Physical Review A

Anomalous depolarization of the 5p2P3/2→8p2Pj′ transitions in atomic 87Rb

S. B. Bayram, Mark D. Havey, Dmitriy V. Kupriyanov, Igor M. Sokolov

Published Jun 7, 2000• 11 citations

Abstract

Measurements of the linear polarization degree of the $5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}$ transitions ${(j}^{\ensuremath{'}}=1/2,3/2)$ in atomic ${}^{87}\mathrm{Rb}$ are reported. The radiative transitions are electric-dipole forbidden, but electric-quadrupole allowed. In addition, because of the relatively strong spin-orbit interaction in Rb, the $p\ensuremath{-}p$ transitions can acquire a magnetic-dipole transition strength that may be a measurable fraction of the electric-quadrupole strength. The polarization measurements can generally provide a different and sensitive way to extract the relative transition strengths. We have measured the linear polarization degree of the $5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}$ transitions over a wide range of Rb density. We report here observations of a different depolarization effect, whereby the measured polarization of the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{1/2}$ transition increases, while that for the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{3/2}$ transition decreases with increasing Rb density. The behavior is attributed to strong laser field effects associated with the $5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}$ resonance transition.

DOI: 10.1103/physreva.62.012503

Related papers

Precision measurement of the 5st2 S1/2 → 5pt2 Pj → 8st2 S1/2 two-photon, two-color polarization spectrum in atomic Rb

A. I. Beger, Mark D. Havey, Rodney P. Meyer

Physical Review AMay 1, 19979 citations

Electric-field modification of two-photon, two-color, quadrupole-dipole depolarization spectra in atomic Cs

B. V. Dobrydnev, Mark D. Havey

Physical Review ANov 1, 19962 citations

Study of the velocity-selection satellites present in the 5P3/2→6PJ ( J=1/2, 3/2 ) electric quadrupole transitions in atomic rubidium

F. Ponciano-Ojeda, Cristian Mojica-Casique, L M Hoyos-Campo +3 more

Journal of Physics B Atomic Molecular and Optical PhysicsSep 8, 20231 citation

Polarization dependence of double-resonance optical pumping and electromagnetically induced transparency in the 5S1/2−5P3/2−5D5/2 transition of 87 Rb atoms

Han Seb Moon, Heung‐Ryoul Noh

Physical Review ASep 15, 201121 citations

Spectroscopy of electric dipole and quadrupole transitions in Ra + 224

Spencer Kofford, Haoran Li, Robert Kwapisz +5 more

arXiv:2409.09873Physical Review AMar 4, 20252 citations

Upper limit on the magnetic dipole contribution to the 5p−8p transition in Rb by use of ultracold atom spectroscopy

R. Pires, Marco Ascoli, Edward E. Eyler +2 more

arXiv:0908.4444Physical Review ADec 2, 200910 citations

Physical Review A

Anomalous depolarization of the 5p2P3/2→8p2Pj′ transitions in atomic 87Rb

S. B. Bayram, Mark D. Havey, Dmitriy V. Kupriyanov, Igor M. Sokolov

Published Jun 7, 2000• 11 citations

Publisher

Abstract

Measurements of the linear polarization degree of the

5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}

transitions

{(j}^{\ensuremath{'}}=1/2,3/2)

in atomic

{}^{87}\mathrm{Rb}

are reported. The radiative transitions are electric-dipole forbidden, but electric-quadrupole allowed. In addition, because of the relatively strong spin-orbit interaction in Rb, the

p\ensuremath{-}p

transitions can acquire a magnetic-dipole transition strength that may be a measurable fraction of the electric-quadrupole strength. The polarization measurements can generally provide a different and sensitive way to extract the relative transition strengths. We have measured the linear polarization degree of the

5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}

transitions over a wide range of Rb density. We report here observations of a different depolarization effect, whereby the measured polarization of the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{1/2}

transition increases, while that for the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{3/2}

transition decreases with increasing Rb density. The behavior is attributed to strong laser field effects associated with the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}

resonance transition.

DOI: 10.1103/physreva.62.012503

Related papers

Precision measurement of the 5st2 S1/2 → 5pt2 Pj → 8st2 S1/2 two-photon, two-color polarization spectrum in atomic Rb

A. I. Beger, Mark D. Havey, Rodney P. Meyer

Precision measurements on the 5s ${\mathrm{}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5p ${\mathrm{}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ \ensuremath{\rightarrow}8s ${\mathrm{}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ two-photon, two-color polarization spectrum in atomic Rb are reported. As a result of interference between the transition amplitudes for the process, the spectrum is strongly frequency and linear polarization dependent in the vicinity of the 5s ${\mathrm{}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5p ${\mathrm{}}^{2}$ ${\mathrm{P}}_{1\mathrm{/}2}$ and 5s ${\mathrm{}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5p ${\mathrm{}}^{2}$ ${\mathrm{P}}_{3\mathrm{/}2}$ resonance transitions, with the linear polarization degree varying from nearly +100% to -100% over the approximate 500-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the data. For absorption of two collinearly polarized photons, complete destructive interference for the process occurs at a critical detuning from the 5s ${\mathrm{}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5p ${\mathrm{}}^{2}$ ${\mathrm{P}}_{3\mathrm{/}2}$ resonance transition given by ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$=-155.83(3) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The location of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$ is determined primarily by the relative transition matrix elements through the 5p ${\mathrm{}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ multiplet, but also depends significantly on contributions from more energetic np ${\mathrm{}}^{2}$ P levels. The null in the excitation occurring at the critical frequency allows experimental determination of a type of sum rule that depends only on the atomic matrix elements and the value of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$. Such sum rules are defined and presented for the present experiment in Rb and for a recent similar experiment in Na.Precision measurements on the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{\mathrm{j}}$\ensuremath{\rightarrow}8s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$ two-photon, two-color polarization spectrum in atomic Rb are reported. As a result of interference between the transition amplitudes for the process, the spectrum is strongly frequency and linear polarization dependent in the vicinity of the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{1\mathrm{/}2}$ and 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transitions, with the linear polarization degree varying from nearly +100% to -100% over the approximate 500-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the data. For absorption of two collinearly polarized photons, complete destructive interference for the process occurs at a critical detuning from the 5s${\mathrm{}}^{2}$${\mathrm{S}}_{1\mathrm{/}2}$\ensuremath{\rightarrow}5p${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$ resonance transition given by ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$=-155.83(3) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The location of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$ is determined primarily by the relative transition matrix elements through the 5p${\mathrm{}}^{2}$${\mathrm{P}}_{\mathrm{j}}$ multiplet, but also depends significantly on contributions from more energetic np${\mathrm{}}^{2}$P levels. The null in the excitation occurring at the critical frequency allows experimental determination of a type of sum rule that depends only on the atomic matrix elements and the value of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$. Such sum rules are defined and presented for the present experiment in Rb and for a recent similar experiment in Na.

Physical Review AMay 1, 19979 citations

Electric-field modification of two-photon, two-color, quadrupole-dipole depolarization spectra in atomic Cs

B. V. Dobrydnev, Mark D. Havey

An earlier study of the 6s ${\mathrm{}}^{2}$ ${\mathit{S}}_{1/2}$ \ensuremath{\rightarrow}5d ${\mathrm{}}^{2}$ ${\mathit{D}}_{\mathit{j}}$ \ensuremath{\rightarrow}11p ${\mathrm{}}^{2}$ ${\mathit{P}}_{3/2}$ two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p ${\mathrm{}}^{2}$ ${\mathit{P}}_{\mathit{j}}$ levels into the ground 6s ${\mathrm{}}^{2}$ ${\mathit{S}}_{1/2}$ level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d ${\mathrm{}}^{2}$ ${\mathit{D}}_{\mathit{j}}$ multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. \textcopyright{} 1996 The American Physical Society.An earlier study of the 6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$\ensuremath{\rightarrow}5d${\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}}$\ensuremath{\rightarrow}11p${\mathrm{}}^{2}$${\mathit{P}}_{3/2}$ two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p${\mathrm{}}^{2}$${\mathit{P}}_{\mathit{j}}$ levels into the ground 6s${\mathrm{}}^{2}$${\mathit{S}}_{1/2}$ level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d${\mathrm{}}^{2}$${\mathit{D}}_{\mathit{j}}$ multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. \textcopyright{} 1996 The American Physical Society.

Physical Review ANov 1, 19962 citations

Study of the velocity-selection satellites present in the 5P3/2→6PJ ( J=1/2, 3/2 ) electric quadrupole transitions in atomic rubidium

F. Ponciano-Ojeda, Cristian Mojica-Casique, L M Hoyos-Campo +3 more

Abstract This article presents detailed experimental and theoretical studies of the satellite fluorescence lines observed when the <?CDATA $5P_{3/2} \to 6P_J $?> 5 P 3 / 2 → 6 P J , ( <?CDATA $J = 1/2 $?> J = 1 / 2 , <?CDATA $3/2$ ?> 3 / 2 ) electric quadrupole transition (E2) is excited in a room temperature vapor of rubidium atoms. The initial state of this E2 transition is prepared by a narrow linewidth (9 MHz) laser locked to one of the dominant <?CDATA $5S_{1/2} \to 5P_{3/2} $?> 5 S 1 / 2 → 5 P 3 / 2 D2 hyperfine excitations for zero-velocity atoms. Effects due to the selection of different atomic velocity classes in this preparation step are responsible for the presence of several satellite lines that can be found in the fluorescence decay spectra of both 85Rb and 87Rb. Compared to the main lines, these satellites do not show a strong dependence on the relative linear polarization directions of the lasers used in the preparation and the electric quadrupole steps. The relative intensities of the satellites decrease as the intensity of the preparation laser increases. Results of a rate equation calculation that explicitly includes selection-of-velocity effects indicate that optical pumping plays a central role in determining the relative intensities and the polarization dependence of the satellite lines. When the preparation laser is locked to the <?CDATA $5S_{1/2} \ F_1 = 1 \to 5P_{3/2} \ F_2 = 0$ ?> 5 S 1 / 2 F 1 = 1 → 5 P 3 / 2 F 2 = 0 low-F cyclic transition in 87Rb, six lines were found in addition to the <?CDATA $5P_{3/2} \ F_2 = 0 \to 6P_{3/2} \ F_3 = 2 $?> 5 P 3 / 2 F 2 = 0 → 6 P 3 / 2 F 3 = 2 lone electric quadrupole transition for zero velocity atoms. In this case, the calculated spectrum is necessary for the correct interpretation of the experimental results, clearly indicating that optical pumping and selection of velocities are responsible for these six additional electric quadrupole lines.Abstract This article presents detailed experimental and theoretical studies of the satellite fluorescence lines observed when the <?CDATA $5P_{3/2} \to 6P_J $?> 5 P 3 / 2 → 6 P J , ( <?CDATA $J = 1/2 $?> J = 1 / 2 , <?CDATA $3/2$?> 3 / 2 ) electric quadrupole transition (E2) is excited in a room temperature vapor of rubidium atoms. The initial state of this E2 transition is prepared by a narrow linewidth (9 MHz) laser locked to one of the dominant <?CDATA $5S_{1/2} \to 5P_{3/2} $?> 5 S 1 / 2 → 5 P 3 / 2 D2 hyperfine excitations for zero-velocity atoms. Effects due to the selection of different atomic velocity classes in this preparation step are responsible for the presence of several satellite lines that can be found in the fluorescence decay spectra of both 85Rb and 87Rb. Compared to the main lines, these satellites do not show a strong dependence on the relative linear polarization directions of the lasers used in the preparation and the electric quadrupole steps. The relative intensities of the satellites decrease as the intensity of the preparation laser increases. Results of a rate equation calculation that explicitly includes selection-of-velocity effects indicate that optical pumping plays a central role in determining the relative intensities and the polarization dependence of the satellite lines. When the preparation laser is locked to the <?CDATA $5S_{1/2} \ F_1 = 1 \to 5P_{3/2} \ F_2 = 0$?> 5 S 1 / 2 F 1 = 1 → 5 P 3 / 2 F 2 = 0 low-F cyclic transition in 87Rb, six lines were found in addition to the <?CDATA $5P_{3/2} \ F_2 = 0 \to 6P_{3/2} \ F_3 = 2 $?> 5 P 3 / 2 F 2 = 0 → 6 P 3 / 2 F 3 = 2 lone electric quadrupole transition for zero velocity atoms. In this case, the calculated spectrum is necessary for the correct interpretation of the experimental results, clearly indicating that optical pumping and selection of velocities are responsible for these six additional electric quadrupole lines.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 8, 20231 citation

Polarization dependence of double-resonance optical pumping and electromagnetically induced transparency in the 5S1/2−5P3/2−5D5/2 transition of 87 Rb atoms

Han Seb Moon, Heung‐Ryoul Noh

The polarization dependence of double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transition of ${}^{87}$ Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.The polarization dependence of double-resonance optical pumping (DROP) in the ladder-type electromagnetically induced transparency (EIT) of the $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ transition of ${}^{87}$Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.

Physical Review ASep 15, 201121 citations

Spectroscopy of electric dipole and quadrupole transitions in Ra + 224

Spencer Kofford, Haoran Li, Robert Kwapisz +5 more

We report on spectroscopy of the low-lying electronic transitions in $^{224}\mathrm{Ra}^{+}$ . We measured the frequencies of the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ cooling transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{5/2}$ clock transition, the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition, and the $^{2}D_{5/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ repump transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{3/2}$ electric quadrupole transition, and the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make ${}^{224}{\mathrm{Ra}}^{+}$ a promising optical clock candidate.We report on spectroscopy of the low-lying electronic transitions in $^{224}\mathrm{Ra}^{+}$. We measured the frequencies of the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ cooling transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{5/2}$ clock transition, the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition, and the $^{2}D_{5/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ repump transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{3/2}$ electric quadrupole transition, and the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make ${}^{224}{\mathrm{Ra}}^{+}$ a promising optical clock candidate.

arXiv:2409.09873Physical Review AMar 4, 20252 citations

Upper limit on the magnetic dipole contribution to the 5p−8p transition in Rb by use of ultracold atom spectroscopy

R. Pires, Marco Ascoli, Edward E. Eyler +2 more

We report on hyperfine-resolved spectroscopic measurements of the electric-dipole-forbidden $5{p}_{3/2}\ensuremath{\rightarrow}8{p}_{1/2}$ transition in a sample of ultracold $^{87}\text{R}\text{b}$ atoms. The hyperfine selection rules enable the weak magnetic dipole $(M1)$ contribution to the transition strength to be distinguished from the much stronger electric quadrupole $(E2)$ contribution. An upper limit on the $M1$ transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the $M1$ matrix element and find that it is less than the upper limit extracted from the experiment.We report on hyperfine-resolved spectroscopic measurements of the electric-dipole-forbidden $5{p}_{3/2}\ensuremath{\rightarrow}8{p}_{1/2}$ transition in a sample of ultracold $^{87}\text{R}\text{b}$ atoms. The hyperfine selection rules enable the weak magnetic dipole $(M1)$ contribution to the transition strength to be distinguished from the much stronger electric quadrupole $(E2)$ contribution. An upper limit on the $M1$ transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the $M1$ matrix element and find that it is less than the upper limit extracted from the experiment.

arXiv:0908.4444Physical Review ADec 2, 200910 citations

Measurements of the linear polarization degree of the

5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}

transitions

{(j}^{\ensuremath{'}}=1/2,3/2)

in atomic

{}^{87}\mathrm{Rb}

are reported. The radiative transitions are electric-dipole forbidden, but electric-quadrupole allowed. In addition, because of the relatively strong spin-orbit interaction in Rb, the

p\ensuremath{-}p

5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{{j}^{\ensuremath{'}}}

transitions over a wide range of Rb density. We report here observations of a different depolarization effect, whereby the measured polarization of the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{1/2}

transition increases, while that for the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}\ensuremath{\rightarrow}8p{}^{2}{P}_{3/2}

transition decreases with increasing Rb density. The behavior is attributed to strong laser field effects associated with the

5s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}5p{}^{2}{P}_{3/2}

resonance transition.

Precision measurements on the 5s

{\mathrm{}}^{2}

{\mathrm{S}}_{1\mathrm{/}2}

\ensuremath{\rightarrow}5p

{\mathrm{}}^{2}

{\mathrm{P}}_{\mathrm{j}}

\ensuremath{\rightarrow}8s

{\mathrm{}}^{2}

{\mathrm{S}}_{1\mathrm{/}2}

two-photon, two-color polarization spectrum in atomic Rb are reported. As a result of interference between the transition amplitudes for the process, the spectrum is strongly frequency and linear polarization dependent in the vicinity of the 5s

{\mathrm{}}^{2}

{\mathrm{S}}_{1\mathrm{/}2}

\ensuremath{\rightarrow}5p

{\mathrm{}}^{2}

{\mathrm{P}}_{1\mathrm{/}2}

and 5s

{\mathrm{}}^{2}

{\mathrm{S}}_{1\mathrm{/}2}

\ensuremath{\rightarrow}5p

{\mathrm{}}^{2}

{\mathrm{P}}_{3\mathrm{/}2}

resonance transitions, with the linear polarization degree varying from nearly +100% to -100% over the approximate 500-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range of the data. For absorption of two collinearly polarized photons, complete destructive interference for the process occurs at a critical detuning from the 5s

{\mathrm{}}^{2}

{\mathrm{S}}_{1\mathrm{/}2}

\ensuremath{\rightarrow}5p

{\mathrm{}}^{2}

{\mathrm{P}}_{3\mathrm{/}2}

resonance transition given by ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$=-155.83(3) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The location of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$ is determined primarily by the relative transition matrix elements through the 5p

{\mathrm{}}^{2}

{\mathrm{P}}_{\mathrm{j}}

multiplet, but also depends significantly on contributions from more energetic np

{\mathrm{}}^{2}

P levels. The null in the excitation occurring at the critical frequency allows experimental determination of a type of sum rule that depends only on the atomic matrix elements and the value of ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{c}}$. Such sum rules are defined and presented for the present experiment in Rb and for a recent similar experiment in Na.

An earlier study of the 6s

{\mathrm{}}^{2}

{\mathit{S}}_{1/2}

\ensuremath{\rightarrow}5d

{\mathrm{}}^{2}

{\mathit{D}}_{\mathit{j}}

\ensuremath{\rightarrow}11p

{\mathrm{}}^{2}

{\mathit{P}}_{3/2}

two-photon, dipole-quadrupole transition in Cs is extended by including the effect of an external static electric field. The dependence of the absorption spectrum on the relative polarizations of the two light sources is found to be greatly modified by a moderately sized electric field, the predominant effect being mixing of the resonant 6p

{\mathrm{}}^{2}

{\mathit{P}}_{\mathit{j}}

levels into the ground 6s

{\mathrm{}}^{2}

{\mathit{S}}_{1/2}

level. Compact theoretical expressions, parametrized in terms of the electric-field strength and the relative transition matrix elements through the 5d

{\mathrm{}}^{2}

{\mathit{D}}_{\mathit{j}}

multiplet levels, are given. Results are presented for the electric-field dependence of a linear depolarization ratio, which is very sensitive to these quantities. \textcopyright{} 1996 The American Physical Society.

3/2

?> 3 / 2 ) electric quadrupole transition (E2) is excited in a room temperature vapor of rubidium atoms. The initial state of this E2 transition is prepared by a narrow linewidth (9 MHz) laser locked to one of the dominant <?CDATA $5S_{1/2} \to 5P_{3/2} $?> 5 S 1 / 2 → 5 P 3 / 2 D2 hyperfine excitations for zero-velocity atoms. Effects due to the selection of different atomic velocity classes in this preparation step are responsible for the presence of several satellite lines that can be found in the fluorescence decay spectra of both 85Rb and 87Rb. Compared to the main lines, these satellites do not show a strong dependence on the relative linear polarization directions of the lasers used in the preparation and the electric quadrupole steps. The relative intensities of the satellites decrease as the intensity of the preparation laser increases. Results of a rate equation calculation that explicitly includes selection-of-velocity effects indicate that optical pumping plays a central role in determining the relative intensities and the polarization dependence of the satellite lines. When the preparation laser is locked to the <?CDATA

5S_{1/2} \ F_1 = 1 \to 5P_{3/2} \ F_2 = 0

?> 5 S 1 / 2 F 1 = 1 → 5 P 3 / 2 F 2 = 0 low-F cyclic transition in 87Rb, six lines were found in addition to the <?CDATA $5P_{3/2} \ F_2 = 0 \to 6P_{3/2} \ F_3 = 2 $?> 5 P 3 / 2 F 2 = 0 → 6 P 3 / 2 F 3 = 2 lone electric quadrupole transition for zero velocity atoms. In this case, the calculated spectrum is necessary for the correct interpretation of the experimental results, clearly indicating that optical pumping and selection of velocities are responsible for these six additional electric quadrupole lines.

{}^{87}

Rb atoms is studied. The transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=2,3,4)$ transition were observed as caused by EIT, DROP, and saturation effects in the various polarization combinations between the probe and coupling lasers. The features of the double-structure transmittance spectra in the $5{S}_{1/2}(F=2)\ensuremath{-}5{P}_{3/2}({F}^{\ensuremath{'}}=3)\ensuremath{-}5{D}_{5/2}({F}^{\ensuremath{'}\ensuremath{'}}=4)$ cycling transition were attributed to the difference in saturation effect according to the transition routes between the Zeeman sublevels and the EIT according to the two-photon transition probability.

We report on spectroscopy of the low-lying electronic transitions in

^{224}\mathrm{Ra}^{+}

. We measured the frequencies of the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ cooling transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{5/2}$ clock transition, the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition, and the $^{2}D_{5/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ cleanout transition. From these measurements we calculate the frequencies of the $^{2}D_{3/2}\ensuremath{\leftrightarrow}^{2}P_{1/2}$ repump transition, the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}D_{3/2}$ electric quadrupole transition, and the $^{2}S_{1/2}\ensuremath{\leftrightarrow}^{2}P_{3/2}$ electric dipole transition. The ion's low charge-to-mass ratio and convenient wavelengths make

{}^{224}{\mathrm{Ra}}^{+}

a promising optical clock candidate.

We report on hyperfine-resolved spectroscopic measurements of the electric-dipole-forbidden $5{p}_{3/2}\ensuremath{\rightarrow}8{p}_{1/2}$ transition in a sample of ultracold

^{87}\text{R}\text{b}

atoms. The hyperfine selection rules enable the weak magnetic dipole

(M1)

contribution to the transition strength to be distinguished from the much stronger electric quadrupole

(E2)

contribution. An upper limit on the

M1

transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the

M1

matrix element and find that it is less than the upper limit extracted from the experiment.