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arXiv:0802.0779 · Physical Review A

Broadening and intensity redistribution in the Na(3p) hyperfine excitation spectra due to optical pumping in the weak excitation limit

Ihor Sydoryk, Nikolai N. Bezuglov, Ilya I. Beterov, K. Miculis, É. Saks, A. Janovs, P. Spels, Aigars Ekers

Published Apr 30, 2008• 26 citations
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Abstract

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 $3{p}_{1/2}$ and $3{p}_{3/2}$ 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.

DOI
10.1103/physreva.77.042511

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•Jan 1, 1991•0 citations
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.
The ground electronic state of even such simple atoms as those of alkali elements has the set of sublevels. These sublevels are hyperfine (HF) components and magnetic sublevels. The collisions with particles of nonmagnetic buffer gas or even with walls (when walls have proper coating) do not mix practically the populations of ground state HF sublevels, if the orbital moment of electrons in the ground state is equal to zero. Due to this reason these sublevels may be extremely long lived. Because of this, for instance, the so-called effects of optical orientation and optical pumping are apparent in atoms of alkali metals. The radiation can pump practically all the atoms (with which there is effective interaction) to a single HF component. In a situation in which optical pumping is a minor effect, the monochromatic absorption line consists of separate lines corresponding to intra-atomic transitions. The optical pumping is not significant, for example, if the radiation intensity is so low that now pumping between HF sublevels occurs in the time it takes the atom to traverse the light beam. Under the conditions of optical pumping and when other nonlinear effects are present, the absorption line profile can undergo considerable alteration. Many theoretical and experimental investigations have been done in the laser spectroscopy of resonant transitions of atoms (atoms of alkali metals) under the conditions of optical pumping within ground state HF structure. A characteristic feature of all such investigations is the velocity-selective excitation of absorbing atoms. Also, as a rule, the value of HF splitting is not very big in comparison to Doppler broadening in these experiments. Under such conditions, the absorption spectra consists of Doppler- broadened lines with nonlinear resonances, which emerge when two fields of different frequencies or different propagation directions are employed. When only one monochromatic traveling wave is employed, optical pumping leads to formation of a single smooth absorption line occupying a position between the resonant transitions frequencies associated with HF components. As HF splitting grows, the line profile remains smooth, its width is approximately equal to the size of the HF splitting. The strength of the optical pumping from one ground state HF component to another is greater for greater HF splitting in comparison to the Doppler width. In this regard, Cs and Rb are the most typical of the alkali atoms (the HF splitting exceeds the Doppler width by a factor close to 20). This is the qualitative picture of the absorption line profile (particularly for a monochromatic radiation) under the conditions of optical pumping between the HF sublevels of the electronic ground state, this qualitative picture had formed by now.
Using a three-level model and semiclassical density matrix formalism, we show that optical pumping influences both line positions and amplitudes in Doppler-broadened alkali-atom D1 and D2 spectra for intensities much lower than the two-level atom saturation intensity. The influence on the D2 spectrum is particularly interesting due to the presence of closed hyperfine transitions unaffected by optical pumping. This effect is of importance for example when lasers are frequency stabilized using linear absorption or when the alkali-atom vapour pressure is determined using absorption measurements.
We have observed a collapse of the Na hyperfine doublet into a single peak due to laser-induced optical pumping when the product of laser power and buffer gas pressure exceeds \ensuremath{\sim}0.1 mW Torr. The complex line shapes observed under these conditions have been quantitatively explained by a model which describes the laser-induced change in the population of the ground-state hyperfine levels and also includes pressure broadening and diffusion of atoms out of the laser beam. The line-shape distortion can occur at laser intensities 103{10}^{3}103 below that required for radiative saturation, and must be considered in experiments involving the line shape or the population of the hyperfine levels.
The time-dependent population dynamics of hyperfine (HF) sublevels of n 2 p 3 / 2 atomic states upon laser excitation in a cold medium of alkali atoms is examined. We demonstrate some peculiarities of the absorption HF multiplet formation in D2-line resulting from a long interaction time (∼200 μ s) interaction between light and Na ( n = 3 ) and Cs ( n = 6 ) atoms in a cold and slow sub-thermal ( T ∼ 1 K) beam. We analytically describe a number of D2-line-shape effects that are of interest in spectroscopic studies of cold dusty white dwarfs: broadening by optical pumping, intensity redistribution within components of D2-line HF multiplet for partially closed transitions and asymmetry of absorption lines induced by AC Stark shifts for cyclic transitions.
We present the results of an experimental and theoretical study of the gain (or absorption) experienced by a weak probe beam propagating through a sodium vapor in the presence of an intense pump field that is nearly resonant with the 3s → 3p atomic transition. The probe-transmission spectrum includes three distinct features that result from the modification of the atomic-level structure by the ac-Stark effect. Two of these features can lead to amplification of the probe wave. We measured the dependence of the probe spectrum on the detuning of the pump beam from resonance and on the pressure of a helium buffer gas. The experimentally obtained spectra are in good agreement with the predictions of a theoretical model based on the solution of the density-matrix equations of motion for a two-level atom and including the effects of Doppler broadening. The maximum gain measured in these experiments occurs at one of the Rabi sidebands and leads to a 38-fold increase in the intensity of the probe wave. Under some experimental conditions, we also observed two additional resonances, which are due to stimulated Raman scattering involving the sodium ground-state hyperfine levels.
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.