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European Frequency and Time Forum

Higher-order shifts of a clock frequency in Sr, Yb and Hg atoms trapped in an optical lattice

Vitalii D Ovsiannikov, Vitalii G Pal'chikov, Hidetoshi Katori

Published Jun 1, 2014• 0 citations
Publisher

Abstract

The recent progress in designing optical frequency standards with an uncertainty at a level of 10-17-10-18 requires unprecedented accuracy in estimating the role of higher-order uncertainties of optical clocks. In this paper, we systematically evaluate the multipole, nonlinear, anharmonic contributions to uncertainty of the optical-lattice-based clocks of alkaline-earth-like-atoms Sr, Yb and Hg.

DOI
10.1109/eftf.2014.7331478

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The recent progress in designing optical frequency standards with an uncertainty at a level of 10-17-10-18 requires unprecedented accuracy in estimating the role of higher-order uncertainties of optical clocks. In this paper, we systematically evaluate the multipole, nonlinear, anharmonic contributions to uncertainty of the optical-lattice-based clocks of alkaline-earth-like-atoms Sr, Yb and Hg.
The development of optical frequency standards with a relative uncertainty of reproducing the time and frequency units at a level as low as 10 −17 –10 −18 calls for an unprecedented accuracy in estimating the role of higher orders of optical nonlinearity, caused by the influence of the optical lattice on the frequency shift of the 'clock transition'. This paper presents a systematic calculation of the contributions of multipole nonlinear anharmonic effects to the error of clocks based on optical lattices for alkaline-earth-like Sr, Yb, and Hg atoms.
The recent progress in designing optical lattice clocks with fractional uncertainties below ${10}^{\ensuremath{-}17}$ requires unprecedented precision in estimating the role of higher-order effects of atom-lattice interactions. In this paper, we present results of systematic theoretical evaluations of the multipole, nonlinear, and anharmonic effects on the optical-lattice-based clocks of alkaline-earth-like atoms. Modifications of the model-potential approach are introduced to minimize discrepancies of theoretical evaluations from the most reliable experimental data. Dipole polarizabilities, hyperpolarizabilities, and multipolar polarizabilities for neutral Ca, Sr, Yb, Zn, Cd, and Hg atoms are calculated in the modified approach.
Recent progress in optical lattice clocks requires unprecedented precision in controlling systematic uncertainties at the ${10}^{\ensuremath{-}18}$ level. Tuning of nonlinear light shifts is shown to reduce lattice-induced clock shift for a wide range of lattice intensity. Based on theoretical multipolar, nonlinear, anharmonic, and higher-order light shifts, we numerically demonstrate possible strategies for Sr, Yb, and Hg clocks to achieve lattice-induced systematic uncertainty below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$.
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​.
Higher-order perturbation theory is used to study frequency shifts of the spin-forbidden 3 P J - 1 S 0 transitions for Mg, Sr and Yb atoms in an external laser field. Calculations of the higher-order dynamic Stark effect have been performed in connection with precise measurements on cooled and trapped atoms and the design of ultra stable optical clock in an engineered light shift trap. The form of the model potential of the valence electrons suggested by Simons is used for the calculation of atomic dynamic characteristics given by second- and fourth-order perturbation theory for the interaction of the atoms with the electromagnetic field. Dispersion properties of the polarizability and hyperpolarizability components and their behavior in the vicinity of both resonances and so-called magic wavelengths for the upper and lower atomic states, are analyzed. Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the 3 P 0 - 1 S 0 clock transition in 87 Sr indicate that the contribution of the higher- order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10 -17 .
The budget of uncertainties of a time-frequency standard on neutral atoms, trapped in an optical lattice with a “magic wavelength” (MWL), includes a number of shift and broadening corrections, coming from interaction of atoms with different fields of environment. The most important corrections are those arising from interaction with the field of lattice wave. The lattice field is essentially stronger than other fields and may introduce severe perturbations on the standard frequency, despite its tuning to the MWL, which was proposed to compensate these perturbations in a standing-wave lattice, ensuring rigorous equality of the working-level shifts, independently of the atomic motion and the laser intensity. The method of determining MWL, based on measuring the shift of the clock frequency in a weak field of a travelling wave accounts for the Stark shift of energy levels, but only linear in the laser intensity, with inclusion of all multipole-interaction terms.