Relativistic and Spin-Orbit Dynamics at Non-Relativistic Intensities in Strong-Field Ionization

Spin-orbit dynamics and relativistic corrections to the kinetic energy in strong-field dynamics, have long been ignored for near- and mid-IR fields with intensities $10^{13}$--$10^{14}$ W/cm$^2$, as the final photoelectron energies are considered too low for these effects to play a role. However, using a precise and flexible path-integral formalism, we include all correction terms from the fine-structure, Breit-Pauli Hamiltonian. This enables a treatment of spin, through coherent spin-states, which is the first model to use this approach in strong-field physics. We are able to show that the most energetically rescattered wavepackets, undergo huge momentum transfer and briefly reach relativistic velocities, which warrants relativistic kinetic energy corrections. We probe these effects and show that they yield notable differences for a $1600$ nm wavelength laser field on the dynamics and the photoelectron spectra. Furthermore, we find that the dynamical spin-orbit coupling is strongly overestimated if relativistic corrections to kinetic energy are not considered. Finally, we derive a new condition that demonstrates that relativistic effects begin to play a role at intensities orders of magnitude lower than expected. Our findings may have important implication for imaging processes such as laser-induced electron diffraction, which includes high-energy photoelectron recollisions.