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arXiv:physics/0301051 · Physical Review A

Theory of dark resonances for alkali-metal vapors in a buffer-gas cell

А. В. Тайченачев, Valeriy I. Yudin, R. Wynands, M. Stähler, John E. Kitching, Leo W. Hollberg

Published Mar 21, 2003• 70 citations
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Abstract

We develop an analytical theory of dark resonances that accounts for the full atomic-level structure, as well as all field-induced effects such as coherence preparation, optical pumping, ac Stark shifts, and power broadening. The analysis uses a model based on relaxation constants, which assumes the total collisional depolarization of the excited state. A good qualitative agreement with the experiments for Cs in Ne is obtained.

DOI
10.1103/physreva.67.033810

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Physical Review A•Sep 1, 1994•8 citations
We develop an analytical theory of dark resonances that accounts for the full atomic-level structure, as well as all field-induced effects such as coherence preparation, optical pumping, ac Stark shifts, and power broadening. The analysis uses a model based on relaxation constants, which assumes the total collisional depolarization of the excited state. A good qualitative agreement with the experiments for Cs in Ne is obtained.
Summary form only given. We develop a new analytical theory, which takes into account the full atomic level structure (both Zeeman and hyperfine) as well as all field-induced effects such as coherence preparation, optical pumping, ac Stark shifts, and power broadening. The crucial assumption is the total collisional depolarization in the excited state. In addition, we add the (optional) approximations of homogeneous broadening and low-saturation. With these approximations, we get a quite general analytical result for the atomic response, which holds for arbitrary excitation schemes (D2 as well as D1 lines), field polarizations, and magnetic field directions. Specifically, in the case of sufficiently large magnetic field, when only two states participate in the coherence preparation, analytical lineshapes coincide exactly with the Lorentz-Lorentz model heuristically introduced to fit experimental data.
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.
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.
Dark resonances with widths below 30 Hz have been observed in a rubidium cell filled with neon as buffer gas at room temperature. We compare an approximate analytic solution of a \ensuremath{\Lambda} system to our data and show that under our experimental conditions the presence of the buffer gas reduces the power broadening of the dark resonances by two orders of magnitude. We also present numerical calculations that take into account the thermal motion and velocity-changing collisions with the buffer-gas atoms. The resulting dark-resonance features exhibit strong Dicke-type narrowing effects and thereby explain the elimination of Doppler shifts and Doppler broadening, leading to observation of a single ultranarrow dark line.
We present a comprehensive theory of nuclear spin polarization of 3He{}^{3}\mathrm{He}3He and 129Xe{}^{129}\mathrm{Xe}129Xe gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with N2{\mathrm{N}}_{2}N2​ or H2{\mathrm{H}}_{2}H2​ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.
The relaxation and generation of multipole orientations in a heavy-alkali-metal vapor in the presence of a weak static magnetic field are theoretically studied both for populations and for Zeeman coherences by taking into account the effects on the evolution of the atomic density matrix of the relaxation processes (by alkali-atom--buffer-gas, alkali-atom--alkali-atom with spin exchange and alkali-atom--cell-wall collisions) and of the optical pumping with any light polarization and spectral distribution. The dependence of the stationary-state multipole orientations on the pumping characteristic parameters is numerically analyzed. The detection process of these orientations is also studied.