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Optics and Spectroscopy

Particularities of optical pumping effects in cold and ultra-slow beams of Na and Cs in the case of cyclic transitions

Martins Bruvelis, A. Cinins, Aleksandrs Leitis, Dmitry K. Efimov, Nikolai N. Bezuglov, A. S. Chirtsov, F. Fuso, Aigars Ekers

Published Dec 1, 2015• 4 citations
Publisher

Abstract

The time-dependent population dynamics of hyperfine (HF) levels of n 2 p 3/2 states is examined for cyclic transitions in alkali atoms. We study a slow and cold atomic beam of Na (n = 3) and Cs (n = 6), taking into account the long interaction time of light with atoms (~200 μs) inside the resonant laser beam. Simple analytical expressions for the populations of the excited states and for the intensities of the absorption lines are derived for a three-level system model. We show that at moderate pump laser power the mixing of HF levels is sufficient to form a flow of population from a cyclic transition to partially open transitions. We discuss various phenomena associated with the evolution of optical pumping that cannot be explained by general analysis of two-level system model.

DOI
10.1134/s0030400x1512005x

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The relative intensities of the Doppler-free signals of 85Rb and Cs D2 lines in saturation spectroscopy were calculated theoretically, taking into account the optical pumping process in a four-level system. The optical pumping effect in saturation spectroscopy is important when atoms with long-lived lower states are pumped by a weak beam. The theoretical results calculated from a simple analysis without any knowledge of the saturation parameters were found to be in good agreement with the experimental results on Rb and Cs D2 lines previously obtained using semiconductor laser.

Japanese Journal of Applied Physics•Jul 1, 1984•27 citations
The time-dependent population dynamics of hyperfine (HF) levels of n 2 p 3/2 states is examined for cyclic transitions in alkali atoms. We study a slow and cold atomic beam of Na (n = 3) and Cs (n = 6), taking into account the long interaction time of light with atoms (~200 μs) inside the resonant laser beam. Simple analytical expressions for the populations of the excited states and for the intensities of the absorption lines are derived for a three-level system model. We show that at moderate pump laser power the mixing of HF levels is sufficient to form a flow of population from a cyclic transition to partially open transitions. We discuss various phenomena associated with the evolution of optical pumping that cannot be explained by general analysis of two-level system model.
By photoionizing hyperfine (HF) levels of the Cs state 62P3/26{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}62P3/2​ in a slow and cold atom beam, we find how their population depends on the excitation laser power. The long time (around $180\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s})$ spent by the slow atoms inside the resonant laser beam is large enough to enable exploration of a unique atom-light interaction regime heavily affected by time-dependent optical pumping. We demonstrate that, under such conditions, the onset of nonlinear effects in the population dynamics and optical pumping occurs at excitation laser intensities much smaller than the conventional respective saturation values. The evolution of population within the HF structure is calculated by numerical integration of the multilevel optical Bloch equations. The agreement between numerical results and experiment outcomes is excellent. All main features in the experimental findings are explained by the occurrence of ``dark'' and ``bright'' resonances leading to power-dependent branching coefficients.
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.
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.
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 evolution of the hyperfine structure magnetic sublevel populations of 87 Rb and 133 Cs atoms in resonant linearly polarized laser fields is theoretically analyzed. Analytical expressions are obtained for stationary populations of the magnetic sublevels of the ground state 5 2 S 1/2 F g = 1, F f = 2 in 87 Rb and 6 2 S 1/2 F g = 3, F f = 4 in 133 Cs under optical pumping at the F g ↔ F e = F g and F f ↔ F e = F f transitions of the D 2 lines ( n 2 S 1/2 n 2 P 3/2 ) versus the initial populations. The characteristic population stabilization time are obtained by numerical solution for the density matrix equations, depending on the intensity of the laser fields and the detuning of the optical resonance. It is shown that the alternation of the polarization direction of the laser field at the transition F f ↔ F e = F f almost completely transfers atoms to the lower sublevel of the "clock" M1 transition F g M = 0 ↔ F f M = 0 in rubidium and cesium frequency standards, which proportionally increases the signal of the recording system.
The relative intensities of the Doppler-free signals of 85Rb and Cs D2 lines in saturation spectroscopy were calculated theoretically, taking into account the optical pumping process in a four-level system. The optical pumping effect in saturation spectroscopy is important when atoms with long-lived lower states are pumped by a weak beam. The theoretical results calculated from a simple analysis without any knowledge of the saturation parameters were found to be in good agreement with the experimental results on Rb and Cs D2 lines previously obtained using semiconductor laser.