arXiv:physics/0502113 · Physical Review Letters

Precision Measurement of Light Shifts in a Single Trapped Ba+ Ion

Jeff A. Sherman, Timo Koerber, Anna Markhotok, Warren Nagourney, E. Norval Fortson

Published Jun 21, 2005• 60 citations

Abstract

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the $6{S}_{1/2}$ and $5{D}_{5/2}$ states to 0.1% precision. We find $R={\ensuremath{\Delta}}_{S}/{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at 514.531 nm where ${\ensuremath{\Delta}}_{S,D}$ are the light shifts of the $m=\ifmmode\pm\else\textpm\fi{}1/2$ splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of $R$ would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.

DOI: 10.1103/physrevlett.94.243001

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Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and the determination of atomic dipole matrix elements

Jeff A. Sherman, A. Andalkar, Warren Nagourney +1 more

arXiv:0808.1826Physical Review ANov 26, 200835 citations

rf Spectroscopy with a Single Ba+ Ion

Timo Koerber, M. Schacht, Kristi R. G. Hendrickson +2 more

Physical Review LettersMar 26, 200225 citations

Precision test of the ac Stark shift in a rubidium atomic vapor

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Measurement of the reduced dipole matrix element in Ba$^+$

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Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

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Rb atoms in a blue-detuned dipole trap: Coherence and ground-state differential ac Stark shift

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arXiv:physics/0502113 · Physical Review Letters

Precision Measurement of Light Shifts in a Single Trapped Ba+ Ion

Jeff A. Sherman, Timo Koerber, Anna Markhotok, Warren Nagourney, E. Norval Fortson

Published Jun 21, 2005• 60 citations

arXiv HTML PDF

Abstract

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the

6{S}_{1/2}

and

5{D}_{5/2}

states to 0.1% precision. We find

R={\ensuremath{\Delta}}_{S}/{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)

at 514.531 nm where

{\ensuremath{\Delta}}_{S,D}

are the light shifts of the

m=\ifmmode\pm\else\textpm\fi{}1/2

splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of

R

would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.

DOI: 10.1103/physrevlett.94.243001

Related papers

Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba+ ion and the determination of atomic dipole matrix elements

Jeff A. Sherman, A. Andalkar, Warren Nagourney +1 more

We have measured the ratio $R$ of the vector ac Stark effect (or light shift) in the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at $514.531\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ $m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at $1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ , $R=+0.4176(8)$ . These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.We have measured the ratio $R$ of the vector ac Stark effect (or light shift) in the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at $514.531\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the $6{S}_{1∕2}$ and $5{D}_{3∕2}$ $m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at $1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, $R=+0.4176(8)$. These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.

arXiv:0808.1826Physical Review ANov 26, 200835 citations

rf Spectroscopy with a Single Ba+ Ion

Timo Koerber, M. Schacht, Kristi R. G. Hendrickson +2 more

We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.We have employed the method of shelving to measure Zeeman resonances of a single trapped Ba+ ion. We use optical pumping to place the ion in a selected magnetic sublevel of either the 6S(1/2) ground state or the 5D(3/2) metastable state. The ion is exposed to an rf field, and a probing/shelving mechanism detects whether spin-flip transitions have taken place. We have observed rf transitions with linewidths of 15 Hz, limited by magnetic-field noise. We have also observed the shift in the Zeeman frequency when the ion is illuminated by off-resonant light. A simultaneous measurement of such light shifts in two atomic states of Ba+ will permit a precise determination of the ratio of transition matrix elements.

Physical Review LettersMar 26, 200225 citations

Precision test of the ac Stark shift in a rubidium atomic vapor

Filippo Levi, James C. Camparo, B. Francois +3 more

The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.The ac Stark shift (also known as the ``light shift'') is one of the most important physical processes that arises in precision spectroscopy, affecting the basic understanding of field-matter interactions, measurements of fundamental constants, and even the atomic clocks onboard GPS satellites. Although the theory of the ac Stark shift was fully developed by the 1960s and 1970s, precision tests of theory have, for the most part, been few. Taking advantage of recent developments in atomic clock technology, specifically the pulsed approach to atomic signal generation, which allows frequency measurements with a resolution of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$, we demonstrate a methodology for measuring the ac Stark shift. Here, we report results from a precision examination of the ac Stark shift in a vapor phase system, examining the resonant frequency of the $^{87}\text{Rb}$ 0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the ${D}_{1}$ absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.

Physical Review AFeb 29, 201625 citations

Measurement of the reduced dipole matrix element in Ba $^+$ Measurement of the reduced dipole matrix element in Ba$^+$

N. Jayjong, M. D. K. Lee, K. J. Arnold +1 more

We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$ . By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$ , corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$ ~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$ , we extract the static value $Δα_0(0) = -73.09(12)$ a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.We present a high-precision measurement of the reduced electric-dipole matrix element $\langle P_{1/2}\|r\|S_{1/2}\rangle$ in $^{138}\mathrm{Ba}^+$. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.322\,7(12)$, corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.866\,3(56)$~ns. Combining our experimental results with a prior model for the differential scalar polarizability $Δα_0(ω)$, we extract the static value $Δα_0(0) = -73.09(12)$a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature $\mathrm{Ba}^+$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

physics.atom-phCross-listedarXiv:2607.20920Jul 24, 2026

Precision Measurement of Transition Matrix Elements via Light Shift Cancellation

Creston D. Herold, Varun Vaidya, Xiao Li +3 more

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

arXiv:1208.4291Physical Review LettersDec 14, 201295 citations

Rb atoms in a blue-detuned dipole trap: Coherence and ground-state differential ac Stark shift

D. Sheng, J. Zhang, Luis A. Orozco

Blue-detuned dipole traps and their ability to preserve atomic coherences are interesting for precision measurement applications. In this paper, we present experimental studies on the differential ac Stark shift of the ground-state hyperfine splitting in ${}^{87}$ Rb atoms confined in a dynamic blue-detuned dipole trap. We systematically study the power and detuning effects on the Rabi resonance frequency (differential ac Stark shift) and its linewidth (coherence) and find that their performance is compatible with future parity violation experiments in Fr.Blue-detuned dipole traps and their ability to preserve atomic coherences are interesting for precision measurement applications. In this paper, we present experimental studies on the differential ac Stark shift of the ground-state hyperfine splitting in ${}^{87}$Rb atoms confined in a dynamic blue-detuned dipole trap. We systematically study the power and detuning effects on the Rabi resonance frequency (differential ac Stark shift) and its linewidth (coherence) and find that their performance is compatible with future parity violation experiments in Fr.

Physical Review AJun 14, 20135 citations

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the

6{S}_{1/2}

and

5{D}_{5/2}

states to 0.1% precision. We find

R={\ensuremath{\Delta}}_{S}/{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)

at 514.531 nm where

{\ensuremath{\Delta}}_{S,D}

are the light shifts of the

m=\ifmmode\pm\else\textpm\fi{}1/2

splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of

R

We have measured the ratio

R

of the vector ac Stark effect (or light shift) in the

6{S}_{1∕2}

and

5{D}_{3∕2}

states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found $R={\ensuremath{\Delta}}_{S}∕{\ensuremath{\Delta}}_{D}=\ensuremath{-}11.494(13)$ at

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

where ${\ensuremath{\Delta}}_{S,D}$ are the vector light shifts of the

6{S}_{1∕2}

and

5{D}_{3∕2}

$m=\ifmmode\pm\else\textpm\fi{}1∕2$ splittings due to circularly polarized light, and now we report the value at

1111.68\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

R=+0.4176(8)

. These observations together yield a value of the $⟨5D\ensuremath{\Vert}er\ensuremath{\Vert}4F⟩$ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.

^{87}\text{Rb}

0-0 hyperfine transition for a perturbing laser tuned over a broad optical frequency range (18 GHz) around the

{D}_{1}

absorption resonance. Over the full frequency range the agreement between semiclassical theory and experiment is very good (better than $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$), and in our experiments we test both the frequency dependence of the scalar and tensor components of the light shift.

Measurement of the reduced dipole matrix element in Ba

^+

We present a high-precision measurement of the reduced electric-dipole matrix element

\langle P_{1/2}\|r\|S_{1/2}\rangle

^{138}\mathrm{Ba}^+

. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be

3.322\,7(12)

, corresponding to a

P_{1/2}

excited-state radiative lifetime of

7.866\,3(56)

~ns. Combining our experimental results with a prior model for the differential scalar polarizability

Δα_0(ω)

, we extract the static value

Δα_0(0) = -73.09(12)

a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature

\mathrm{Ba}^+

optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

{}^{87}

Rb atoms confined in a dynamic blue-detuned dipole trap. We systematically study the power and detuning effects on the Rabi resonance frequency (differential ac Stark shift) and its linewidth (coherence) and find that their performance is compatible with future parity violation experiments in Fr.