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Physical Review A

Alignment in two-step pulsed laser excitation of Rydberg levels in light atoms: The example of sodium

Keith B. MacAdam, Michael A. Morrison

Published Aug 1, 1993• 9 citations
Publisher

Abstract

Aligned atomic Rydberg states of sodium can be prepared using two-step excitation from the ground state by linearly polarized pulsed lasers. Information that is normally inaccessible, e.g., sublevel partial cross sections in charge-transfer experiments, can be obtained when aligned targets are used. The calculations of orbital alignment must carefully allow for fine and hyperfine structure, laser linewidths, pulse widths and delays, sublevel coherences, and other factors. In this paper we derive the orbital alignments and time-averaged d-state sublevel populations for 3 $^{2}$${\mathit{S}}_{1/2}$\ensuremath{\rightarrow}3 $^{2}$${\mathit{P}}_{\mathit{J}1}$\ensuremath{\rightarrow}n $^{2}$D excitations in Na using angular-momentum and density-matrix methods. We consider both quadrupole alignment ${\mathit{A}}^{(2)}$ and hexadecapole alignment ${\mathit{A}}^{(4)}$, with excitation through either ${\mathit{J}}_{1}$=1/2 or 3/2 intermediate states considered on the same footing. We show sublevel populations for \ensuremath{\Vert}${\mathit{M}}_{\mathit{L}}$\ensuremath{\Vert}=0, 1, and 2 analytically and graphically. Finally, we formulate the experimental design problem quantitatively in order to ascertain how to optimize the choice of polarizer angles for extraction of sublevel partial cross sections. Although perhaps the commonest instance, two-step excitation of Na(nd) is but one of a large number of interesting cases, and this study is further intended to illustrate and guide the application of these methods to other light atoms.

DOI
10.1103/physreva.48.1345

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Determination of anisotropy-dependent inelastic collision cross sections in atomic sodium using linear polarization spectroscopy

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We report on the measurement of the linear polarization degree of the $3s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ $\ensuremath{\rightarrow}$ $3p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}$ $\ensuremath{\rightarrow}$ $5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transition in atomic sodium. A linearly polarized pump laser creates an alignment in the excited ${}^{23}$Na $3p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}$ level. From the spectra, we extracted the inelastic collision cross section for the disalignment of the excited atoms by collisions with ground-level argon or xenon atoms. Measurements were done by monitoring the intensity of the cascade fluorescence from the $4p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}$ $\ensuremath{\rightarrow}$ $3s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}$ transition at 330.29 nm, in the presence of Ar and Xe for pressures ranging from 5.3 to 146.6 mbar. We demonstrated that the polarization measurement can provide important information about the alignment-dependent inelastic process in alkali-metal--rare-gas collisions. A depolarization cross-section value of 196 (22) \AA{}${}^{2}$ for Na-Ar and 357 (21) \AA{}${}^{2}$ for Na-Xe are obtained.

Physical Review A•Dec 7, 2012•4 citations
Aligned atomic Rydberg states of sodium can be prepared using two-step excitation from the ground state by linearly polarized pulsed lasers. Information that is normally inaccessible, e.g., sublevel partial cross sections in charge-transfer experiments, can be obtained when aligned targets are used. The calculations of orbital alignment must carefully allow for fine and hyperfine structure, laser linewidths, pulse widths and delays, sublevel coherences, and other factors. In this paper we derive the orbital alignments and time-averaged d-state sublevel populations for 3 ^{2}$${\mathit{S}}_{1/2}\ensuremath{\rightarrow}3 ^{2}$${\mathit{P}}_{\mathit{J}1}\ensuremath{\rightarrow}n 2^{2}2D excitations in Na using angular-momentum and density-matrix methods. We consider both quadrupole alignment A(2){\mathit{A}}^{(2)}A(2) and hexadecapole alignment A(4){\mathit{A}}^{(4)}A(4), with excitation through either J1{\mathit{J}}_{1}J1​=1/2 or 3/2 intermediate states considered on the same footing. We show sublevel populations for \ensuremath{\Vert}ML{\mathit{M}}_{\mathit{L}}ML​\ensuremath{\Vert}=0, 1, and 2 analytically and graphically. Finally, we formulate the experimental design problem quantitatively in order to ascertain how to optimize the choice of polarizer angles for extraction of sublevel partial cross sections. Although perhaps the commonest instance, two-step excitation of Na(nd) is but one of a large number of interesting cases, and this study is further intended to illustrate and guide the application of these methods to other light atoms.
Quadrupolar and hexadecapolar alignment can be produced in Na(nd) Rydberg states that are used for collision targets by adjusting the linear polarization of the photoexciting yellow (589 nm) and blue (c.410 nm) pulsed laser beams. Varying the orbital alignment, or equivalently the relative {vert_bar}m{ell}{vert_bar}-sublevel populations, facilitates the measurement of sublevel partial cross sections for Rydberg charge transfer of other beam-target collision processes. We have completed a thorough angular-momentum analysis of sublevel populations in Na(nd), excited through either 3p{sub 1/2} or 3p{sub 3/2} intermediate states, in a mutually perpendicular beam geometry and will present results in analytical and graphical form.
The possibility of probing the collisions of aligned Rydberg atoms by stimulated emission is assessed with studies of a polarized state and a new measurement of a collisional alignment effect in atomic Ca. The stimulated emission method uses a laser to dump the desired state to a lower level which subsequently fluoresces. The technique can be used to obtain populations and polarization dependent information. First, the method is tested by applying it to an aligned Ca(4s17d 1D2) state. Alignment curves are measured when the initial state is prepared with both parallel and perpendicular relative polarizations. The experimentally observed alignment compares well with that derived from theoretical considerations of a saturated stimulated transition. Second, a two-vector collisional alignment experiment (initial state and relative velocity vector) is performed to study the energy transfer process Ca(4s7d 1D2)+He→Ca(4s6f 1F3)+He+ΔE=17.7 cm−1, and alignment effects are measured by both stimulated emission and conventional direct fluorescence detection. A preference for the ‖m‖=1 and 2 initial states is observed in the relative cross sections. Essentially identical data are obtained with the two detection methods when elliptically polarized light is used for the stimulated emission detection method. The stimulated emission technique can provide alignment and population information of the final states, making it an excellent new tool for both three-vector correlation experiments and state-to-state Rydberg transitions.
New experimental results have been obtained in collisions of singly charged ions with Na Rydberg atoms. (a) The distribution of final n states populated by electron capture shows non-monotonic variations of width with incident energy over the range 60-2100 eV. (b) The total capture cross section for alkali ions on Rydberg targets shows peaks and dips over the same energy range, correlated with particular reduced velocities v and the polarization of the exciting laser. (c) {ell}-Changing collision of Na{sup +} on Na(nd) targets, n=26 and 28, at low v preferentially transfer multiple units {h_bar} of orbital angular momentum under single-collision conditions, despite very large impact parameters. (d) Inelastic impacts of Na{sup f+} on Na 36s and 30p states, perturbed by electric fields, populate a strongly field-dependent mixture of nearby Stark levels. A synopsis of recent progress will be given.
A J=0J=0J=0 to J=1J=1J=1 to J=0J=0J=0 ladder scheme can be used as a prototype for probing optical coherence transfer in an atom array. Two incident ${\ensuremath{\sigma}}_{\ensuremath{-}}$ polarized fields drive transitions from the ground state to the intermediate state and the intermediate state to the uppermost state in the atoms. The uppermost state is taken to be a long-lived Rydberg level. In the absence of any atom-atom interactions, excitation to the Rydberg level is not allowed, owing to the selection rules. However, dipole-dipole interactions can provide a transfer of the state amplitude associated with the $m=\ensuremath{-}1$ sublevel in one atom to the m=+1m=+1m=+1 sublevel in another atom. The overall process of field excitation and optical coherence transfer can then lead to an excitation of the Rydberg level. One can then apply a readout pulse to obtain phase-matched emission from the array. For a linear array of atoms, the phase-matched signal can increase more rapidly than N2{N}^{2}N2, where NNN is the number of atoms in the array. For arrays that are invariant under a rotation $\ensuremath{\delta}\ensuremath{\phi}<\ensuremath{\pi}$ about the zzz axis, however, it turns out that the total field intensity vanishes identically in the phase-matched direction. For such arrays, the Rydberg state population can serve as a measure of the optical coherence transfer.
In this study we explored the angular momentum alignment-to-orientation conversion occurring in various alkali metals -- K, Rb, Cs. We used a theoretical model that is based on Optical Bloch equations and uses the density matrix formalism. Our model includes the interaction of all neighboring hyperfine levels, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. Additionally we simulated signals where the ground- or the excited-state coherent processes were switched off allowing us to determine the origins of obtained signals. We also performed experiments on Cs atoms with two laser beams: linearly polarised Cs D1 pump and circularly polarized Cs D2 probe. We used the pump beam to create angular momentum alignment in the ground state and observed the transmission signal of the probe beam as we changed the magnetic field. Full analysis of the experimentally obtained transmission signal from a single circularly polarized probe laser component is provided.
We report on the measurement of the linear polarization degree of the 3s2S1/23s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}3s2S1/2​ $\ensuremath{\rightarrow}$ 3p2P3/23p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}3p2P3/2​ $\ensuremath{\rightarrow}$ 5s2S1/25s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}5s2S1/2​ transition in atomic sodium. A linearly polarized pump laser creates an alignment in the excited 23{}^{23}23Na 3p2P3/23p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{3/2}3p2P3/2​ level. From the spectra, we extracted the inelastic collision cross section for the disalignment of the excited atoms by collisions with ground-level argon or xenon atoms. Measurements were done by monitoring the intensity of the cascade fluorescence from the 4p2P1/24p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{P}_{1/2}4p2P1/2​ $\ensuremath{\rightarrow}$ 3s2S1/23s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}{S}_{1/2}3s2S1/2​ transition at 330.29 nm, in the presence of Ar and Xe for pressures ranging from 5.3 to 146.6 mbar. We demonstrated that the polarization measurement can provide important information about the alignment-dependent inelastic process in alkali-metal--rare-gas collisions. A depolarization cross-section value of 196 (22) \AA{}2{}^{2}2 for Na-Ar and 357 (21) \AA{}2{}^{2}2 for Na-Xe are obtained.