arXiv:1910.09736 · Physical Review A

Magic wavelength of the Ba+138 6s S1/22–5d D5/22 clock transition

Sapam Ranjita Chanu, V. P. W. Koh, K. J. Arnold, R. Kaewuam, Ting Rei Tan, Zhiqiang Zhang, Marianna S. Safronova, M. D. Barrett

Published Apr 22, 2020• 9 citations

arXiv HTML PDF

Abstract

The zero crossing of the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ clock transition in $^{138}\mathrm{Ba}^{+}$ has been determined to be $459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}$. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

DOI: 10.1103/physreva.101.042507

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Zero crossings of the differential scalar polarizability of Ba$^+$ clock transition

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Abstract We present precise values of the dipole polarizabilities ( α ) of the ground [ 4 f 14 6 s ] 2 S 1 / 2 and metastable [ 4 f 14 5 d ] 2 D 3 / 2 states of Yb + , that are important in reducing systematics in the clock frequency of the [ 4 f 14 6 s ] 2 S 1 / 2 → [ 4 f 14 5 d ] 2 D 3 / 2 transition. The static values of α for the ground and [ 4 f 14 5 d ] 2 D 3 / 2 states are estimated to be 9.8 ( 1 ) × 10

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arXiv:1910.09736 · Physical Review A

Magic wavelength of the Ba+138 6s S1/22–5d D5/22 clock transition

Sapam Ranjita Chanu, V. P. W. Koh, K. J. Arnold, R. Kaewuam, Ting Rei Tan, Zhiqiang Zhang, Marianna S. Safronova, M. D. Barrett

Published Apr 22, 2020• 9 citations

arXiv HTML PDF

Abstract

The zero crossing of the dynamic differential scalar polarizability of the

{S}_{1/2}\ensuremath{-}{D}_{5/2}

clock transition in

^{138}\mathrm{Ba}^{+}

has been determined to be

459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}

. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range (

\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}

). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

DOI: 10.1103/physreva.101.042507

Related papers

Zero crossings of the differential scalar polarizability of Ba $^+$ clock transitionZero crossings of the differential scalar polarizability of Ba$^+$ clock transition

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

The differential scalar polarizability $Δα_0(ω)$ of the Ba $^+$ S $_{1/2}$ -to-D $_{5/2}$ clock transition has a zero crossing near 481nm, which is measured to be 623.603\,13(17)\,THz. From this measurement, we infer a ratio of reduced matrix elements $\langle P_{3/2}\|r\|S_{1/2}\rangle/\langle P_{1/2}\|r\|S_{1/2}\rangle=1.411\,81(13)$ , which provides a stringent test of atomic structure calculations and experimental determination of matrix elements. Additionally, it enables the construction of an accurate approximation to $Δα_0(ω)$ , valid for frequencies up to 450\,THz, with only one reduced matrix element, $\langle P_{1/2}\|r\|S_{1/2}\rangle$ , appearing in the model's parameterization. We discuss the achievable accuracy of the model, the application to the assessment of blackbody radiation (BBR) shifts in ion-based clocks, and the applicability of the approach to other alkaline-earth ions.The differential scalar polarizability $Δα_0(ω)$ of the Ba$^+$ S$_{1/2}$-to-D$_{5/2}$ clock transition has a zero crossing near 481nm, which is measured to be 623.603\,13(17)\,THz. From this measurement, we infer a ratio of reduced matrix elements $\langle P_{3/2}\|r\|S_{1/2}\rangle/\langle P_{1/2}\|r\|S_{1/2}\rangle=1.411\,81(13)$, which provides a stringent test of atomic structure calculations and experimental determination of matrix elements. Additionally, it enables the construction of an accurate approximation to $Δα_0(ω)$, valid for frequencies up to 450\,THz, with only one reduced matrix element, $\langle P_{1/2}\|r\|S_{1/2}\rangle$, appearing in the model's parameterization. We discuss the achievable accuracy of the model, the application to the assessment of blackbody radiation (BBR) shifts in ion-based clocks, and the applicability of the approach to other alkaline-earth ions.

physics.atom-phCross-listedarXiv:2603.10740Mar 12, 2026

Polarizability assessments of ion-based optical clocks

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It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in $^{138}\mathrm{Ba}^{+}$ can be determined to an inaccuracy below $0.5%$ across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same $0.5%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with $^{138}\mathrm{Ba}^{+}$ . The approach would be equally applicable to ${\mathrm{Sr}}^{+}$ and ${\mathrm{Ca}}^{+}$ , with the latter being immediately applicable to ${\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}$ quantum logic clocks.It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in $^{138}\mathrm{Ba}^{+}$ can be determined to an inaccuracy below $0.5%$ across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same $0.5%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with $^{138}\mathrm{Ba}^{+}$. The approach would be equally applicable to ${\mathrm{Sr}}^{+}$ and ${\mathrm{Ca}}^{+}$, with the latter being immediately applicable to ${\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}$ quantum logic clocks.

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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)Jul 1, 20171 citation

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arXiv:2202.07828Feb 16, 20221 citation

Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the 6S 1/2 5D 3/2 clock transition in Yb +

A Roy, S De, Bindiya Arora +1 more

arXiv:1710.00339Journal of Physics B Atomic Molecular and Optical PhysicsSep 29, 201723 citations

The zero crossing of the dynamic differential scalar polarizability of the

{S}_{1/2}\ensuremath{-}{D}_{5/2}

clock transition in

^{138}\mathrm{Ba}^{+}

has been determined to be

459.1614(28)\phantom{\rule{0.28em}{0ex}}\mathrm{THz}

\ensuremath{\gtrsim}700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}

). In particular, it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.

Zero crossings of the differential scalar polarizability of Ba

^+

clock transition

The differential scalar polarizability

Δα_0(ω)

of the Ba

^+

_{1/2}

-to-D

_{5/2}

clock transition has a zero crossing near 481nm, which is measured to be 623.603\,13(17)\,THz. From this measurement, we infer a ratio of reduced matrix elements

\langle P_{3/2}\|r\|S_{1/2}\rangle/\langle P_{1/2}\|r\|S_{1/2}\rangle=1.411\,81(13)

, which provides a stringent test of atomic structure calculations and experimental determination of matrix elements. Additionally, it enables the construction of an accurate approximation to

Δα_0(ω)

, valid for frequencies up to 450\,THz, with only one reduced matrix element,

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

, appearing in the model's parameterization. We discuss the achievable accuracy of the model, the application to the assessment of blackbody radiation (BBR) shifts in ion-based clocks, and the applicability of the approach to other alkaline-earth ions.

It is shown that the dynamic differential scalar polarizability of the ${S}_{1/2}\ensuremath{-}{D}_{5/2}$ transition in

^{138}\mathrm{Ba}^{+}

can be determined to an inaccuracy below

0.5%

across a wide wavelength range ($\ensuremath{\lambda}>700\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-Stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same

0.5%

level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarizability measurements for clock transitions in other ions, through comparison with

^{138}\mathrm{Ba}^{+}

. The approach would be equally applicable to

{\mathrm{Sr}}^{+}

and

{\mathrm{Ca}}^{+}

, with the latter being immediately applicable to

{\mathrm{Al}}^{+}/{\mathrm{Ca}}^{+}

quantum logic clocks.

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.

Measurement of infrared magic wavelength for an all-optical trapping of

^{40}

^{+}

ion clock

For the first time, we experimentally determine the infrared magic wavelength for the

^{40}

^{+}

4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}

electric quadrupole transition by observation of the light shift canceling in

^{40}

^{+}

optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor of about 300. Using this measured magic wavelength we also derive the differential static polarizability to be

-44.32(32)

~a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of

^{40}

^{+}

optical clock.