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Optics Letters

Compensation of the multipolar polarizability shift in optical lattice clocks

Artem A. Golovizin

Published May 8, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1364/ol.524104

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Compensation of the multipolar polarizability shift in optical lattice clocks

Artem A. Golovizin

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.

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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.

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Multipolar and higher-order lattice shifts in the Sr and Mg clocks

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The progress in optical clock with uncertainty at a level of $10^{-18}$ 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 $-2.09(43)\times10^{7}$ a.u., which agrees well with the recent theoretical and measurement results. Our differential multipolar polarizability of the Sr clock is $2.68(94)\times 10^{-5}$ 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 $5.3(1)E_R$ that allows the total light shift reduced to less than $1\times 10^{-18}$ over the trap depth variation of $4.1E_R<U<6.4E_R$.

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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 $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$.

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Experimental determination of the E2-M1 polarizability of the strontium clock transition

Sören Dörscher, J. Klose, S. Marathapalli +1 more

To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few $10^{-18}$, as the resulting lattice light shift corrections deviate by up to $1 \times 10^{-17}$ from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our ${}^{87}\mathrm{Sr}$ lattice clock and find a value of $Δα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}$. This result is in very good agreement with the value reported by Ushijima et al.

arXiv:2210.14727•Oct 26, 2022•1 citation
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.
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.
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.
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 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.
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 $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$.
To operate an optical lattice clock at a fractional uncertainty below 10−1710^{-17}10−17, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states (5s5p) 3P0(5s5p)\,{}^{3}\mathrm{P}_{0}(5s5p)3P0​ and (5s2) 1S0(5s^2)\,{}^{1}\mathrm{S}_{0}(5s2)1S0​ of strontium [Ushijima et al., Phys. Rev. Lett. 121 263202 (2018); Porsev et al., Phys. Rev. Lett. 120, 063204 (2018)]. This largely precludes operating strontium clocks with uncertainties of few 10−1810^{-18}10−18, as the resulting lattice light shift corrections deviate by up to 1×10−171 \times 10^{-17}1×10−17 from each other at typical trap depths. We have measured the E2-M1 polarizability difference using our 87Sr{}^{87}\mathrm{Sr}87Sr lattice clock and find a value of Δαqm=−987−223+174  μHzΔα_{\mathrm{qm}} = -987^{+174}_{-223} \; \mathrm{μHz}Δαqm​=−987−223+174​μHz. This result is in very good agreement with the value reported by Ushijima et al.