arXiv:0808.1826 · Physical Review A

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, E. Norval Fortson

Published Nov 26, 2008• 35 citations

Abstract

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.

DOI: 10.1103/physreva.78.052514

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arXiv:0808.1826 · Physical Review A

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, E. Norval Fortson

Published Nov 26, 2008• 35 citations

arXiv HTML PDF

Abstract

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)

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.

DOI: 10.1103/physreva.78.052514

Related papers

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

Jeff A. Sherman, Timo Koerber, Anna Markhotok +2 more

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.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.

arXiv:physics/0502113Physical Review LettersJun 21, 200560 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.

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Experimental and Theoretical Study of Dynamic Polarizabilities in the 5S1/2 – 5D5/2 Clock Transition in Rubidium-87 and Determination of Electric Dipole Matrix Elements

Rhona Hamilton, Benjamin M. Roberts, Sarah K. Scholten +4 more

The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$ -- $5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$ -- $5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$ -- $5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.The interaction between light and an atom causes perturbations in the atom's energy levels, known as the light shift. These light shifts are a key source of inaccuracy in atomic clocks, and can also deteriorate their precision. We present a study of light shifts and associated dynamic polarizabilities for a two-photon atomic clock based on the $5{S}_{1/2}$--$5{D}_{5/2}$ transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the $5{P}_{3/2}$--$5{D}_{5/2}$ transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the $5{P}_{3/2}$--$5{D}_{5/2}$ resonance, and the corresponding reduced E1 matrix element $1.80(6)e{a}_{0}$ (experimental) and $1.96(15)e{a}_{0}$ (theoretical). These values resolve a previous discrepancy between theory and experiment.

arXiv:2212.10743Physical Review AppliedMay 18, 20239 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

Obtaining Atomic Matrix Elements from Vector Tune-Out Wavelengths Using Atom Interferometry

Adam Fallon, Charles A. Sackett

Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. To date, tune-out wavelength measurements have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are thus useful for constraining theory and broadening the application of experimental values. To date, tune-out wavelength measurements have focused on zeros of the scalar polarizability, but in general the vector polarizability also contributes. We show here that combined measurements of the vector and scalar polarizabilities can provide more detailed information about the matrix element ratios, and in particular can distinguish small contributions from the atomic core and the valence tail states. These small contributions are the leading error sources in current parity violation calculations for cesium.

arXiv:1603.09277AtomsMar 30, 201612 citations

State-insensitive trapping of Rb atoms: Linearly versus circularly polarized light

Bindiya Arora, B. K. Sahoo

We study the cancellation of differential ac Stark shifts in the $5s$ and $5p$ states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the $4d$ and $6s$ states of this atom are ameliorated.We study the cancellation of differential ac Stark shifts in the $5s$ and $5p$ states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the $4d$ and $6s$ states of this atom are ameliorated.

arXiv:1209.0613Physical Review ASep 17, 201259 citations

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)

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⟩

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.

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.

5{S}_{1/2}

5{D}_{5/2}

transition in rubidium-87 over the range 770--800 nm. We determine experimental and theoretical values for a magic wavelength in this range and the electric dipole (E1) matrix element for the

5{P}_{3/2}

5{D}_{5/2}

transition. We find a magic wavelength of 776.179(5) nm (experimental) and 776.21 nm (theoretical) in the vicinity of the

5{P}_{3/2}

5{D}_{5/2}

resonance, and the corresponding reduced E1 matrix element

1.80(6)e{a}_{0}

(experimental) and

1.96(15)e{a}_{0}

(theoretical). These values resolve a previous discrepancy between theory and experiment.

We study the cancellation of differential ac Stark shifts in the

5s

and

5p

states of the rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single and double excitations and at the important valence triple excitation approximation including all possible nonlinear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. ``Magic wavelengths'' are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. The possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light is discussed. Using the optimized matrix elements, the lifetimes of the

4d

and

6s

states of this atom are ameliorated.