Spin-orbit-resolved strong-field ionization from real-time relativistic dynamics.

Strong-field ionization exhibits rich ultrafast dynamics arising from intricate electron-field interactions. However, the role of spin-orbit coupling in the strong-field ionization of many-electron systems remains largely unexplored. Here, we develop a fully relativistic framework that combines a complex absorbing potential (CAP) with the exact two-component (X2C) real-time time-dependent density functional theory. We apply this approach to investigate the real-time strong-field dynamics of atomic krypton with a variational treatment of spin-orbit coupling. The CAP-X2C method captures the spin-orbit-resolved ionization-rate trends of the Kr 4p shell. Moreover, we uncover a previously inaccessible coherent population transfer channel between the 4p12 and 4p32 states, opened by spin-orbit coupling, which lifts the nonrelativistic symmetry restriction that forbids their mixing. This work provides a practical framework for exploring strong-field dynamics in systems where spin-orbit coupling plays a significant role.