Magic wavelengths and triple magic trapping conditions for $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms

Abstract

The static and dynamic electric dipole polarizabilities of the $5s^2~^1\!S_0$ and $5s5p~^3\!P_{0,2}$ states of Sr atoms are calculated using the relativistic configuration interaction plus the many-body perturbation theory (RCI+MBPT) method. Magic wavelengths are determined for the transitions $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{0}$, $5s^2~^1\!S_0\rightarrow 5s5p~^3\!P_{2}$, and $5s5p~^3\!P_0\rightarrow 5s5p~^3\!P_{2}$. A comprehensive study is conducted on the dependence of magic wavelengths on the angle between the laser polarization and the magnetic field. Furthermore, the conditions for realizing triple magic trapping at 813.4~nm for the $5s^2~^1\!S_0$, $5s5p~^3\!P_{0}$ and $5s5p~^3\!P_{2}$ states are investigated. In the case of linearly polarized light, when the angle ($θ_p$) between the laser polarization direction and the magnetic field is $79.1(0.7)^\circ$, triple magic trapping for the $5s^2~^1\!S_0$, $5s5p~^3\!P_{0}$, and $5s5p~^3\!P_{2}~M=0$ states can be achieved. This result agrees well with the recent experimental measurement (78.49(3)$^\circ$)[Phys. Rev. Lett. 135, 143401 (2025)]. Meanwhile, triple magic trapping involving the $5s5p~^3\!P_{2}~M=2$ state can be achieved when $θ_p= 37.4(0.3)^\circ$. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.