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 2s2 1S0 and 2s2p 3P0 states are determined. Two magic wavelengths, 300.03 and 252.28nm, of 2s2 1S0 → 2s2p 3P0 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 ∼ 15.9 kW/cm2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7 ∼ 40.9MHz, the fractional Stark shifts of the clock transition are less than the level of 1.0 × 10−18. While, when I is in the range of 15.01 ∼ 15.46 kW/cm2 and δ is in the range of 40.73 ∼ 40.76 MHz, the fractional Stark shifts are lower than the level of 1.0 × 10−19. These will provide important support for developing ultra-high-precision Be optical clocks.

Theoretical calculation of “tune-out” wavelengths for clock states of Al⁺

“…极化率矢量和张量分量的贡献都与原子态的角 动量磁量子数有关 [7,[19][20][21] . 本文所涉及的Al + 两个 钟态3s 2 1 S 0 和3s3p 3 P 0 的总角动量量子数J都为 0, 这使得其极化率的矢量和张量分量都为0.…”

“…CI+MBPT方法是相对论框架下的一种原子 结构计算方法 [20,[22][23][24] , 它充分结合了CI和MBPT 两种方法的优点. CI方法在"冻结"原子实的近似 下, 考虑了价电子(VV)之间的关联效应, MBPT 方法处理原子实电子间和原子实与价电子间的关 联效应.…”