arXiv:1901.00480 · Physical Review A

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

George Toh, Amy Damitz, Nathan Glotzbach, Jonah Quirk, Ian Stevenson, J. Choi, Marianna S. Safronova, Daniel S. Elliott

Published Mar 5, 2019• 22 citations

Abstract

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.

DOI: 10.1103/physreva.99.032504

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

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Physical Review AFeb 6, 200419 citations

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

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Oct 10, 20230 citations

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arXiv:1901.00480 · Physical Review A

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

George Toh, Amy Damitz, Nathan Glotzbach, Jonah Quirk, Ian Stevenson, J. Choi, Marianna S. Safronova, Daniel S. Elliott

Published Mar 5, 2019• 22 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.99.032504

Related papers

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

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).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).

Physical Review AFeb 6, 200419 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

Determination of magic wavelengths for the 7s S1/22−7p P3/2,1/22 transitions in Fr

Sukhjit Singh Sehra, B. K. Sahoo, Bindiya Arora

Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7{P}_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the $7P$ states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.Magic wavelengths (${\ensuremath{\lambda}}_{\mathrm{magic}}$) for the $7{S}_{1/2}\ensuremath{-}7{P}_{1/2,3/2}$ transitions (D lines) in Fr were reported by Dammalapati et al. [U. Dammalapati, K. Harada, and Y. Sakemi, Phys. Rev. A 93, 043407 (2016)]. These ${\ensuremath{\lambda}}_{\mathrm{magic}}$ were determined by plotting dynamic polarizabilities ($\ensuremath{\alpha}$) of the involved states with the above transitions against a desired range of wavelengths. Electric dipole (E1) matrix elements listed in [J. E. Sansonetti, J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7{P}_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the $7P$ states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.

arXiv:1608.02073Physical Review AAug 29, 201613 citations

Fast-beam laser lifetime measurements of the cesium 6p2P1/2,3/2 states

Robert J. Rafac, Carol E. Tanner, A. E. Livingston +1 more

We provide a detailed description of our fast-beam laser lifetime measurements in atomic cesium. Selective excitation of the neutral ${}^{133}\mathrm{Cs}$ $6p{}^{2}{P}_{1/2}$ and $6p{}^{2}{P}_{3/2}$ states is accomplished with resonant diode laser light directed transversely to the atomic velocity. The in-flight decay of the excited-state fluorescence is observed with a position-correlated single photon-counting detector. The Doppler-shifted $6p{}^{2}{P}_{3/2}$ resonance, when probed with longitudinally propagating laser radiation, provides a precise means for determination of the beam velocity, and converts the position scale to a time scale. Our lifetime results are $35.07\ifmmode\pm\else\textpm\fi{}0.10 \mathrm{ns}$ for the $6p{}^{2}{P}_{1/2}$ state and $30.57\ifmmode\pm\else\textpm\fi{}0.07 \mathrm{ns}$ for the $6p{}^{2}{P}_{3/2}$ state. These results represent a data set larger than in our previous work, and include beam divergence corrections which have been evaluated by two different methods. We present comparisons of our results with previous measurements and with relativistic many-body calculations of atomic transition matrix elements in this neutral alkali system.We provide a detailed description of our fast-beam laser lifetime measurements in atomic cesium. Selective excitation of the neutral ${}^{133}\mathrm{Cs}$ $6p{}^{2}{P}_{1/2}$ and $6p{}^{2}{P}_{3/2}$ states is accomplished with resonant diode laser light directed transversely to the atomic velocity. The in-flight decay of the excited-state fluorescence is observed with a position-correlated single photon-counting detector. The Doppler-shifted $6p{}^{2}{P}_{3/2}$ resonance, when probed with longitudinally propagating laser radiation, provides a precise means for determination of the beam velocity, and converts the position scale to a time scale. Our lifetime results are $35.07\ifmmode\pm\else\textpm\fi{}0.10 \mathrm{ns}$ for the $6p{}^{2}{P}_{1/2}$ state and $30.57\ifmmode\pm\else\textpm\fi{}0.07 \mathrm{ns}$ for the $6p{}^{2}{P}_{3/2}$ state. These results represent a data set larger than in our previous work, and include beam divergence corrections which have been evaluated by two different methods. We present comparisons of our results with previous measurements and with relativistic many-body calculations of atomic transition matrix elements in this neutral alkali system.

Physical Review ANov 1, 199992 citations

Precision determination of dipole transition matrix elements with a single trapped ion

Hua Guan

Abstract In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift and the parity-violating amplitude of the clock transition, and can be used as probes to test quantum electrodynamic effects, especially at the $10^{-3}$ - $10^{-4}$ level. We developed a universal experimental approach to precise determination of the dipole transition matrix element with a energy level of two transition channels at various atomic species by using the quantum shelving technique. In which, the time-increased pulses were utilized to induce quantum shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited $^{2}\!P_{1/2}$ state to the $^{2}\!S_{1/2}$ ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this method to single Yb $^+$ ion, and determined the $6p~^{2}\!P_{1/2}$ - $5d~^{2}\!D_{3/2}$ transition matrix element of 2.9395(21)~ $ea_{0}$ , which represents an order of magnitude improvement over previous determination. By combining our result with the $6p~^{2}\!P_{1/2}$ lifetime of 8.12(2)~ns, we extracted the $6s~^{2}\!S_{1/2}$ - $6p~^{2}\!P_{1/2}$ transition matrix element to be 2.4695(31)~ $ea_{0}$ .Abstract In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift and the parity-violating amplitude of the clock transition, and can be used as probes to test quantum electrodynamic effects, especially at the $10^{-3}$-$10^{-4}$ level. We developed a universal experimental approach to precise determination of the dipole transition matrix element with a energy level of two transition channels at various atomic species by using the quantum shelving technique. In which, the time-increased pulses were utilized to induce quantum shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited $^{2}\!P_{1/2}$ state to the $^{2}\!S_{1/2}$ ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this method to single Yb$^+$ ion, and determined the $6p~^{2}\!P_{1/2}$ - $5d~^{2}\!D_{3/2}$ transition matrix element of 2.9395(21)~$ea_{0}$, which represents an order of magnitude improvement over previous determination. By combining our result with the $6p~^{2}\!P_{1/2}$ lifetime of 8.12(2)~ns, we extracted the $6s~^{2}\!S_{1/2}$ - $6p~^{2}\!P_{1/2}$ transition matrix element to be 2.4695(31)~$ea_{0}$.

Oct 10, 20230 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

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}

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).

7{P}_{1/2,3/2}

states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $\ensuremath{\alpha}$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P\ensuremath{-}7S, 7P\ensuremath{-}8S$, and $7P\ensuremath{-}6D$ transitions to $\ensuremath{\alpha}$ of the

7P

states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $\ensuremath{\alpha}$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $\ensuremath{\alpha}$ are found to be in excellent agreement with the other available theoretical results, whereas substituting the E1 matrix elements used by Dammalapati et al. gives very small $\ensuremath{\alpha}$ values for the

7P

states. Owing to this, we find disagreement in ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported by Dammalapati et al. for linearly polarized light, especially at wavelengths close to the D lines and in the infrared region. As a consequence, a ${\ensuremath{\lambda}}_{\mathrm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $\ensuremath{\alpha}$ will be very useful for guiding experiments to carry out their measurements.

We provide a detailed description of our fast-beam laser lifetime measurements in atomic cesium. Selective excitation of the neutral

{}^{133}\mathrm{Cs}

6p{}^{2}{P}_{1/2}

and

6p{}^{2}{P}_{3/2}

states is accomplished with resonant diode laser light directed transversely to the atomic velocity. The in-flight decay of the excited-state fluorescence is observed with a position-correlated single photon-counting detector. The Doppler-shifted

6p{}^{2}{P}_{3/2}

resonance, when probed with longitudinally propagating laser radiation, provides a precise means for determination of the beam velocity, and converts the position scale to a time scale. Our lifetime results are $35.07\ifmmode\pm\else\textpm\fi{}0.10 \mathrm{ns}$ for the

6p{}^{2}{P}_{1/2}

state and $30.57\ifmmode\pm\else\textpm\fi{}0.07 \mathrm{ns}$ for the

6p{}^{2}{P}_{3/2}

state. These results represent a data set larger than in our previous work, and include beam divergence corrections which have been evaluated by two different methods. We present comparisons of our results with previous measurements and with relativistic many-body calculations of atomic transition matrix elements in this neutral alkali system.

10^{-3}

10^{-4}

level. We developed a universal experimental approach to precise determination of the dipole transition matrix element with a energy level of two transition channels at various atomic species by using the quantum shelving technique. In which, the time-increased pulses were utilized to induce quantum shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited

^{2}\!P_{1/2}

state to the

^{2}\!S_{1/2}

ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this method to single Yb

^+

ion, and determined the

6p~^{2}\!P_{1/2}

5d~^{2}\!D_{3/2}

transition matrix element of 2.9395(21)~

ea_{0}

, which represents an order of magnitude improvement over previous determination. By combining our result with the

6p~^{2}\!P_{1/2}

lifetime of 8.12(2)~ns, we extracted the

6s~^{2}\!S_{1/2}

6p~^{2}\!P_{1/2}

transition matrix element to be 2.4695(31)~

ea_{0}

{\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.