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Quantum Electronics

Nonlinear optical higher-order effects in an optical lattice clock

V. D. Ovsyannikov, S. I. Marmo, Sergey N. Mokhnenko, Vitalii G Pal'chikov

Published May 9, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1070/qel16347

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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 $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$.
In neutral atom optical clocks, the higher-order atomic polarizability terms lead to the clock transition frequency shift which is motion-state dependent and nonlinear with the optical lattice depth. We propose to use an auxiliary optical lattice to compensate the influence of the E2-M1 differential polarizability or tune the associated coefficient to a favorable value. We show that by applying this method to Sr and Hg optical lattice clocks, the low or even sub-10-19 clock transition frequency uncertainty from the optical lattice becomes feasible. Finally, the proposed scheme is simple for experimental realization and can be implemented and tested in the existing setups.
In neutral atom optical clocks, the higher-order atomic polarizability terms lead to the clock transition frequency shift that is motion-state dependent and nonlinear with the optical lattice depth. We propose to use an auxiliary optical lattice to compensate the influence of the E2–M1 differential polarizability or tune the associated coefficient to a favorable value. We show that by applying this method to Sr and Hg optical lattice clocks, the low or even sub-10 −19 clock transition frequency uncertainty from the optical lattice becomes feasible. Finally, the proposed scheme is simple for experimental realization, is compatible with the use of an enhancement cavity, and can be implemented and tested in the existing setups.
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.