Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Alignment effects of ‖J=3〉 states prepared by three-photon excitation: Sixfold symmetry in collisional energy transfer, Ca(4s4f ,1 F3 )+He→Ca(4 p2 ,1 S0 )+He

Jan P. J. Driessen, Christopher J. M. Smith, Stephen R. Leone

Published Aug 1, 1991• 10 citations
Publisher

Abstract

Rank-6 symmetry in energy transfer collisions is observed. A Ca(4s4f${,}^{1}$${\mathit{F}}_{3}$) state is prepared by three-photon excitation. The angular wave function of the Ca${(}^{1}$${\mathit{F}}_{3}$) state depends on the angles of the three laser polarizations with respect to each other. The alignment effect for energy transfer, Ca(4s4f${,}^{1}$${\mathit{F}}_{3}$)+He\ensuremath{\rightarrow}Ca(4${\mathit{p}}^{2}$${,}^{1}$${\mathit{S}}_{0}$)+He, is determined for two different initial angular wave functions. Each alignment curve can be analyzed in terms of the same set of relative cross sections for the individual Ca${(}^{1}$${\mathit{F}}_{3}$) magnetic sublevels, providing an independent verification of the data.

DOI
10.1103/physreva.44.r1431

Related papers

Experimental investigation of the initial-state alignment dependence in the energy pooling process: Ca(4s4p3P1)+Ca(4s4p3P1)→Ca(4s4p1P1)+Ca(4s2)

Harold Parks, Eileen M. Spain, John E. Smedley +1 more

A pulsed laser investigation is performed to study the detailed effects of electronic angular-momentum alignment on the cross section for the energy-transfer process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ A uniform magnetic field imposed by a set of Helmholtz coils is used to systematically precess the initial state orbitals with a well-defined period, allowing different alignments to be sampled at different time delays after the pulsed laser excites and aligns the $\mathrm{Ca}(4s4p{}^{3}{P}_{1})$ states. The polarization effects in this collision process are striking. For example, the cross section for two atoms both in the ${m}_{j}=0$ magnetic substrate is 13 times larger than the cross section for two atoms that are both in the ${m}_{j}=1$ (or -1) substrate, where the quantization axis is taken to be along the relative velocity vector of the collision. The initial m-sublevel dependence of this three-vector correlation process can be completely described with eight fundamental parameters, five of which are accurately obtained. In addition, the coarse energy dependence of these parameters is deduced.

Physical Review A•Sep 1, 1998•7 citations

Laser preparation and probing of initial and final orbital alignment in collision-induced energy transfer Ca(4s5p, 1P1) +He→Ca(4s5p, 3P2)+He

Christopher J. M. Smith, Jan P. J. Driessen, Larry Eno +1 more

In a crossed beam atomic energy transfer experiment, relative cross sections are measured between initial and final magnetic substates of atomic orbitals in a three vector correlation experiment. A pulsed laser beam prepares Ca(4s5p 1P1) in a single magnetic sublevel ‖j1mi〉 with respect to the laser polarization vector. Subsequent collision with He at a well-defined relative velocity yields Ca(4s5p 3P2). The near-resonant Ca(4s5p 3P2) is probed by a second polarized pulsed laser, revealing its magnetic sublevel ‖j2mf〉 distribution with respect to the probe laser polarization vector. The experiment is analyzed in the collision frame where the direction of the initial relative velocity vector serves as the quantization axis. In this frame, the initial and final Ca states are characterized by substates ‖j1m1〉 and ‖j2m2〉, respectively. Fourteen collision frame cross sections are needed to describe the energy transfer completely. Eight of these cross sections are real and positive (conventional type—describing population transfer) and six are complex (coherence type—containing phase information). By symmetry, only 15 unique parameters for the real and imaginary parts of the cross sections are required, nine of which are obtained here using linear polarizations and collinear laser beams. Possible cases for circularly polarized light are also tabulated; measurement of these cases would provide several more parameters. For initial parallel preparation of the 1P1 p orbital with respect to the relative velocity (m1=0), the final 3P2 state is highly aligned in the m2=±1 and m2=±2 sublevels. Initial preparation of the p orbital perpendicular to the relative velocity vector (m1=±1) produces an aligned 3P2 state with greater population in the m2=0 and m2=±1 sublevels compared to the m2=±2 sublevels. Using the coherence information and symmetry, orientation cross sections are obtained into the m2=±1 sublevels (i.e., m preserving 1→1 and m-changing 1→−1) and are nearly identical. Preparation of the Ca p orbital perpendicular to the initial relative velocity enhances the state-specific collisional transfer of 1P1→3P2 by a factor of 2.2±0.2 over initial parallel preparation.

The Journal of Chemical Physics•Jun 1, 1992•34 citations

Initial and final orbital alignment probing of the fine-structure-changing collisions among the Ca (4s)1(4p)1, 3P J states with He: determination of coherence and conventional cross-sections

Christopher J. M. Smith, Eileen M. Spain, Mark J. Dalberth +2 more

A laser pump–probe experiment is used to study the orbital alignment effects, orientation effects and vector correlations of collisional transfer of the Ca (4s)1(4p)1, 3P1 state to the Ca (4s)1(4p)1, 3P2, 0 levels. The experiment is configured in a single-collision crossed-beam arrangement between Ca and He, and multi-structure cross-sections are determined using appropriate combinations of linear and circular laser light for the pump/probe steps. Real and imaginary parts of coherence cross-sections are obtained along with the conventional population cross-sections for the m1→m2 magnetic sublevel transitions into the 3P2 level. The total relative cross-section ratio for the perpendicular (m1=±1) to parallel (m1= 0) polarization preparation of 3P1 transferring to 3P2 is 1.46 ± 0.15. For initial 3P1 preparation with laser light linearly polarized perpendicular to the initial relative velocity vector, the transfer into the m2-sublevels of the 3P2 state show a distinct preference for the sign-changing m1=+ 1 →m2=–1 transition. Preparation of Ca 3P1 with laser light linearly polarized parallel to the initial relative velocity vector produces population transfer into the 3P2 level that is completely aligned in the ±1 and ±2 sublevels, consistent with symmetry considerations. The magnitudes of the coherence cross-sections range from a few percent to greater than 100% of some of the population transfer conventional cross-sections. Study of the alignment effect into the final 3P0 state found a very large observed effect (σ|m|= 1/σ|m|= 0) of 23 ± 0.9. Interpretation of the energy transfer results indicates that the energy transfer obeys symmetry rules and follows predictions of curve crossings between the Σ and Π potentials, where for the transfer into 3P2 only indirect coupling can occur.

Journal of the Chemical Society Faraday Transactions•Jan 1, 1993•36 citations

Initial- and final-state alignment and orientation effects in Ca energy pooling

Harold Parks, Stephen R. Leone

An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial $\mathrm{Ca}(4s4p{}^{3}{P}_{1})$ state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.

Physical Review A•Oct 1, 1999•5 citations

Alignment probing of Rydberg states by stimulated emission

Eileen M. Spain, Mark J. Dalberth, Paul D. Kleiber +3 more

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.

The Journal of Chemical Physics•Jun 22, 1995•9 citations

Effects of alignment on strontium energy pooling collisions

Jonathan Andrew Neuman, Alan Gallagher

The dependence of energy pooling cross sections on the alignment of atomic angular momentum with respect to the collision axis is investigated. In a vapor cell, excitation with counter-propagating polarized laser beams that define the collision axis prepares aligned strontium atoms in the $5s5p{}^{3}{P}_{1}$ level. Excited-state energy pooling collision products from the endothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s6s{}^{1}{S}_{0}{+5s}^{2}{}^{1}{S}_{0}$ reaction and the exothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s5p{}^{1}{P}_{1}{+5s}^{2}{}^{1}{S}_{0}$ reaction are studied. Alignment effects are studied as a function of collision energy, using pulsed laser excitation followed by delayed fluorescence detection to lower the transverse collision velocity and laser detuning to vary the collision velocity in the laser-beam direction. The rate coefficient for energy transfer to the $6{}^{1}{S}_{0}$ state is enhanced by $38\ifmmode\pm\else\textpm\fi{}13%$ when the ${M}_{J}$ alignment of the collision partners is perpendicular to the collision axis and parallel to each other compared to when there is no alignment of the collision partners. No alignment dependence is observed for energy transfer to the $5{}^{1}{P}_{1}$ state. This experiment offers the unique capability of simultaneously and independently controlling collision velocity and angular momentum alignment.

Physical Review A•Mar 1, 1998•2 citations
Rank-6 symmetry in energy transfer collisions is observed. A Ca(4s4f{,}^{1}$${\mathit{F}}_{3}) state is prepared by three-photon excitation. The angular wave function of the Ca{(}^{1}$${\mathit{F}}_{3}) state depends on the angles of the three laser polarizations with respect to each other. The alignment effect for energy transfer, Ca(4s4f{,}^{1}$${\mathit{F}}_{3})+He\ensuremath{\rightarrow}Ca(4{\mathit{p}}^{2}$${,}^{1}$${\mathit{S}}_{0})+He, is determined for two different initial angular wave functions. Each alignment curve can be analyzed in terms of the same set of relative cross sections for the individual Ca{(}^{1}$${\mathit{F}}_{3}) magnetic sublevels, providing an independent verification of the data.
A pulsed laser investigation is performed to study the detailed effects of electronic angular-momentum alignment on the cross section for the energy-transfer process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ A uniform magnetic field imposed by a set of Helmholtz coils is used to systematically precess the initial state orbitals with a well-defined period, allowing different alignments to be sampled at different time delays after the pulsed laser excites and aligns the Ca(4s4p3P1)\mathrm{Ca}(4s4p{}^{3}{P}_{1})Ca(4s4p3P1​) states. The polarization effects in this collision process are striking. For example, the cross section for two atoms both in the mj=0{m}_{j}=0mj​=0 magnetic substrate is 13 times larger than the cross section for two atoms that are both in the mj=1{m}_{j}=1mj​=1 (or -1) substrate, where the quantization axis is taken to be along the relative velocity vector of the collision. The initial m-sublevel dependence of this three-vector correlation process can be completely described with eight fundamental parameters, five of which are accurately obtained. In addition, the coarse energy dependence of these parameters is deduced.
In a crossed beam atomic energy transfer experiment, relative cross sections are measured between initial and final magnetic substates of atomic orbitals in a three vector correlation experiment. A pulsed laser beam prepares Ca(4s5p 1P1) in a single magnetic sublevel ‖j1mi〉 with respect to the laser polarization vector. Subsequent collision with He at a well-defined relative velocity yields Ca(4s5p 3P2). The near-resonant Ca(4s5p 3P2) is probed by a second polarized pulsed laser, revealing its magnetic sublevel ‖j2mf〉 distribution with respect to the probe laser polarization vector. The experiment is analyzed in the collision frame where the direction of the initial relative velocity vector serves as the quantization axis. In this frame, the initial and final Ca states are characterized by substates ‖j1m1〉 and ‖j2m2〉, respectively. Fourteen collision frame cross sections are needed to describe the energy transfer completely. Eight of these cross sections are real and positive (conventional type—describing population transfer) and six are complex (coherence type—containing phase information). By symmetry, only 15 unique parameters for the real and imaginary parts of the cross sections are required, nine of which are obtained here using linear polarizations and collinear laser beams. Possible cases for circularly polarized light are also tabulated; measurement of these cases would provide several more parameters. For initial parallel preparation of the 1P1 p orbital with respect to the relative velocity (m1=0), the final 3P2 state is highly aligned in the m2=±1 and m2=±2 sublevels. Initial preparation of the p orbital perpendicular to the relative velocity vector (m1=±1) produces an aligned 3P2 state with greater population in the m2=0 and m2=±1 sublevels compared to the m2=±2 sublevels. Using the coherence information and symmetry, orientation cross sections are obtained into the m2=±1 sublevels (i.e., m preserving 1→1 and m-changing 1→−1) and are nearly identical. Preparation of the Ca p orbital perpendicular to the initial relative velocity enhances the state-specific collisional transfer of 1P1→3P2 by a factor of 2.2±0.2 over initial parallel preparation.
A laser pump–probe experiment is used to study the orbital alignment effects, orientation effects and vector correlations of collisional transfer of the Ca (4s)1(4p)1, 3P1 state to the Ca (4s)1(4p)1, 3P2, 0 levels. The experiment is configured in a single-collision crossed-beam arrangement between Ca and He, and multi-structure cross-sections are determined using appropriate combinations of linear and circular laser light for the pump/probe steps. Real and imaginary parts of coherence cross-sections are obtained along with the conventional population cross-sections for the m1→m2 magnetic sublevel transitions into the 3P2 level. The total relative cross-section ratio for the perpendicular (m1=±1) to parallel (m1= 0) polarization preparation of 3P1 transferring to 3P2 is 1.46 ± 0.15. For initial 3P1 preparation with laser light linearly polarized perpendicular to the initial relative velocity vector, the transfer into the m2-sublevels of the 3P2 state show a distinct preference for the sign-changing m1=+ 1 →m2=–1 transition. Preparation of Ca 3P1 with laser light linearly polarized parallel to the initial relative velocity vector produces population transfer into the 3P2 level that is completely aligned in the ±1 and ±2 sublevels, consistent with symmetry considerations. The magnitudes of the coherence cross-sections range from a few percent to greater than 100% of some of the population transfer conventional cross-sections. Study of the alignment effect into the final 3P0 state found a very large observed effect (σ|m|= 1/σ|m|= 0) of 23 ± 0.9. Interpretation of the energy transfer results indicates that the energy transfer obeys symmetry rules and follows predictions of curve crossings between the Σ and Π potentials, where for the transfer into 3P2 only indirect coupling can occur.
An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial Ca(4s4p3P1)\mathrm{Ca}(4s4p{}^{3}{P}_{1})Ca(4s4p3P1​) state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.
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.
The dependence of energy pooling cross sections on the alignment of atomic angular momentum with respect to the collision axis is investigated. In a vapor cell, excitation with counter-propagating polarized laser beams that define the collision axis prepares aligned strontium atoms in the 5s5p3P15s5p{}^{3}{P}_{1}5s5p3P1​ level. Excited-state energy pooling collision products from the endothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s6s{}^{1}{S}_{0}{+5s}^{2}{}^{1}{S}_{0}$ reaction and the exothermic $5s5p{}^{3}{P}_{1}+5s5p{}^{3}{P}_{1}\ensuremath{\rightarrow}5s5p{}^{1}{P}_{1}{+5s}^{2}{}^{1}{S}_{0}$ reaction are studied. Alignment effects are studied as a function of collision energy, using pulsed laser excitation followed by delayed fluorescence detection to lower the transverse collision velocity and laser detuning to vary the collision velocity in the laser-beam direction. The rate coefficient for energy transfer to the 61S06{}^{1}{S}_{0}61S0​ state is enhanced by $38\ifmmode\pm\else\textpm\fi{}13%$ when the MJ{M}_{J}MJ​ alignment of the collision partners is perpendicular to the collision axis and parallel to each other compared to when there is no alignment of the collision partners. No alignment dependence is observed for energy transfer to the 51P15{}^{1}{P}_{1}51P1​ state. This experiment offers the unique capability of simultaneously and independently controlling collision velocity and angular momentum alignment.