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Numerical analysis of the optical pumping process coupled with 23Na D2 manifold modeled as a partially resolved hyperfine structure

Xiaoxu Zhang, Xingqiao Ma, Yiping Chen, Qiongying Ren, Hua Zhao

Published Apr 1, 2020• 0 citations
Publisher

Abstract

All magnetometers using alkali atoms rely on the monochromatic light driving the optical pumping process in the D1 or D2 line to create spin-polarized atoms. In the study of a sodium (Na) magnetometer, we find that 23Na exhibits the same hyperfine structure as exhibited by the 87Rb atom but differs from Rb in terms of level splitting. The narrowly split hyperfine levels of the 23Na 3P3/2 excited state are comparable to its natural broadening (9.8 MHz). We have modeled the nearly unresolved hyperfine structure as a partially resolved multilevel system in which the absorption at each photon detuning will induce adjacent allowed transition pathways simultaneously. Thus, the corresponding optical pumping processes of 23Na and 87Rb are governed by similar rate equations but result in different redistributed populations. By numerically solving the rate equations, we demonstrate that optically pumped 23Na has a much smaller spin polarization than that of 87Rb because the population imbalances between the ground state Zeeman levels of 23Na are very small. The inefficient optical pumping can explain why Na magnetometers are not studied extensively. The investigation into the optical pumping process of 23Na is helpful in preparing a highly spin-polarized atomic medium and optimizing the sensitivity of Na magnetometers.

DOI
10.1063/5.0002064

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All magnetometers using alkali atoms rely on the monochromatic light driving the optical pumping process in the D1 or D2 line to create spin-polarized atoms. In the study of a sodium (Na) magnetometer, we find that 23Na exhibits the same hyperfine structure as exhibited by the 87Rb atom but differs from Rb in terms of level splitting. The narrowly split hyperfine levels of the 23Na 3P3/2 excited state are comparable to its natural broadening (9.8 MHz). We have modeled the nearly unresolved hyperfine structure as a partially resolved multilevel system in which the absorption at each photon detuning will induce adjacent allowed transition pathways simultaneously. Thus, the corresponding optical pumping processes of 23Na and 87Rb are governed by similar rate equations but result in different redistributed populations. By numerically solving the rate equations, we demonstrate that optically pumped 23Na has a much smaller spin polarization than that of 87Rb because the population imbalances between the ground state Zeeman levels of 23Na are very small. The inefficient optical pumping can explain why Na magnetometers are not studied extensively. The investigation into the optical pumping process of 23Na is helpful in preparing a highly spin-polarized atomic medium and optimizing the sensitivity of Na magnetometers.
A new method has been designed for obtaining the hyperfine optical pumping of Na vapor. The pumping lamp is placed in a magnetic field and the light emitted in the field direction is used for excitation after crossing a circular polarizer selecting one of the Zeeman lines. This method has two interesting features: (i) The atoms can be pumped either in the lower or in the upper hyperfine sublevel by simply rotating a polarizer by an angle of $\frac{1}{2}\ensuremath{\pi}$; (ii) the hyperfine pumping is obtained using both the D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines without filtering losses. The pumping efficiency is good and it has been possible to measure the spin-exchange cross section between sodium atoms by studying the hyperfine relaxation rates as a function of the sodium density. The result is ${\ensuremath{\sigma}}_{\mathrm{ex}}=(1.109\ifmmode\pm\else\textpm\fi{}0.005)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2.
We describe optically pumping a beam of sodium atoms to >96% mS and >92% mS, mI state selection. (We have accurately measured the population of every mS, mI state in the optically pumped beam.) For the optical pumping both ground hyperfine states are pumped, using single-mode cw dye-laser radiation tuned to the 3S1/2–3P1/2 transition that is phase modulated in a LiTaO3 crystal to produce first-order sidebands at approximately the 1772-MHz hyperfine splitting of the ground state. The z-directed optical pumping is performed in a z-directed magnetic field of ~5 G. The state-selected atoms then move, in ~1 cm, into an ~200 G, z-directed field. The downstream probe laser beam is scanned through the 3S1/2 (mS, mI) → 3P3/2 (mS′, mI) transitions, which are spectroscopically resolved at 200 G, and the fluorescence intensities portray the residual populations in each of the eight 3S1/2 states.
Abstract A theory is developed for the optical pumping of alkali atoms with allowance for Zeeman and hyperfine structures and atomic motion in the model of instantaneous mixing between the Zeeman and hyperfine sublevels in an excited state. The appearance of the angular momentum in the 87Rb and 133Cs atoms that is opposite to the momentum of the photons pumping these atoms is studied. This effect is found to be most pronounced in the D2 line. The influence of the buffer gas pressure and the optical pumping intensity on the features of this effect is analyzed. The influence of the counterpolarization effect on the parameters of high-sensitivity quantum magnetometers is discussed.
Detailed analysis of spectral line broadening and variations in relative intensities of hyperfine spectral components due to optical pumping is presented. Hyperfine levels of sodium 3p1/23{p}_{1/2}3p1/2​ and 3p3/23{p}_{3/2}3p3/2​ levels are selectively excited in a supersonic beam at various laser intensities under the conditions when optical pumping time is shorter than transit time of atoms through the laser beam. The excitation spectra exhibit significant line broadening at laser intensities well below the saturation intensity, and redistribution of intensities of hyperfine spectral components is observed, which in some cases is contradicting with intuitive expectations. Theoretical analysis of the dynamics of optical pumping shows that spectral line broadening sensitively depends on the branching coefficient of the laser-driven transition. Analytical expressions for branching ratio dependent critical Rabi frequency and critical laser intensity are derived, which give the threshold for onset of noticeable line broadening by optical pumping. The critical laser intensity has its smallest value for transitions with branching coefficient equal to 0.5, and it can be much smaller than the saturation intensity. Transitions with larger and smaller branching coefficients are relatively less affected. The theoretical excitation spectra were calculated numerically by solving density matrix equations of motion using the split propagation technique, and they well-reproduce the observed effects of line broadening and peak intensity variations. The calculations also show that presence of dark (i.e., not laser coupled) Zeeman sublevels in the lower state results in effective branching coefficients which vary with laser intensity and differ from those implied by the sum rules, and this can lead to peculiar changes in peak ratios of hyperfine components of the spectra.
We present ab initio reduced rate equation models to study the interplay of Zeeman and hyperfine pumping, which determines the Doppler-broadened absorption spectra of an arbitrarily polarized probe laser, in thermal atomic vapor. Our simple models (with maximum seven levels) accurately predict the dependence of probe absorption on its polarization for the 87Rb D2 line (residual error <2%) without any fitting parameters, while being ∼100× less computational resource intensive as compared to numerically complex full multi-level models that treat all (up to 23) the magnetic (m F ) sub-levels present in the system individually. We demonstrate that either Zeeman or hyperfine pumping dominates depending on whether the atomic transitions being probed are primarily closed or open.
We present the results of a pump-probe laser spectroscopic investigation of the Doppler-broadened sodium D1D1D1 resonance line. We find 13 resonances in the resulting spectra. These observations are well described by the numerical predictions of a four-level atomic model of the hyperfine structure of the sodium D1D1D1 line. We also find that many, but not all, of these features can be understood in terms of processes originating in a two-level or three-level subset of the full four-level model. The processes we observed include forward near-degenerate four-wave mixing and saturation in a two-level system, difference-frequency crossing and nondegenerate four-wave mixing in a three-level V system, electromagnetically induced transparency and optical pumping in a three-level lambda system, cross-transition resonance in a four-level double-lambda system, and conventional optical pumping. Most of these processes lead to sub-Doppler or even subnatural linewidths. The dependence of these resonances on the pump intensity and pump detuning from atomic resonance are also studied.