arXiv:1905.04976 · Physical Review A

Polarizability assessments of ion-based optical clocks

M. D. Barrett, K. J. Arnold, Marianna S. Safronova

Published Oct 24, 2019• 23 citations

Abstract

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.

DOI: 10.1103/physreva.100.043418

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arXiv:1905.04976 · Physical Review A

Polarizability assessments of ion-based optical clocks

M. D. Barrett, K. J. Arnold, Marianna S. Safronova

Published Oct 24, 2019• 23 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1103/physreva.100.043418

Related papers

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

Sapam Ranjita Chanu, V. P. W. Koh, K. J. Arnold +5 more

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.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.

arXiv:1910.09736Physical Review AApr 22, 20209 citations

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

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Scheme for Quantum-Logic Based Transfer of Accuracy in Polarizability Measurement for Trapped Ions Using a Moving Optical Lattice

Fabian Wolf

Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.Optical atomic clocks based on trapped ions suffer from systematic frequency shifts of the clock transition due to interaction with blackbody radiation from the environment. These shifts can be compensated if the blackbody radiation spectrum and the differential dynamic polarizability is known to a sufficient precision. Here, we present a new measurement scheme, based on quantum logic that allows a direct transfer of precision for polarizability measurements from one species to the other. This measurement circumvents the necessity of calibrating laser power below the percent level, which is the limitation for state-of-the-art polarizability measurements in trapped ions. Furthermore, the presented technique allows one to reference the polarizability transfer to hydrogenlike ions for which the polarizability can be calculated with high precision.

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S. G. Porsev, Andrew D. Ludlow, Martin M. Boyd +1 more

We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the $5{s}^{2}$ $^{1}S_{0}$ and $5s5p$ $^{3}P_{0}^{o}$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the $^{3}P_{0}^{o}$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^{3}P_{0}^{o}$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.We have carried out calculations towards the goal of reducing the inaccuracy of the Sr optical atomic clock to $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ and below. In particular, we focused on ac polarizabilities of the $5{s}^{2}$ $^{1}S_{0}$ and $5s5p$ $^{3}P_{0}^{o}$ clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the $^{3}P_{0}^{o}$ clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the $^{3}P_{0}^{o}$ state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.

arXiv:0807.1381Physical Review ASep 5, 200879 citations

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}

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.

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.

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.

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.

5{s}^{2}

^{1}S_{0}

and

5s5p

^{3}P_{0}^{o}

clock states that are important for reducing the uncertainty of black-body radiation-induced frequency shifts for the $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}^{o}$ clock transition. Four low-lying even-parity states have been identified, whose total contribution to the static polarizability of the

^{3}P_{0}^{o}

clock state is at the level of 90%. We show that if the contribution of these states is experimentally known with 0.1% accuracy, the same accuracy can be achieved for the total polarizability of the

^{3}P_{0}^{o}

state. The corresponding uncertainty for the blackbody shift at a fixed room temperature will be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$. The calculations are confirmed by a number of experimental measurements on various Sr properties.