Be optical lattice clocks with the fractional Stark shift up to the level of 10${}^{-19}$

Abstract

The energy levels and electric dipole ($E1$) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic $E1$, magnetic dipole ($M1$) and electric quadrupole ($E2$) polarizabilities as well as the hyperpolarizabilities of the $2s^2{}^1{S}_0$ and $2s2p{}^3{P}_0$ states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of $2s^2{}^1{S}_0\to 2s2p{}^3{P}_0$ clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity $I$ is in the range of 14.3 $\sim$ 15.9 kW/cm${}^2$ and the detuning $\delta$ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7 $\sim$ 40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 $\times$ 10${}^{-18}$. While, when $I$ is in the range of 15.01 $\sim$ 15.46 kW/cm${}^2$ and $\delta$ is in the range of 40.73 $\sim$ 40.76 MHz, the fractional Stark shifts are lower than 1.0 $\times$ 10${}^{-19}$.

18 pages, 3 figures

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Cited by in corpus (2)

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