Theoretical Study Of The Polarizabilities And Magic Wavelengths For Ca~+ Ions

In recent years,with the development of femtosecond laser optical frequency comb,laser trapping cooling and detection technology,the research of optical atomic clock has made rapid progress.Calcium ions,as alkaline earth metal ions,have been extensively utilized in precision measurement,quantum information,atomic clocks and cold atomic physics due to their simple energy level structure and long lifetime of low excited state 3d_5/2.At present,the uncertainty of calcium ion optical clock has reached 10^-17,which is the highest precision optical clock in China,but there is still a certain gap with the accuracy of international optical clock.In order to increase the system uncertainty of the calcium ion optical clock to 10^-18,all-optical magic trapping technology is one of the most worth trying at present.But the realization of all-optical magic trapping is challenging.In experiment,we need to find the appropriate magic wavelength of Ca⁺ions,and in theory we need to determine the atomic structure parameters accurately.In this work,the relativistic configuration interaction plus model potential method is used to solve the Dirac equation of atomic real and valence electrons,and the wave function and energy level structure of the Ca⁺ions are calculated.The static polarizabilities and dynamic polarizabilities of the ground state 4s and some low-lying states 4p_1/2,3/2 3d_3/2,5/2 are calculated,and the magic wavelengths from the ground state4s to the low-lying excited states 4p_1/2,3/2 3d_3/2,5/2 are further determined.It is found that measuring the specific magic wavelengths can be used to determine the oscillator strength.The main research contents are as follows:1.Basic atomic parameters such as the energy levels of calcium ions,reduced matrix elements,etc.are calculated by using the relativistic configuration interaction plus model potential method.The static polarizabilities of the ground state 4s and some low-lying excited states 4p_1/2,3/2 3d_3/2,5/2 of calcium ions are given and related to the theoretical and experimental results have been compared in detail.At the same time,the black body radiation frequency shift of the calcium ion clock transition was also calculated.2.In the case of linearly polarized light and circularly polarized light,the dynamic polarizabilities of the ground state 4s and some low-lying states 4p_1/2,3/23d_3/2,5/2 of calcium ions are calculated,and the magic wavelengths of the transition from the ground state to the low-excited state are obtained.The contributions of each transition to the dynamic polarizability at the magic wavelength are analyzed.We suggest that accurate measurements on the magic wavelengths near 851 nm for the4s_1/2?4p_3/2 transitions can be used to determine the ratio of the oscillator strengths for the 4p_3/2?3d_3/2 and 4p_3/2?3d_5/2 transitions.3.In the case of linearly polarized light,angle-dependence magic wavelengths are studied.There are only two magic wavelengths,which are located near 395 and1000 nm,respectively.We find that magic wavelengths near 395 nm are insensitive to angle.These magic wavelengths are very close to the resonant wavelength.They are not good for the use of magic trapping,as the near resonant light has high photon spontaneous scattering rates which result in a high heating process.However,the longest magic wavelength near 1000 nm is very sensitive to angle.We analyzed the contribution of dynamic polarizability at the longest magic wavelength.It is found that accurate measurements on the longest magic wavelengths for the 4s_1/2?3d_5/2 and4s_1/2?3d_3/2 transitions can be used to determine the oscillator strengths for the 4s_1/2?4p_1/2,3/2,3d_5/2?4p_3/2,and 3d_3/2?4p_1/2,3/2 transitions,and the difference of the static polarizabilities of the 4s_1/2 and 3d_5/2 states,and the tensor polarizability of the 3d_5/2state.