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Physical Review A

Interaction-time-averaged optical pumping in alkali-metal-atom Doppler spectroscopy

Thomas Lindvall, Ilkka Juhani Tittonen

Published Sep 9, 2009• 18 citations
Publisher

Abstract

We study the influence of optical pumping on Doppler-broadened alkali-metal-atom $D$ line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.

DOI
10.1103/physreva.80.032505

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European Journal of Physics•Aug 14, 2009•13 citations
We study the influence of optical pumping on Doppler-broadened alkali-metal-atom DDD line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.
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.
Laser spectroscopy experiments are often conducted with a probe that does not significantly alter the medium’s properties. For a two-level atom a clear measure of the strength of a probe beam in terms of the saturation intensity is known. We show that for a multilevel atom the situation is very different, and the effects of optical pumping are crucial to understanding the opacity of the medium. We present a simple theoretical analysis for Doppler-broadened spectroscopy of alkali metals on the D2 line that emphasizes the importance of the transient nature of the population dynamics, and the crucial role of the distribution of the times of flight of atoms through the probe beam. Experimental results are obtained with room temperature rubidium vapor probed by an extended-cavity diode laser and confirm our theoretical prediction.
Alkali metals have played an important role in optical and atomic physics from the very beginning. This thesis deals with three aspects and applications of alkali-metal atoms, in particular rubidium (Rb). Optical pumping changes both the amplitudes and the center positions of the absorption profiles in the Doppler-broadened D-line spectra of the alkali-metal atoms. This effect has been studied by reducing the multilevel system to an effective three-level system and by treating the finite interaction time and collisions with the vapor-cell walls in two different ways: as ground-state relaxation and by averaging the time-dependent absorption over the distribution of interaction times. The former is a computationally efficient way to compare theoretical spectra to experimental results, and the latter reveals lineshape details that are due to the coupling between the Doppler shift and the interaction times through the longitudinal velocity of the atoms. Using coherent population trapping (CPT) in 85Rb, an all-optical atomic clock has been realized. The good noise properties of the diode laser, an optimized buffer gas, and a very low light intensity allow detection of ultranarrow CPT resonances < 20 Hz, apparently the narrowest optically induced hyperfine CPT resonance ever measured. The Q value of this resonance, 1.5 × 108, is comparable to Q values in cesium clocks and the stability of the CPT clock is sufficient for many high-precision applications. Trapping of Rb atoms in microscopic magneto-optical traps (MOTs) a few hundred micrometers from the surface of an optically transparent ferrite-garnet permanent-magnet atom chip has been demonstrated. The required magnetic fields are created by magnetic patterns magneto-optically written into the ferrite-garnet film and the transparency of the chip allows using a conventional MOT geometry. The magnetic patterns can be erased and re-written in situ, even during the experiments. Magnetic traps with a trap depth up to 1 mK could be realized using this type of atom chip.
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.
The two-photon spectrum of sodium atoms, excited by two counterpropagating evanescent waves, is investigated both experimentally and theoretically. Sub-Doppler linewidths are observed, which are quantitatively reproduced by a rigorous theoretical approach that takes into account optical pumping and transit time broadening due to the translational motion of the arriving and departing atoms through the evanescent-wave fields. The velocity distribution of the atoms desorbing from the surface is found to obey a cosine law, which has a significant influence on the observed line shapes.
We present the analytic solutions of the saturated absorption spectrum for an atomic medium composed of two-level atoms and describe the effects of saturation and optical pumping on the spectrum. The background-subtracted Doppler-free spectrum is Lorentzian-shaped with an amplitude and width given by 1 − {1 + s 0 [1 + (γ 2 t /2)]} −1/2 and γ t [1 + {1 + s 0 [1 + (γ 2 t /2)]} 1/2 ], respectively, where γ t is the transverse decay rate, γ 2 is the decay rate to energy levels other than the ground state, s 0 is the saturation parameter and t is the interaction time of the atoms with laser beams. Analytic results are compared with numerical results and show good agreement with one another. This paper is intended for graduate students who have started to study basic atomic physics.