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arXiv:1210.7272 · Physical Review A

Blackbody-radiation shift in the Sr optical atomic clock

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

Published Jan 23, 2013• 140 citations
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Abstract

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.

DOI
10.1103/physreva.87.012509

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Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr_{2} molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10^{-16} level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr_{2} and provides a framework for evaluating BBR shifts in other homonuclear molecules.
The progress in optical clock with uncertainty at a level of 10−1810^{-18}10−18 requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Previous theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the 813 nm magic wavelength of the Sr clock differ substantially. We employ the sum-over-states method to calculate dynamic multipolar polarizabilities and hyperpolarizabilities for the Sr and Mg clocks. Our differential dynamic hyperpolarizability at the magic wavelength of 813.4280(5) nm for the Sr clock is −2.09(43)×107-2.09(43)\times10^{7}−2.09(43)×107 a.u., which agrees well with the recent theoretical and measurement results. Our differential multipolar polarizability of the Sr clock is 2.68(94)×10−52.68(94)\times 10^{-5}2.68(94)×10−5 a.u., which is consistent with the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)]. In addition, the lattice light shifts as the detuning and trap depth changed are studied in detail by using present multipolar polarizability and hyperpolarizability. It illustrates that for the Mg clock, there exists a distinctive operational lattice depth of 5.3(1)ER5.3(1)E_R5.3(1)ER​ that allows the total light shift reduced to less than 1×10−181\times 10^{-18}1×10−18 over the trap depth variation of 4.1ER<U<6.4ER4.1E_R<U<6.4E_R4.1ER​<U<6.4ER​.
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 6s6p3P16s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}6s6p3P1​ and 5d6s3D15d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}5d6s3D1​, we report the clock shift due to an ideal 300 K blackbody environment to 0.05% precision.
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