s): in the present work they are completely unresolved at the centre of the magnetic resonance, which is studied a t 1 kc/s. The principal resonance phenomena are observed as before under the new conditions: they are centred on a field near to zero, while their width is greater than 1G. New resonance phenomena are also studied, which do not appear when the resonance frequency is greater than the natural width of the levels. A theory, previously published, is applied to predict the form of the new resonance curves. An identical result is predicted by the use of a classical model.

DOI
10.1098/rspa.1963.0125

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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.

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Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Jul 5, 1966•87 citations
Abstract This is an investigation, at low frequencies, of the modulation of fluorescent light which has already been found a t higher frequencies in a double resonance experiment. In the earlier work, in which the frequency of magnetic resonance was of order 10 Mc/s, the Zeeman levels of the excited atom s were well separated compared with their natural width (1 M c/s): in the present work they are completely unresolved at the centre of the magnetic resonance, which is studied a t 1 kc/s. The principal resonance phenomena are observed as before under the new conditions: they are centred on a field near to zero, while their width is greater than 1G. New resonance phenomena are also studied, which do not appear when the resonance frequency is greater than the natural width of the levels. A theory, previously published, is applied to predict the form of the new resonance curves. An identical result is predicted by the use of a classical model.
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.
Further experiments are reported in which resonance fluorescence of an atomic vapour is excited by modulated light. The system studied was the 3 P 1 level of cadmium excited by the λ 3261 λ intercombination line modulated at 462 kHz. Resonant changes in the amplitude of modulation of the fluorescent light have been observed in both static and time-dependent magnetic fields whenever the modulation frequency matches a frequency separation between the states of the excited atoms. Quantitative investigations of the shape and position of the observed resonances show good agreement between theory and experiment. The application of the technique to the spectroscopy of excited atoms is considered.
A type of double resonance experiment is reported in which resonance fluorescence from an atomic vapour is excited by modulated light. The amplitude of modulation of the fluorescent light undergoes changes which indicate an atomic resonance when the frequency of modulation is equal to the Larmor frequency of the atoms in an applied magnetic field, or equal to twice that frequency. The effects have been studied in the intercombination line, λ 3261 A, of cadmium. They are in good agreement with theoretical predictions. The method could be applied to the spectroscopy of excited atoms.
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 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.