arXiv:physics/0406018 · Physical Review A

Wavelength-dependent ac Stark shift of the S01‐P13 transition at 657nm in Ca

C. Degenhardt, Hardo Stoehr, Uwe Sterr, F. Riehle, Christian Lisdat

Published Aug 27, 2004• 46 citations

Abstract

We have measured the ac Stark shift of the $4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}$ line in $^{40}\mathrm{Ca}$ for perturbing laser wavelengths between $780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ with a time domain Ramsey-Bord\'e atom interferometer. We found a zero crossing of the shift for the ${m}_{S}=0--{m}_{P}=0$ transition and $\ensuremath{\sigma}$ polarized perturbation at $800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The data was analyzed by a model deriving the energy shift from known transition wavelengths and strengths. To fit our data, we adjusted the Einstein $A$ coefficients of the $4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ and $4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P$ fine structure multiplets. With these we can predict vanishing ac Stark shifts for the $^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1$ transition and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light at $983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and at $735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for the transition to the $^{3}P_{0}$ level.

DOI: 10.1103/physreva.70.023414

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Sensitive measurement of phase shifts due to the ac Stark effect in a Ca optical Ramsey interferometer

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Magic-zero and magic wavelengths of the Ca atom

Ru-Kui Zhang, Jun Jiang, Chenzhong Dong +1 more

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Dispersion-shaped ac Stark phase shift of Ca intercombination transitions with a time-domain atom interferometer

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Stark-shift measurement of the (6s )2 1 S0 →(6s6p )1 P1 barium transition

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Physical Review AMay 1, 199511 citations

Dynamic Stark effect and forbidden-transition spectral line shapes

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arXiv:physics/0512111Physical Review AApr 27, 200646 citations

arXiv:physics/0406018 · Physical Review A

Wavelength-dependent ac Stark shift of the S01‐P13 transition at 657nm in Ca

C. Degenhardt, Hardo Stoehr, Uwe Sterr, F. Riehle, Christian Lisdat

Published Aug 27, 2004• 46 citations

arXiv HTML PDF

Abstract

We have measured the ac Stark shift of the

4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}

line in

^{40}\mathrm{Ca}

for perturbing laser wavelengths between

780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and

1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

with a time domain Ramsey-Bord'e atom interferometer. We found a zero crossing of the shift for the

{m}_{S}=0--{m}_{P}=0

transition and

\ensuremath{\sigma}

polarized perturbation at

800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

. The data was analyzed by a model deriving the energy shift from known transition wavelengths and strengths. To fit our data, we adjusted the Einstein

A

coefficients of the

4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

and

4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

fine structure multiplets. With these we can predict vanishing ac Stark shifts for the

^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1

transition and

{\ensuremath{\sigma}}^{\ensuremath{-}}

light at

983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and at

735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

for the transition to the

^{3}P_{0}

level.

DOI: 10.1103/physreva.70.023414

Related papers

Sensitive measurement of phase shifts due to the ac Stark effect in a Ca optical Ramsey interferometer

Atsuo Morinaga, Toshiharu Tako, Nobuhiko Ito

We constructed an optical Ramsey atomic interferometer, which has a resolution of 8 fm for the difference between arms of the interferometer, and used it to examine the phase shift due to the ac Stark effect of the excited state of the intercombination line ${(}^{1}$ ${\mathit{S}}_{0}$ ${\mathrm{\ensuremath{-}}}^{3}$ ${\mathit{P}}_{1}$ ) of Ca. It was clearly observed that the phase shift is in proportion to the field power and in inverse proportion to the detuning frequency of the laser. The proportionality coefficient obtained was in good agreement with the theoretical one.We constructed an optical Ramsey atomic interferometer, which has a resolution of 8 fm for the difference between arms of the interferometer, and used it to examine the phase shift due to the ac Stark effect of the excited state of the intercombination line ${(}^{1}$${\mathit{S}}_{0}$${\mathrm{\ensuremath{-}}}^{3}$${\mathit{P}}_{1}$) of Ca. It was clearly observed that the phase shift is in proportion to the field power and in inverse proportion to the detuning frequency of the laser. The proportionality coefficient obtained was in good agreement with the theoretical one.

Physical Review AAug 1, 199331 citations

Magic-zero and magic wavelengths of the Ca atom

Ru-Kui Zhang, Jun Jiang, Chenzhong Dong +1 more

The relativistic configuration interaction plus many-body perturbation (RCI $+$ MBPT) method is utilized to calculate the wave functions, energy levels, and reduced $E1$ transition matrix elements of Ca atoms in detail. The static and dynamic polarizabilities of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}, 4s4p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ , and $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$ states are determined by the sum-over-states method. A number of magic-zero wavelengths for the ground and $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ states, as well as magic wavelengths for the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, are obtained. We suggest that the measurements of the magic-zero wavelengths of the $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ states can be used to determine oscillator strengths with high precision. In addition, the angle-dependent magic wavelengths of each magnetic sublevel transition of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition are provided, which are of particular interest for optical frequency measurements, Bose-Einstein condensate generation, and superradiant laser technology.The relativistic configuration interaction plus many-body perturbation (RCI $+$ MBPT) method is utilized to calculate the wave functions, energy levels, and reduced $E1$ transition matrix elements of Ca atoms in detail. The static and dynamic polarizabilities of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}, 4s4p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$, and $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$ states are determined by the sum-over-states method. A number of magic-zero wavelengths for the ground and $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ states, as well as magic wavelengths for the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, are obtained. We suggest that the measurements of the magic-zero wavelengths of the $4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ states can be used to determine oscillator strengths with high precision. In addition, the angle-dependent magic wavelengths of each magnetic sublevel transition of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition are provided, which are of particular interest for optical frequency measurements, Bose-Einstein condensate generation, and superradiant laser technology.

Physical Review AJul 7, 20237 citations

Dispersion-shaped ac Stark phase shift of Ca intercombination transitions with a time-domain atom interferometer

Tomoya Akatsuka, Kazuya Tanihara, Kenji Komito +2 more

A time-domain atom interferometer with a cold calcium atomic ensemble has been developed with a phase resolution ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}=140/\sqrt{\ensuremath{\tau}}$ mrad/s ${}^{1/2}$ at the integration time $\ensuremath{\tau}$. Using this atom interferometer, the dispersion-shaped ac Stark phase shift with a sharp reversal on resonance was demonstrated under the perturbation light near the resonance frequency of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{4pt}{0ex}}{m}_{J}=0{\ensuremath{-}}^{3}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{P}_{1},\phantom{\rule{4pt}{0ex}}{m}_{J}=\ensuremath{-}1$ transition. The phase shift was well described by a convolution of functions of the ac Stark potential and a Rabi excitation, and it was found that the lifetime of the ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.A time-domain atom interferometer with a cold calcium atomic ensemble has been developed with a phase resolution ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}=140/\sqrt{\ensuremath{\tau}}$ mrad/s${}^{1/2}$ at the integration time $\ensuremath{\tau}$. Using this atom interferometer, the dispersion-shaped ac Stark phase shift with a sharp reversal on resonance was demonstrated under the perturbation light near the resonance frequency of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{4pt}{0ex}}{m}_{J}=0{\ensuremath{-}}^{3}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{P}_{1},\phantom{\rule{4pt}{0ex}}{m}_{J}=\ensuremath{-}1$ transition. The phase shift was well described by a convolution of functions of the ac Stark potential and a Rabi excitation, and it was found that the lifetime of the ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.

Physical Review AAug 28, 20121 citation

Measurement of the tune-out wavelength for Cs133 at 880 nm

Apichayaporn Ratkata, Philip D. Gregory, Andrew D. Innes +6 more

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$ , ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$ , ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$ . At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the ${D}_{1}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and ${D}_{2}$, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for $^{133}\mathrm{Cs}$ in the ground hyperfine state $(F=3,{m}_{F}=+3)$. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a $^{133}\mathrm{Cs}$ Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

arXiv:2110.00043Physical Review ANov 22, 202115 citations

Stark-shift measurement of the (6s )2 1 S0 →(6s6p )1 P1 barium transition

Junlei Li, William Arie van Wijngaarden

The Stark shift of the (6s ${)}^{2}$ $^{1}$ ${\mathit{S}}_{0}$ \ensuremath{\rightarrow}(6s6p ${)}^{1}$ ${\mathit{P}}_{1}$ transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark-shift rate was found to be -28.532\ifmmode\pm\else\textpm\fi{}0.060 kHz/(kV/cm ${)}^{2}$ . The hyperfine splitting of the $^{135,137}\mathrm{Ba}$ F=1/2 level relative to $^{138}\mathrm{Ba}$ of the (6s6p ${)}^{1}$ ${\mathit{P}}_{1}$ state was determined to be -549.47\ifmmode\pm\else\textpm\fi{}0.12 MHz, where the minus sign indicates that the $^{138}\mathrm{Ba}$ transition is at a lower frequency.The Stark shift of the (6s${)}^{2}$ $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}(6s6p${)}^{1}$${\mathit{P}}_{1}$ transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark-shift rate was found to be -28.532\ifmmode\pm\else\textpm\fi{}0.060 kHz/(kV/cm${)}^{2}$. The hyperfine splitting of the $^{135,137}\mathrm{Ba}$ F=1/2 level relative to $^{138}\mathrm{Ba}$ of the (6s6p${)}^{1}$${\mathit{P}}_{1}$ state was determined to be -549.47\ifmmode\pm\else\textpm\fi{}0.12 MHz, where the minus sign indicates that the $^{138}\mathrm{Ba}$ transition is at a lower frequency.

Physical Review AMay 1, 199511 citations

Dynamic Stark effect and forbidden-transition spectral line shapes

J. E. Stalnaker, Dmitry Budker, S. J. Freedman +3 more

We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s^{3}D_{1}$ transition at $408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}$ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parametrizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5d6s^{3}D_{1}$ transition at $408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the $6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}$ ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.

arXiv:physics/0512111Physical Review AApr 27, 200646 citations

We have measured the ac Stark shift of the

4{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P_{1}

line in

^{40}\mathrm{Ca}

for perturbing laser wavelengths between

780\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and

1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

with a time domain Ramsey-Bord'e atom interferometer. We found a zero crossing of the shift for the

{m}_{S}=0--{m}_{P}=0

transition and

\ensuremath{\sigma}

polarized perturbation at

800.8(22)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

. The data was analyzed by a model deriving the energy shift from known transition wavelengths and strengths. To fit our data, we adjusted the Einstein

A

coefficients of the

4s3d\phantom{\rule{0.2em}{0ex}}^{3}D--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

and

4s5s\phantom{\rule{0.2em}{0ex}}^{3}S--4s4p\phantom{\rule{0.2em}{0ex}}^{3}P

fine structure multiplets. With these we can predict vanishing ac Stark shifts for the

^{1}S_{0}\phantom{\rule{0.2em}{0ex}}m=0--^{3}P_{1}\phantom{\rule{0.2em}{0ex}}m=1

transition and

{\ensuremath{\sigma}}^{\ensuremath{-}}

light at

983(12)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

and at

735.5(20)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

for the transition to the

^{3}P_{0}

level.

{(}^{1}

{\mathit{S}}_{0}

${\mathrm{\ensuremath{-}}}^{3}$

{\mathit{P}}_{1}

) of Ca. It was clearly observed that the phase shift is in proportion to the field power and in inverse proportion to the detuning frequency of the laser. The proportionality coefficient obtained was in good agreement with the theoretical one.

The relativistic configuration interaction plus many-body perturbation (RCI

+

MBPT) method is utilized to calculate the wave functions, energy levels, and reduced

E1

transition matrix elements of Ca atoms in detail. The static and dynamic polarizabilities of the

4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}, 4s4p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}

, and

4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}

states are determined by the sum-over-states method. A number of magic-zero wavelengths for the ground and

4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}

states, as well as magic wavelengths for the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, are obtained. We suggest that the measurements of the magic-zero wavelengths of the

4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}

states can be used to determine oscillator strengths with high precision. In addition, the angle-dependent magic wavelengths of each magnetic sublevel transition of the $4{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}4s4p\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition are provided, which are of particular interest for optical frequency measurements, Bose-Einstein condensate generation, and superradiant laser technology.

A time-domain atom interferometer with a cold calcium atomic ensemble has been developed with a phase resolution ${\ensuremath{\sigma}}_{\ensuremath{\varphi}}=140/\sqrt{\ensuremath{\tau}}$ mrad/s

{}^{1/2}

at the integration time $\ensuremath{\tau}$. Using this atom interferometer, the dispersion-shaped ac Stark phase shift with a sharp reversal on resonance was demonstrated under the perturbation light near the resonance frequency of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0},\phantom{\rule{4pt}{0ex}}{m}_{J}=0{\ensuremath{-}}^{3}\phantom{\rule{-0.16em}{0ex}}\phantom{\rule{-0.16em}{0ex}}{P}_{1},\phantom{\rule{4pt}{0ex}}{m}_{J}=\ensuremath{-}1$ transition. The phase shift was well described by a convolution of functions of the ac Stark potential and a Rabi excitation, and it was found that the lifetime of the

{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}

state is 0.45 \ifmmode\pm\else\textpm\fi{} 0.03 ms.

We perform a measurement of the tune-out wavelength, ${\ensuremath{\lambda}}_{0}$, between the

{D}_{1}

, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{1/2}$, and

{D}_{2}

, ${6}^{2}{S}_{1/2}\ensuremath{\rightarrow}{6}^{2}{P}_{3/2}$, transitions for

^{133}\mathrm{Cs}

in the ground hyperfine state

(F=3,{m}_{F}=+3)

. At ${\ensuremath{\lambda}}_{0}$, the frequency-dependent scalar polarizability is zero leading to a zero scalar ac Stark shift. We measure the polarizability as a function of wavelength using Kapitza-Dirac scattering of a

^{133}\mathrm{Cs}

Bose-Einstein condensate in a one-dimensional optical lattice, and determine the tune-out wavelength to be ${\ensuremath{\lambda}}_{0}=880.21790{(40)}_{\text{stat}}{(8)}_{\text{sys}}$ nm. From this measurement we determine the ratio of reduced matrix elements to be ${|\ensuremath{\langle}6{P}_{3/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}/{|\ensuremath{\langle}6{P}_{1/2}\ensuremath{\parallel}d\ensuremath{\parallel}6{S}_{1/2}\ensuremath{\rangle}|}^{2}=1.9808(2)$. This represents an improvement of a factor of 10 over previous results derived from excited-state lifetime measurements. We use the present measurement as a benchmark test of high-precision theory.

The Stark shift of the (6s

{)}^{2}

^{1}

{\mathit{S}}_{0}

\ensuremath{\rightarrow}(6s6p

{)}^{1}

{\mathit{P}}_{1}

transition in barium was measured using a laser to excite an atomic beam as it traversed a uniform electric field and a field-free region. The laser frequency was scanned across the transition while fluorescence produced by the radiative decay of the excited state was detected. The frequency scan was calibrated using an acousto-optic modulator which frequency shifted the laser by a specified amount. The Stark-shift rate was found to be -28.532\ifmmode\pm\else\textpm\fi{}0.060 kHz/(kV/cm

{)}^{2}

. The hyperfine splitting of the

^{135,137}\mathrm{Ba}

F=1/2 level relative to

^{138}\mathrm{Ba}

of the (6s6p

{)}^{1}

{\mathit{P}}_{1}

state was determined to be -549.47\ifmmode\pm\else\textpm\fi{}0.12 MHz, where the minus sign indicates that the

^{138}\mathrm{Ba}

transition is at a lower frequency.

408\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the

6{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}

ground state. A detailed description of the experiment and analysis is presented. A biproduct of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb.