单、双价电子原子体系的Magic波长和tune-out波长的高精度理论计算

Recently，the fractional uncertainty of optical lattice clock has achieved 10^{-18} by using particular magic wavelengths. Further development of even more precise is a destination for the researchers. Because the fractional shifts of the clock frequency due to hyperpolarizablility of the atoms and the multipole interactions of atom-lattice field are in the range of 10^{-17}-10^{-19}, to this end, the role of the higher-order and multipole atom-lattice interaction should be considered in the further studies. In the present project, based on the configuration interactions with a semi-empirical core potential (CICP) approach, a full relativistic configuration interactions with a semi-empirical core potential (RCICP) method and program will be developed. In this method, the L-Spinor basis which has been developed by Grant and Quiney (Phys. Rev. A 62, 022508 (2000)) will be used. Combining RCICP method and the Multi-Configuration Dirac-Fock (MCDF) method and corresponding packages GRASP92/2K, the wave functions and dipole and multipole matrix elements of one-electron and two-electron atom systems will be calculated. Meanwhile, the dipole and multi-pole polarizabilities and hyperpolarizabilities for these atoms will be studied. The contributions of the hyperpolarizabilities and atom-lattice multipole interactions on the ac stark shift will be studied systematically. Further more, the high accuracy magic wavelength will be determined, in which the high order effects will be considered in detail.

近年来，人们利用魔法囚禁(magic-tranpping)技术，实验上已实现了精度为10^{-18}的光学原子钟，进一步提高原子钟的精度成为下一步研究目标。由于超极化率以及光与原子的高阶相互作用可以导致10^{-17}到10^{-19}的不确定度，因此，对这些效应的研究将变得非常重要。本项目拟基于非相对论半经验极化势组态相互作用（CICP）方法，发展一套L-Spinor基的全相对论CICP方法和程序，并结合多组态Dirac-Fock方法，精确计算单电、双价电子原子体系的波函数和偶极以及多极跃迁矩阵元，详细研究这些原子的偶极极化率、多极极化率以及超极化率。同时，我们将系统地研究动态超极化率以及光与原子的高阶相互作用对动态Stark效应的贡献，进一步确定高精度的魔法波长（magic-wavelength）和调谐波长（tune-out wavelength)，为相关实验提供理依据。

在项目的资助下，自主开发了一套基于L-spinnor和S-spinnor基矢的全相对论组态相互作用模型势方法和程序，并结合多组态Dirac-Fock方法，完成了对Sr+离子的能级、偶极和四极振子强度5p1/2,5p3/2,4d3/2,4d5/2的寿命以及5s,5p,4d的静态和动态极化率的计算，精确确定了基态5s分别到5p1/2,5p3/2,4d3/2,4d5/2跃迁的Magic波长。我们从理论上发现，如果实验室能够精确测量5s-4d3/2,5/2跃迁的417nm的Magic波长，人们将可以精确确定f5s-5p1/2和f5s-5p3/2跃迁矩阵元的比值，这样确定的比值要比常规实验确定的比值精确几个数量级。我们也完成了铷85和87基态和部分低激发态的静态和动态极化率的研究,得到了高精度铷原子精细能级的Tune-out波长以及超精细能级的动态极化率和Tune-out波长，铷87原子超精细基态5s1/2,F=2Tune-out波长为790.032602(193)nm,该理论结果与目前最精确的实验数据相差仅仅0.000214nm,5s1/2,F=1,mf=0的Tune-out波长为与目前最精确的实验数据相差仅仅0.00045nm。同时，我们预言了铷85原子超精细基态的tune-out波长，我们详细研究了Ca+离子线偏振和圆偏振光的动态偶极极化率，得到了4s、4p和3d态之间的Magic波长。发现了一些新的Magic波长，详细研究了Magic波长随角度的依赖关系，这些波长对建立态选择的全光囚禁Ca+离子钟有非常重要的应用价值。计算了镱原子基态和低激发态的静态和动态极化率。确定了基态到低激发态6s2-6s6p跃迁的魔幻波长，发现1035.7(2)nm、612.9(2)nm、1517.68(6)nm等魔幻波长对于实现中性Yb原子的状态不敏感冷却、俘获量子操纵是特别重要的。