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

TL;DR

This paper calculates magic wavelengths and triple magic trapping conditions for Sr atom states using advanced relativistic methods, providing theoretical guidance for precision atomic trapping experiments and matching recent experimental results.

Contribution

It introduces a comprehensive theoretical analysis of magic wavelengths and triple trapping conditions for Sr atoms, including dependence on laser polarization angles, using the RCI+MBPT method.

Findings

Triple magic trapping at 813.4 nm with specific polarization angles.

Agreement of theoretical angle with recent experimental measurement.

Conditions for triple magic trapping with various polarizations provided.

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 ($\theta_p$) 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 $\theta_p= 37.4(0.3)^\circ$. The conditions for achieving triple magic trapping with circularly and arbitrarily elliptically polarized light are also presented.