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Physical Review

Modulation of a Fluorescent Light Beam by an Optically Pumped Vapor Undergoing a Double-Quantum Resonance

W. Franzen, P.B. Newell, Dean S. Edmonds

Published Jun 5, 1968• 7 citations
Publisher

Abstract

The high-frequency modulation of a light beam scattered by optically-pumped ${\mathrm{Rb}}^{85}$ vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized ${D}_{1}$ pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a ${D}_{2}$ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of ${\mathrm{Rb}}^{85}$, such a modulation has been observed, and its resonant behavior has been found to agree with theory.

DOI
10.1103/physrev.170.17

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Physical Review Applied•Mar 25, 2025•4 citations
The high-frequency modulation of a light beam scattered by optically-pumped Rb85{\mathrm{Rb}}^{85}Rb85 vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a \ensuremathσ+{\ensuremath{\sigma}}^{+}\ensuremathσ+-polarized D1{D}_{1}D1​ pumping beam and a \ensuremathπ\ensuremath{\pi}\ensuremathπ-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a \ensuremathσ\ensuremath{\sigma}\ensuremathσ polarizer and a D2{D}_{2}D2​ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of Rb85{\mathrm{Rb}}^{85}Rb85, such a modulation has been observed, and its resonant behavior has been found to agree with theory.
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.
Abstract : A method for the optical observation of nutational resonance in optically pumped rubidium vapor has been studied both experimentally and theoretically. The method consists of pulsemodulating an rf magnetic field a one of the Zeeman resonance frequencies of the vapor and observing the resulting damped transient modulation in the transmitted light intensity. Of particular interest is the application of this method to a study of the spin relaxation of vapor atoms as influenced by the physical parameters of the system, in the case where the applied steady magnetic field is intense enough to cause individual Zeeman intervals to become noticeably unequal. Both single and double quantum resonances at a wide spectrum of Zeeman transitions of Rb-85 vapor diffusing through neon and helium buffer gases have been observed and identified, and the damping of the transient nutations in light intensity has been recorded under a variety of conditions. (Author)
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.
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.
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.
The detection of narrow and high-amplitude optical resonances in atomic cells is of crucial importance for the development of compact and high-stability lasers or vapor-cell optical references. In this work, using monochromatic light and appropriate polarization settings for the counterpropagating pump and probe beams, we demonstrate the detection of enhanced-absorption sub-Doppler resonances on the D1{D}_{1}D1​ line of the Rb\mathrm{Rb}Rb atom. We report a theoretical model showing that the Zeeman coherence induced between magnetic sublevels---especially in the $F\ensuremath{\rightarrow}{F}^{\ensuremath{'}}=F\ensuremath{-}1$ systems, with FFF and ${F}^{\ensuremath{'}}$ being the hyperfine quantum numbers of the ground and excited states, respectively---plays a key role in the observed enhanced-absorption process. The theoretically predicted behavior matches the experimental observations well. The impact of light polarization, laser intensity, magnetic field, and cell temperature on the Doppler-free resonance features is experimentally investigated. For application, two identical diode lasers are frequency-stabilized onto enhanced-absorption sub-Doppler resonances. The fractional frequency stability of the laser beatnote is measured to be $1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 1s1\phantom{\rule{0.1em}{0ex}}\mathrm{s}1s and $8.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at 104s{10}^{4}\phantom{\rule{0.1em}{0ex}}\mathrm{s}104s. These results demonstrate the potential of this scheme for the implementation of a compact or even chip-scale optical frequency reference, which might find applications in instrumentation, navigation, and metrology.