arXiv:1208.1456 · Physical Review Letters

Ytterbium in Quantum Gases and Atomic Clocks: van der Waals Interactions and Blackbody Shifts

Marianna S. Safronova, S. G. Porsev, Charles W. Clark

Published Dec 5, 2012• 51 citations

Abstract

We evaluated the C(6) coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, C(6)=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s(2) (1)S(0)-6s6p (3)P(0)(o) clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the 10(-18) level.

DOI: 10.1103/physrevlett.109.230802

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arXiv:1208.1456 · Physical Review Letters

Ytterbium in Quantum Gases and Atomic Clocks: van der Waals Interactions and Blackbody Shifts

Marianna S. Safronova, S. G. Porsev, Charles W. Clark

Published Dec 5, 2012• 51 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.109.230802

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.

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The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at ${10}^{\ensuremath{-}18}$ uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of $6s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}$ and $5d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}$ , we report the clock shift due to an ideal 300 K blackbody environment to 0.05 $%$ precision.The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at ${10}^{\ensuremath{-}18}$ uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of $6s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}$ and $5d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}$, we report the clock shift due to an ideal 300 K blackbody environment to 0.05$%$ precision.

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We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$ , $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ , and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the $6{s}^{2\phantom{\rule{0.16em}{0ex}}1}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the ${C}_{6}$ coefficients for the Yb-Yb ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}$ and ${}^{3}{P}_{0}^{o}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}$ dimers and ${C}_{8}$ coefficients for the ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ and ${}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}$ dimers.

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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.

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6s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}

and

5d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}

, we report the clock shift due to an ideal 300 K blackbody environment to 0.05

%

precision.

We evaluate the electric-dipole and electric-quadrupole static and dynamic polarizabilities for the

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

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0}^{o}

, and

6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

states and estimate their uncertainties. A first-principles relativistic method is developed for an accurate calculation of the van der Waals coefficients of dimers involving excited-state atoms with strong decay channel to the ground state. This method is used for evaluation of the long-range interaction coefficients of particular experimental interest, including the

{C}_{6}

coefficients for the Yb-Yb

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1}^{o}

and

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

dimers and

{C}_{8}

coefficients for the

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}

and

{}^{1}{S}_{0}+{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{1}^{o}

dimers.

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.