Al^(+)光钟态“幻零”波长的理论计算

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

本文使用组态相互作用加多体微扰理论方法对Al^(+)光钟态3s^(2)^(1)S_(0)和3s3p^(3)P_(0)的“幻零”波长进行了理论计算.3s^(2)^(1)S_(0)态的“幻零”波长为266.994(1)nm,3s3p^(3)P_(0)态的“幻零”波长为184.56(7)nm,174.4(1)nm,121.5(1)nm和119.7(2)nm.精确测量这些“幻零”波长,有助于高精度确定光钟态相关跃迁的振子强度或者约化矩阵元,进而降低Al^(+)光钟黑体辐射频移评估的不确定度.同时,对这些“幻零”波长的精密测量,对研究Al~+原子结构具有重要意义.

In quantum optical experiments,the polarizabilities of atomic systems play a very important role,which can be used to describe the interactions of atomic systems with external electromagnetic fields.When subjected to a specific electric field such as a laser field with a particular frequency,the frequency-dependent electric-dipole(E1)dynamic polarizability of an atomic state can reach zero.The wavelength corresponding to such a frequency is referred to as the“turn-out”wavelength.In this work,the“turn-out”wavelengths for the 3s21S0 and 3s3p ^(3)P_(0) clock states of Al^(+)are calculated by using the configuration interaction plus many-body perturbation theory(CI+MBPT)method.The values of energy and E1 reduced matrix elements of low-lying states of Al+are calculated.By combining these E1 reduced matrix elements with the experimental energy values,the E1 dynamic polarizabilities of the 3s^(2)^(1)S_(0) and 3s3p ^(3)P_(0) clock states are determined in the angular frequency range of(0,0.42 a.u.).The“turn-out”wavelengths are found at the zero-crossing points of the frequency-dependent dynamic polarizability curves for both the 3s21S0 and 3s3p 3P0 states.For the ground state 3s21S0,a single“turn-out”wavelength at 266.994(1)nm is observed.On the other hand,the excited state 3s3p ^(3)P_(0) exhibits four distinct“turn-out”wavelengths,namely 184.56(1)nm,174.433(1)nm,121.52(2)nm,and 119.71(2)nm.The contributions of individual resonant transitions to the dynamic polarizabilities at the“turn-out”wavelengths are examined.It is observed that the resonant lines situated near a certain“turn-out”wavelength can provide dominant contributions to the polarizability,while the remaining resonant lines generally contribute minimally.When analyzing these data,we recommend accurately measuring these“turn-out”wavelengths to accurately determine the oscillator strengths or reduced matrix elements of the relevant transitions.This is crucial for minimizing the uncertainty of the blackbody radiation(BBR)frequency shift in Al+optical clock and suppressing the systematic uncertainty.Meanwhile,precisely measuring these“turn-out”wavelengths is also helpful for further exploring the atomic structure of Al^(+).