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Physical Review A

Saturation of the 0-0 hyperfine-transition linewidth enhancement factor in optically pumped alkali-metal vapors

James C. Camparo, R. P. Frueholz

Published Sep 1, 1985• 23 citations
Publisher

Abstract

In a previous publication [Phys. Rev. A 31, 1440 (1985)], we determined the linewidth enhancement factor (LEF) of the microwave-power-broadened linewidth of the 0-0 hyperfine transition in optically pumped alkali-metal vapors. This factor is essentially a measure of the ratio of the transition linewidth to the microwave Rabi frequency. In the previous study, optical pumping out of only one hyperfine multiplet was considered. In the present study, the expressions are generalized to include optical pumping out of both hyperfine multiplets simultaneously. Dramatic changes in the behavior of the LEF as a function of the optical-pumping rate are predicted.

DOI
10.1103/physreva.32.1888

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In this thesis, we present new studies of alkali-hyperfine resonances, new optical pumping of alkali-metal atoms, and the new measurements of binary spin-exchange cross-section between alkali-metal atoms and xenon atoms. We report a large light narrowing effect of the hyperfine end-resonance signals, which was predicted from our theory and observed in our experiments. By increasing the intensity of the circularly polarized pumping beam, alkali-metal atoms are optically pumped into a state of static polarization, and trapped into the hyperfine end-state. Spin exchange between alkali-metal atoms has minimal effect on the end-resonance of the highly spinpolarized atoms. This new result will possibly benefit the design of atomic clocks and magnetometer. We also studied the pressure dependence of the atomic-clock resonance linewidth and pointed out that the linewidth was overestimated by people in the community of atomic clock. Next, we present a series study of coherent population trapping (CPT), which is a promising technique with the same or better performance compared to the traditional microwave spectroscopy. For miniature atomic clocks, CPT method is thought to be particularly advantages. From our studies, we invented a new optical-pumping method, push-pull optical pumping, which can pump atoms into nearly pure 0-0 superposition state, the superposition state of the two ground-state hyperfine sublevels with azimuthal quantum number m = 0. We believe this new invention will bring a big advantage to CPT frequency standards, the quantum state preparation for cold atoms or hot vapor, etc. We also investigated the pressure dependence of CPT excitation and the line shape of the CPT resonance theo-

•Jan 1, 2005•3 citations
In a previous publication [Phys. Rev. A 31, 1440 (1985)], we determined the linewidth enhancement factor (LEF) of the microwave-power-broadened linewidth of the 0-0 hyperfine transition in optically pumped alkali-metal vapors. This factor is essentially a measure of the ratio of the transition linewidth to the microwave Rabi frequency. In the previous study, optical pumping out of only one hyperfine multiplet was considered. In the present study, the expressions are generalized to include optical pumping out of both hyperfine multiplets simultaneously. Dramatic changes in the behavior of the LEF as a function of the optical-pumping rate are predicted.
A generalized model for the magnetic resonance signal corresponding to the 0-0 hyperfine transition in an optically pumped alkali-metal vapor is presented. Under conditions of microwave power broadening, the model predicts ``anomalous'' light broadening and ``anomalous'' relaxation narrowing of the magnetic resonance linewidth. Good agreement between theory and experiment was obtained in an experiment that confirmed the prediction of anomalous light broadening. These results show that the 0-0 hyperfine transition cannot be described as a simple two-level system; rather, the alkali-atom's nuclear spin plays an important role in determining the magnetic resonance linewidth.
The steady-state distribution of the populations of the hyperfine sublevels of the ground state of alkali atoms is calculated for the case in which the atoms are subjected to a spectrally selective optical pumping on /sup 2/S/sub 1//sub ///sub 2/--/sup 2/P/sub 1/2,3/2/ transitions and a simultaneous pumping by microwave fields which are at resonance with transitions in the hyperfine structure of the ground state, F-italic = 2, M-italic/sub F-italic/ = +- 2, +- 1bold-arrow-left-rightF-italic = 1, M-italic/sub F-italic/ = +- 1. The addition of the microwave pumping is shown to substantially increase the population difference for the O--O transition in the hyperfine structure. During selective optical pumping of the F-italic = 1 level, the population inversion which can be achieved for the O--O transition is limited by the effect of population capture. This capture can be eliminated by using incoherent microwave fields. The quality factor of the O--O resonance is calculated as a function of the parameters of the pump. The outlook for the use of composite pumping in frequency-stabilization systems is discussed.
Rate equations for the optical pumping of alkali-metal vapors simultaneously subject to pumping, relaxation in the excited state, and relaxation in the ground state are shown to yield analytic solutions for the alkali-metal electronic and nuclear-spin polarizations in the limit of weak pumping. Nuclear-spin and hyperfine-interaction effects are properly included. Analysis of the double-exponential form of the pumping transient of the ground-state electronic-spin polarization is shown to yield new methods for the measurement of cross sections for collisional relaxation in both the ground and excited states. Formulas are derived that relate relaxation cross sections to experimentally measurable parameters. Formulas describing the influence of nuclear spin on signals obtained from standard depolarization of resonance-radiation experiments also are provided. Ambiguities in earlier optical-pumping experiments and calculations arising from oversimplified descriptions of relaxation processes are discussed.
An extension of a theory of the relaxation, generation, and detection of Zeeman components in the presence of a weak static magnetic field to experiments where hyperfine coherences are also involved is presented. Our study focuses on the geometrical aspects of the optical-microwave double-resonance experiments without considering the transition-profile related phenomena. We determine the coupled evolution equations of the Zeeman and hyperfine components of the atomic density matrix in the irreducible formalism and calculate the stationary solutions to these equations. \textcopyright{} 1996 The American Physical Society.
Optical pumping is fundamental to high-precision measurement using thermal alkali-metal atoms in vapor cells. In applications such as atomic magnetometry, buffer gases (e.g., N2\mathrm{N}_2N2​ or He\mathrm{He}He) at specific pressures are introduced to quench fluorescence and mitigate wall relaxation. In the high-pressure limit (e.g., the N2\mathrm{N}_2N2​ pressure pN2>1p_{\mathrm{N}_2}> 1pN2​​>1~atm), where collisional broadening exceeds hyperfine splittings of the atoms, optical pumping theory provides a clear description of the angular momentum exchange between photons and atomic spins. However, in many magnetic sensing scenarios, the high-pressure approximation becomes inadequate as its pressure conditions are not strictly satisfied. Consequently, an explicit description of optical pumping under realistic pressures is critical for selecting operating points and enhancing system performance. To address this, we develop a unified theoretical framework of optical pumping in the quasi-high-pressure regime, where collisional broadening is comparable to the ground-state hyperfine splitting. We demonstrate that light absorption, spin polarization, and magnetic-resonance linewidth in this regime differ significantly from those predicted by the high-pressure limit and offer favorable operating conditions. Our study extends conventional modeling and offers critical guidance for atomic magnetometry operating under realistic buffer gas pressures.
In this thesis, we present new studies of alkali-hyperfine resonances, new optical pumping of alkali-metal atoms, and the new measurements of binary spin-exchange cross-section between alkali-metal atoms and xenon atoms. We report a large light narrowing effect of the hyperfine end-resonance signals, which was predicted from our theory and observed in our experiments. By increasing the intensity of the circularly polarized pumping beam, alkali-metal atoms are optically pumped into a state of static polarization, and trapped into the hyperfine end-state. Spin exchange between alkali-metal atoms has minimal effect on the end-resonance of the highly spinpolarized atoms. This new result will possibly benefit the design of atomic clocks and magnetometer. We also studied the pressure dependence of the atomic-clock resonance linewidth and pointed out that the linewidth was overestimated by people in the community of atomic clock. Next, we present a series study of coherent population trapping (CPT), which is a promising technique with the same or better performance compared to the traditional microwave spectroscopy. For miniature atomic clocks, CPT method is thought to be particularly advantages. From our studies, we invented a new optical-pumping method, push-pull optical pumping, which can pump atoms into nearly pure 0-0 superposition state, the superposition state of the two ground-state hyperfine sublevels with azimuthal quantum number m = 0. We believe this new invention will bring a big advantage to CPT frequency standards, the quantum state preparation for cold atoms or hot vapor, etc. We also investigated the pressure dependence of CPT excitation and the line shape of the CPT resonance theo-