Physical Review A

Polarizabilities of the beryllium clock transition

J. Mitroy

Published Nov 22, 2010• 10 citations

Abstract

The polarizabilities of the three lowest states of the beryllium atom are determined from a large basis configuration interaction calculation. The polarizabilities of the $2{s}^{2}$ ${}^{1}{S}^{e}$ ground state ($37.73$${a}_{0}^{3}$) and the $2s2p$ ${}^{3}{P}_{0}^{o}$ metastable state ($39.04$${a}_{0}^{3}$) are found to be very similar in size and magnitude. This leads to an anomalously small blackbody radiation shift at $300$ K of $\ensuremath{-}$$0.018(4)$ Hz for the $2{s}^{2}$ ${}^{1}{S}^{e}$--$2s2p$ ${}^{3}{P}_{0}^{o}$ clock transition. Magic wavelengths for simultaneous trapping of the ground and metastable states are also computed.

DOI: 10.1103/physreva.82.052516

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Dynamic polarizabilities and related properties of clock states of the ytterbium atom

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Blackbody-radiation shift in the Sr optical atomic clock

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Dynamic polarizabilities and triply magic trapping conditions for 5s2S01→5s5p3P0,2 transitions of Cd atoms

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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

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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Physical Review A

Polarizabilities of the beryllium clock transition

J. Mitroy

Published Nov 22, 2010• 10 citations

Publisher

Abstract

The polarizabilities of the three lowest states of the beryllium atom are determined from a large basis configuration interaction calculation. The polarizabilities of the

2{s}^{2}

{}^{1}{S}^{e}

ground state (

37.73$${a}_{0}^{3}

) and the

2s2p

{}^{3}{P}_{0}^{o}

metastable state (

39.04$${a}_{0}^{3}

) are found to be very similar in size and magnitude. This leads to an anomalously small blackbody radiation shift at

300

K of

\ensuremath{-}$$0.018(4)

Hz for the

2{s}^{2}

{}^{1}{S}^{e}

2s2p

{}^{3}{P}_{0}^{o}

clock transition. Magic wavelengths for simultaneous trapping of the ground and metastable states are also computed.

DOI: 10.1103/physreva.82.052516

Related papers

Dynamic polarizabilities and related properties of clock states of the ytterbium atom

V. A. Dzuba, Andrei Derevianko

We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s 2 1 S 0 and the first excited 6s6p 3 P o 0 states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s 2 1 S 0 –6s6p 3 P o 0 transition. We determine (i) the first four magic wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the fourth magic wavelengths to be 551 nm, 465 nm and 413 nm. (ii) We re-evaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at T = 300 K being −1.41(17) Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C 6 (6s 2 1 S 0 + 6s 2 1 S 0 ) = 1909(160), C 6 (6s 2 1 S 0 + 6s6p 3 P 0 ) = 2709(338) and C 6 (6s6p 3 P 0 + 6s6p 3 P 0 ) = 3886(360). Finally, we determine the atom-wall interaction coefficients (in a.u.), C 3 (6s 2 1 S 0 ) = 3.34 and C 3 (6s6p 3 P 0 ) = 3.68. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s 2 1 S 0 and the first excited 6s6p 3 P o 0 states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s 2 1 S 0 –6s6p 3 P o 0 transition. We determine (i) the first four magic wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the fourth magic wavelengths to be 551 nm, 465 nm and 413 nm. (ii) We re-evaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at T = 300 K being −1.41(17) Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C 6 (6s 2 1 S 0 + 6s 2 1 S 0 ) = 1909(160), C 6 (6s 2 1 S 0 + 6s6p 3 P 0 ) = 2709(338) and C 6 (6s6p 3 P 0 + 6s6p 3 P 0 ) = 3886(360). Finally, we determine the atom-wall interaction coefficients (in a.u.), C 3 (6s 2 1 S 0 ) = 3.34 and C 3 (6s6p 3 P 0 ) = 3.68. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.

arXiv:0908.2278Journal of Physics B Atomic Molecular and Optical PhysicsMar 19, 2010110 citations

Blackbody-radiation shift in the Sr optical atomic clock

Marianna S. Safronova, S. G. Porsev, Marianna S. Safronova +2 more

We evaluated the static and dynamic polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1 $%$ uncertainty; $\ensuremath{-} $0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$ %$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.We evaluated the static and dynamic polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1$%$ uncertainty; $\ensuremath{-}$0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7$%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.

arXiv:1210.7272Physical Review AJan 23, 2013140 citations

Polarizability and magic wavelength of Yb+clock transition2S1/2 →2D3/2

Atish Roy, Subhadeep De, Bindiya Arora +1 more

Differential static polarizability and black body radiation (BBR) shift for Ytterbium ion (171Yb+) clock transition from ground state2S1/2to metastable state2D3/2corresponding to the wavelength 435.5 nm are calculated accurately for frequency standard applications. The values are found to be −7.5(5) × 10−40Jm2/V and −0.4(1) Hz, respectively, which are well in agreement with pre-available data and more accurate than the previous theoretical results. We further determine the values of dynamic polarizability of these states to find out the magic and tune-out wavelengths for the above mentioned clock transition.Differential static polarizability and black body radiation (BBR) shift for Ytterbium ion (171Yb+) clock transition from ground state2S1/2to metastable state2D3/2corresponding to the wavelength 435.5 nm are calculated accurately for frequency standard applications. The values are found to be −7.5(5) × 10−40Jm2/V and −0.4(1) Hz, respectively, which are well in agreement with pre-available data and more accurate than the previous theoretical results. We further determine the values of dynamic polarizability of these states to find out the magic and tune-out wavelengths for the above mentioned clock transition.

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

Determination of Sr properties for a high-accuracy optical clock

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

Dynamic polarizabilities and triply magic trapping conditions for 5s2S01→5s5p3P0,2 transitions of Cd atoms

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

The dynamic electric dipole polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ , $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ , and $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ states for Cd atoms are calculated using the relativistic configuration interaction plus many-body perturbation theory method. The magic wavelengths for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ transitions within a range of 300--500 nm are identified. The possibility of achieving triple magic trapping for the transitions $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ is investigated. It is found that no common magic wavelength could be identified for achieving triple magic trapping with the linearly polarized light. However, if the degree of ellipticity is between 0.358 and 1, the triple magic trapping can be achieved at 419.88 nm for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ $({M}_{i}=\ifmmode\pm\else\textpm\fi{}2)$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ transitions.The dynamic electric dipole polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$, $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$, and $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ states for Cd atoms are calculated using the relativistic configuration interaction plus many-body perturbation theory method. The magic wavelengths for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ transitions within a range of 300--500 nm are identified. The possibility of achieving triple magic trapping for the transitions $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ is investigated. It is found that no common magic wavelength could be identified for achieving triple magic trapping with the linearly polarized light. However, if the degree of ellipticity is between 0.358 and 1, the triple magic trapping can be achieved at 419.88 nm for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ $({M}_{i}=\ifmmode\pm\else\textpm\fi{}2)$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ transitions.

arXiv:2403.05898Physical Review AMar 27, 20247 citations

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 polarizabilities of the three lowest states of the beryllium atom are determined from a large basis configuration interaction calculation. The polarizabilities of the

2{s}^{2}

{}^{1}{S}^{e}

ground state (

37.73$${a}_{0}^{3}

) and the

2s2p

{}^{3}{P}_{0}^{o}

metastable state (

39.04$${a}_{0}^{3}

) are found to be very similar in size and magnitude. This leads to an anomalously small blackbody radiation shift at

300

K of

\ensuremath{-}$$0.018(4)

Hz for the

2{s}^{2}

{}^{1}{S}^{e}

2s2p

{}^{3}{P}_{0}^{o}

clock transition. Magic wavelengths for simultaneous trapping of the ground and metastable states are also computed.

We evaluated the static and dynamic polarizabilities of the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}

and

5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}

states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1

%

uncertainty; $\ensuremath{-}

0.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (7

%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.

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.

The dynamic electric dipole polarizabilities of the

5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}

, and

5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}

states for Cd atoms are calculated using the relativistic configuration interaction plus many-body perturbation theory method. The magic wavelengths for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ transitions within a range of 300--500 nm are identified. The possibility of achieving triple magic trapping for the transitions $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ is investigated. It is found that no common magic wavelength could be identified for achieving triple magic trapping with the linearly polarized light. However, if the degree of ellipticity is between 0.358 and 1, the triple magic trapping can be achieved at 419.88 nm for the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}$ $({M}_{i}=\ifmmode\pm\else\textpm\fi{}2)$ and $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}\ensuremath{\rightarrow}5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ transitions.