Theoretical Study Of Dynamic Dipole Polarizabilities Tune-out Wavelengths And Magic Wavelengths Of Yb~+ Ions

The Yb⁺ ions is a very important candidate elements for the optical frequency standard,which has not only two long-lived,narrow linewidth,high-Q metastable states 4f¹⁴6s²D_3/2 and 4f¹⁴6s²D_5/2,but also a 4f¹³6s^{2 2}F_7/2 state with a lifetime of more than ten years.In addition to being used as an optical frequency standard,Yb⁺ions can also be used for testing fundamental physics,probing parity nonconservation effect,testing local Lorentz invariance and processing quantum information.Due to the non-spherical symmetry structure of the 5d_3/2,5/2 states,the degree of polarization of light and the angle between the direction of the magnetic field and the direction of laser polarization have great influence on the magic wavelength.It is very difficult to accurately measure magic wavelengths in experiments.Therefore,it is important to provide high-precision correlations of fundamental structural parameters and magic wavelengths in theory to provide theoretical data for experiments.The ground configuration of Yb⁺ions is 4f¹⁴ 6s,and it is complex to accurately calculate atomic structure parameters.In this paper,a semiempirical model potential RCICP method is used to calculate the wave functions,the energy levels,the transition matrix elements,as well as the dipole static and dynamic polarizabilities of the ground state 6s_1/2、low-lying excited states 6p_1/2,3/2 and 5d_3/2,5/2 of Yb⁺ions.The tune-out wavelengths of ground state 6s_1/2 and the magic wavelengths of the transitions 6s_1/2→5d_5/2,3/2 and 6s_1/2→6p_3/2,1/2 in the linearly,right-handed and left-handed polarized light are further obtained.The dependence of these magic wavelengths upon the angle between the direction of the magnetic field and the direction of laser polarization is analyzed in detail.We found that:1.For the ground-state 6s_1/2,only one tune-out wavelength is found,which lies between the 6s_1/2→6p_1/2 and 6s_1/2→6p_3/2 resonance transitions with a wavelength value of 355.85（43）nm.The tune-out wavelength is mainly caused by the cancellation of the contribution of the 6s_1/2→6p_1/2 and 6s_1/2→6p_3/2 transitions to the dynamic polarizabilities of the electric dipole.Therefore,we propose that high-precision measurements on the tune-out wavelength could be used to determine the f6s_1/2→6p_3/2/fs_1/2→6p_1/22.For the clock transitions 6s_1/2→5d_5/2,3/2.The magic wavelengths,which lies between the resonance wavelengths of 6s_1/2→6P_1/2 and 6s_1/2→6p_3/2 transitions,is sensitive to the degree of polarization of light,but not to the angle between the direction of the magnetic field and the direction of laser polarization,in the case of linearly and left-handed polarized light.Another one is larger than 6p_3/2→5d_3/2 resonance transitions,and this magic wavelength is extremely sensitive to the degree of polarization of light and the angle between the direction of the magnetic field and the direction of laser polarization.In the case of right-handed polarized light,we have only found magic wavelengths longer than 1300 nm.All of these magic wavelengths are extremely sensitive to the degree of polarization of light and the angle between the direction of the magnetic field and the direction of laser polarization because dynamic polarizability varies gently with laser wavelength.3.For the 6s_1/2→6p_3/2,1/2 transitions,in the case of left-handed polarized light,magic wavelengths shorter than 350 nm with a transition of 6s_1/2,m=1/2→6p_1/2,m=1/2 is insensitive to the degree of polarization of light,and other magic wavelengths are very sensitive to the degree of polarization of light.In the case of right-handed polarized light,except for the magic wavelength of 348.0（9）nm of the 6s_1/2,m=1,2→6p_3/2,m=3/2 transition,which is not sensitive to the degree of polarization of light,other magic wavelengths are very sensitive.