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Physical Review A

Thermalization of velocity-selected excited-state populations by resonance exchange collisions and radiation trapping

John Huennekens, R. K. Namiotka, J. Sagle, Z. J. Jabbour, M. Allegrini

Published Jun 1, 1995• 25 citations
Publisher

Abstract

Populations of excited atoms that all have the same z component of velocity can be produced by pumping a vapor with a narrow-band laser. This velocity-selected population is then thermalized by velocity-changing collisions. However, in a pure vapor, even at low densities where velocity-changing collisions can be ignored, the mechanisms of radiation trapping and resonance exchange collisions can still lead to substantial thermalization of excited-atom velocity distributions. In this paper, we present data demonstrating these effects. We compare our data with results from a simple model of these processes. The model is in qualitative agreement with the experimental results.

DOI
10.1103/physreva.51.4472

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Populations of excited atoms that all have the same z component of velocity can be produced by pumping a vapor with a narrow-band laser. This velocity-selected population is then thermalized by velocity-changing collisions. However, in a pure vapor, even at low densities where velocity-changing collisions can be ignored, the mechanisms of radiation trapping and resonance exchange collisions can still lead to substantial thermalization of excited-atom velocity distributions. In this paper, we present data demonstrating these effects. We compare our data with results from a simple model of these processes. The model is in qualitative agreement with the experimental results.
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We have investigated collisions involving fast, excited Cs atoms produced by photodissociating Cs2{\mathrm{Cs}}_{2}Cs2​ molecules with a pulsed dye laser. The velocities of the atoms in the 5D5D5D state formed by the process ${\mathrm{Cs}}_{2}(X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+})+\ensuremath{\hbar}{\ensuremath{\omega}}_{\text{pump}}\ensuremath{\rightarrow}{\mathrm{Cs}}_{2}^{*}\ensuremath{\rightarrow}\mathrm{Cs}(5D)+\mathrm{Cs}(6S)$ are much greater than typical thermal velocities associated with the cell temperature. Using a narrow-band cw probe laser to observe the increased Doppler broadening of the $5{D}_{3∕2}\ensuremath{\rightarrow}5{F}_{5∕2}$ excitation line shape, we are able to monitor the time evolution of the velocity distribution of these 5D5D5D atoms. We analyze the data using a model that predicts the time-dependent excitation line shape of the fast atoms. Because the photons used to dissociate the molecules have a well-defined energy, the velocity distribution of the excited atoms in the early time after they are produced can be fairly well determined. Over time, velocity-changing collisions with ground-state Cs atoms cause the velocity distribution of excited atoms to approach the thermal limit. An analysis based on the strong-collision model leads to a prediction that the observed line shape at intermediate times will be a linear combination of contributions from distinct ``fast'' and ``thermalized'' atomic populations. By fitting our data to this model, a rate coefficient for velocity-changing collisions of fast Cs(5D3∕2)\mathrm{Cs}(5{D}_{3∕2})Cs(5D3∕2​) atoms with ground-state Cs atoms has been determined. The result ${k}_{\mathrm{VCC}}=(6.1\ifmmode\pm\else\textpm\fi{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ corresponds to an effective velocity-changing collision cross section of ${\ensuremath{\sigma}}_{\mathrm{VCC}}^{\mathrm{Cs},\mathrm{eff}}=(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$.
We extend the theory of velocity-selective laser optical pumping in atomic vapors, allowing for arbitrarily rapid velocity-changing collisional rates. The results yield a simple relationship between the line-shape areas of narrow spectroscopic features present in optically pumped samples. This relationship gives directly the ground- and excited-state velocity-changing collision rates and cross sections. We use the results to analyze the data from a laser optical-pumping experiment in 6Li^{6}\mathrm{Li}6Li vapor perturbed by Ar buffer gas.
Experiments have shown the novel combination of laser optical pumping and velocity-changing collisions (between active- and buffer-gas atoms) to be very effective in producing vapors with high atomic or nuclear polarizations. This paper presents a theory which has proven successful in analyzing these experiments. The theory predicts the amount of polarization attainable for particular experimental conditions and establishes the general criteria for optimum polarization. The theory is based on sets of coupled rate equations, which contain terms describing the pumping process (i.e., stimulated absorption or emission), radiative branching, relaxation, and velocity-changing collisions. The collision terms are written in the strong-collision approximation, which assumes that a single collision, on average, thermalizes the velocity distribution. Expressions are derived for the polarization and level populations.
The velocity changing collisions (vcc) play an important role in the description of velocity redistribution of particles caused by nearly resonant interaction with the laser light and collisions (1). Collision relaxation rates are conveniently described by collision kernels which, in turn, depend on interatomic potential and scattering amplitudes and is proportional to the collision cross section. The population kernel gives the probability density per unit time that an active particle in state 1 i> undergoes collisions with perturbers (usually a noble gas atom or impurity), which changes the active particle velocity from v′ to v. Due to the fact that perturber-active particle interaction is state dependent the collisions cause different changes in the ground and excited states of active particle. Although the shape of the populations distributions resembles those from well-known Bennett hole theory, the distribution of the total population has two peaks and obviously is asymmetrical (2). Vcc together with velocity selective laser excitation lead to the asymmetry of the ground and excited state population. The flux of excited particles has properties which are different from that of ground state because of interaction collision potentials for both states. The intensity of the laser light strongly influences the velocity distributions of the ground and excited state populations.
We report on the use of a stimulated Raman transition in a slowed atomic beam to produce a narrow velocity distribution of atoms in a selected electronic state, which could be used for atomic collisions studies in the low temperature regime(1). The velocity selection is part of the deceleration process and in this sense it is unique. The atomic beam is decelerated by the radiation pressure force exerted on the atoms by a counter- propagating laser beam. The resonance condition is maintained along the deceleration path because the changing Doppler shift is compensated by Zeeman tuning the electronic sublevels(2) with a spatialy inhomogneous magnetic field. At the end of the slowing process, the initial Maxwell-Boltzman distribution is compressed to a narrow velocity distribution (Δv ~ 50 m/s), centered close to v = 0. This velocity bunching(3) increases considerably the number of atoms in each velocity class, allowing the use of velocity selection techniques as a feasible way of studying low velocity collisions.