Physical Review A

Combined experimental and theoretical study of the 6p2Pj→8s2S1/2 relative transition matrix elements in atomic Cs

A. Sieradzan, Mark D. Havey, Marianna S. Safronova

Published Feb 6, 2004• 19 citations

Abstract

A combined experimental and theoretical study of transition matrix elements of the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an $\ensuremath{\approx}200{\mathrm{cm}}^{\ensuremath{-}1}$ range on the low-frequency side of the $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{}^{2}{P}_{3/2}$ resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance $6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}\mathrm{np}{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}$ transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the $6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}(j=1/2,3/2)$ transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).

DOI: 10.1103/physreva.69.022502

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Electric dipole matrix elements for the 6p2PJ→7s2S1/2 transition in atomic cesium

George Toh, Amy Damitz, Nathan Glotzbach +5 more

arXiv:1901.00480Physical Review AMar 5, 201922 citations

Two-photon, two-color polarization spectroscopy of the 3ts2 S1/2 → 5ts2 S1/2 stransitionin atomic Na: Measurement of relative transition matrix elements

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

Physical Review AJan 1, 19979 citations

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

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Nonlinear optical approach to matrix-element spectroscopy of the 5s2S1/2→ 5p2Pj→ 5d2Dj′transitions in87Rb

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arXiv:physics/0308092Journal of Physics B Atomic Molecular and Optical PhysicsMay 15, 20068 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

Theoretical investigation of two-color, two-photon, 6s 2 S1/2 →5d 2 Dj →11p 2 P3/2 excitation and depolarization spectra in atomic Cs

B. V. Dobrydnev, Mark D. Havey

Physical Review ANov 1, 19955 citations

Physical Review A

Combined experimental and theoretical study of the 6p2Pj→8s2S1/2 relative transition matrix elements in atomic Cs

A. Sieradzan, Mark D. Havey, Marianna S. Safronova

Published Feb 6, 2004• 19 citations

Publisher

Abstract

A combined experimental and theoretical study of transition matrix elements of the

6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}

transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an

\ensuremath{\approx}200{\mathrm{cm}}^{\ensuremath{-}1}

range on the low-frequency side of the

6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{}^{2}{P}_{3/2}

resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance

6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}\mathrm{np}{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}

transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the

6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}(j=1/2,3/2)

transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).

DOI: 10.1103/physreva.69.022502

Related papers

Electric dipole matrix elements for the 6p2PJ→7s2S1/2 transition in atomic cesium

George Toh, Amy Damitz, Nathan Glotzbach +5 more

We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of $R=1.5270(27)$ . Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of $R$ . Combined with our recent determination of the lifetime of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.We report a measurement of the ratio of electric dipole transition matrix elements of cesium for the $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ and $6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rightarrow}7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ transitions. We determine this ratio of matrix elements through comparisons of two-color, two-photon excitation rates of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of $R=1.5270(27)$. Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of $R$. Combined with our recent determination of the lifetime of the $7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}$ state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.

arXiv:1901.00480Physical Review AMar 5, 201922 citations

Two-photon, two-color polarization spectroscopy of the 3ts2 S1/2 → 5ts2 S1/2 stransitionin atomic Na: Measurement of relative transition matrix elements

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

Precise measurements are reported on the linear polarization spectrum associated with two-photon, two-color spectroscopy of the 3 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition in atomic Na. Measurements are made in an approximately 40-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range in the vicinity of the 3 ${\mathrm{p}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ (j=1/2,3/2) levels, which serve as the principal intermediate levels for the two-photon transitions. Because of interference between the transition amplitudes through each fine-structure multiplet component, the polarization varies from nearly 100% to -100% within this spectral range. Modeling the data to include the effects of more energetic p levels and allowing for a j-dependent ratio of transition amplitudes R results in an excellent fit to the data. Estimation of the contribution of higher p levels allows extraction of a value and sign for R=+1.0012(12). This result is combined with recent measurements of the lifetime of the resonance transitions in Na to obtain a value for the ratio of excited-state transition-matrix elements for the 3 ${\mathrm{p}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ \ensuremath{\rightarrow}5 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition (j=3/2 compared to j=1/2) of 1.0013(15).Precise measurements are reported on the linear polarization spectrum associated with two-photon, two-color spectroscopy of the 3 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ \ensuremath{\rightarrow}5 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition in atomic Na. Measurements are made in an approximately 40-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range in the vicinity of the 3 ${\mathrm{p}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ (j=1/2,3/2) levels, which serve as the principal intermediate levels for the two-photon transitions. Because of interference between the transition amplitudes through each fine-structure multiplet component, the polarization varies from nearly 100% to -100% within this spectral range. Modeling the data to include the effects of more energetic p levels and allowing for a j-dependent ratio of transition amplitudes R results in an excellent fit to the data. Estimation of the contribution of higher p levels allows extraction of a value and sign for R=+1.0012(12). This result is combined with recent measurements of the lifetime of the resonance transitions in Na to obtain a value for the ratio of excited-state transition-matrix elements for the 3 ${\mathrm{p}}^{2}$ ${\mathrm{P}}_{\mathrm{j}}$ \ensuremath{\rightarrow}5 ${\mathrm{s}}^{2}$ ${\mathrm{S}}_{1\mathrm{/}2}$ transition (j=3/2 compared to j=1/2) of 1.0013(15).

Physical Review AJan 1, 19979 citations

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

Nonlinear optical approach to matrix-element spectroscopy of the 5s2S1/2→ 5p2Pj→ 5d2Dj′transitions in87Rb

Servet Bayram, Mark D. Havey, Marianna S. Safronova +1 more

We present in this paper results of a nonlinear optical spectroscopy approach to measurement of excited-state transition matrix elements. Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 3/2 two-photon transitions in atomic 87 Rb. Previous measurements were made to high precision, but further improvement of the accuracy was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present paper, we show that theoretical relative transition amplitudes for the excited state 5p 2 P j → 5d 2 D 3/2 doublet (ratio = 1.098(9)) are now in excellent agreement with experiment (ratio = 1.090(6)). This result, combined with our recent work on caesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. Detailed discussion of the experimental technique and supporting data, including polarization measurements on the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 5/2 transitions, is also presented.We present in this paper results of a nonlinear optical spectroscopy approach to measurement of excited-state transition matrix elements. Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 3/2 two-photon transitions in atomic 87 Rb. Previous measurements were made to high precision, but further improvement of the accuracy was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present paper, we show that theoretical relative transition amplitudes for the excited state 5p 2 P j → 5d 2 D 3/2 doublet (ratio = 1.098(9)) are now in excellent agreement with experiment (ratio = 1.090(6)). This result, combined with our recent work on caesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. Detailed discussion of the experimental technique and supporting data, including polarization measurements on the 5s 2 S 1/2 → 5p 2 P j → 5d 2 D 5/2 transitions, is also presented.

arXiv:physics/0308092Journal of Physics B Atomic Molecular and Optical PhysicsMay 15, 20068 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

Theoretical investigation of two-color, two-photon, 6s 2 S1/2 →5d 2 Dj →11p 2 P3/2 excitation and depolarization spectra in atomic Cs

B. V. Dobrydnev, Mark D. Havey

Results of a theoretical investigation of two-photon, two-color excitation and linear depolarization spectra in atomic cesium are presented. The case of two-beam excitation, where one photon is absorbed through a quadrupole amplitude and the other through a dipole amplitude, is considered. When excitation is through a spin multiplet, the final-state population produced depends sensitively on the relative transition amplitudes through the nondengenerate spin-multiplet terms. In addition, the transition rate contains interference terms depending on the relative directions of the two beams. These terms are manifested strongly when the intermediate states are nonresonant and when the two beams have approximately the same frequency. Application of the results to the 6s ${\mathrm{}}^{2}$ ${\mathit{S}}_{1/2}$ \ensuremath{\rightarrow}5d ${\mathrm{}}^{2}$ ${\mathit{D}}_{\mathit{j}}$ \ensuremath{\rightarrow}11p ${\mathrm{}}^{2}$ ${\mathit{P}}_{3/2}$ , quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.Results of a theoretical investigation of two-photon, two-color excitation and linear depolarization spectra in atomic cesium are presented. The case of two-beam excitation, where one photon is absorbed through a quadrupole amplitude and the other through a dipole amplitude, is considered. When excitation is through a spin multiplet, the final-state population produced depends sensitively on the relative transition amplitudes through the nondengenerate spin-multiplet terms. In addition, the transition rate contains interference terms depending on the relative directions of the two beams. These terms are manifested strongly when the intermediate states are nonresonant and when the two beams have approximately the same frequency. Application of the results to 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}$, quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.

Physical Review ANov 1, 19955 citations

A combined experimental and theoretical study of transition matrix elements of the

6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}

transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an

\ensuremath{\approx}200{\mathrm{cm}}^{\ensuremath{-}1}

range on the low-frequency side of the

6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{}^{2}{P}_{3/2}

resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance

6s{}^{2}{S}_{1/2}\ensuremath{\rightarrow}\mathrm{np}{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}

6p{}^{2}{P}_{j}\ensuremath{\rightarrow}8s{}^{2}{S}_{1/2}(j=1/2,3/2)

transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).

7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

state using laser beams with polarizations parallel to one another vs perpendicular to one another. Our result of $R\ensuremath{\equiv}\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}/\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=1.5272(17)$ is in excellent agreement with a theoretical prediction of

R=1.5270(27)

. Moreover, the accuracy of the experimental ratio is sufficiently high to differentiate between various theoretical approaches. To our knowledge, there are no prior experimental measurements of

R

. Combined with our recent determination of the lifetime of the

7s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}

state, we determine reduced matrix elements for these two transitions, $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{3/2}\ensuremath{\rangle}=\ensuremath{-}6.489(5)\phantom{\rule{4pt}{0ex}}{a}_{0}$ and $\ensuremath{\langle}7s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}||r||6p{\phantom{\rule{4pt}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rangle}=\ensuremath{-}4.249(4)\phantom{\rule{4pt}{0ex}}{a}_{0}$. These matrix elements are also in excellent agreement with theoretical calculations. These measurements improve knowledge of Cs properties needed for parity violation studies and provide benchmarks for tests of high-precision theory.

Precise measurements are reported on the linear polarization spectrum associated with two-photon, two-color spectroscopy of the 3

{\mathrm{s}}^{2}

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

\ensuremath{\rightarrow}5

{\mathrm{s}}^{2}

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

transition in atomic Na. Measurements are made in an approximately 40-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range in the vicinity of the 3

{\mathrm{p}}^{2}

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

(j=1/2,3/2) levels, which serve as the principal intermediate levels for the two-photon transitions. Because of interference between the transition amplitudes through each fine-structure multiplet component, the polarization varies from nearly 100% to -100% within this spectral range. Modeling the data to include the effects of more energetic p levels and allowing for a j-dependent ratio of transition amplitudes R results in an excellent fit to the data. Estimation of the contribution of higher p levels allows extraction of a value and sign for R=+1.0012(12). This result is combined with recent measurements of the lifetime of the resonance transitions in Na to obtain a value for the ratio of excited-state transition-matrix elements for the 3

{\mathrm{p}}^{2}

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

\ensuremath{\rightarrow}5

{\mathrm{s}}^{2}

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

transition (j=3/2 compared to j=1/2) of 1.0013(15).

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.

{\mathrm{}}^{2}

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

\ensuremath{\rightarrow}5d

{\mathrm{}}^{2}

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

\ensuremath{\rightarrow}11p

{\mathrm{}}^{2}

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

, quadrupole-dipole transition in atomic Cs is made. Polarization-dependent excitation spectra are presented for this case. Effects of hyperfine interactions are also considered.