Relativistic and Spin-Orbit Dynamics at Non-Relativistic Intensities in Strong-Field Ionization
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Spin is commonly ignored in strong-field physics, given that it is only through spin-orbit coupling for states with high orbital-angular momentum and with an elliptically polarized field that it has been shown to play a role, while in experiment, spin-resolved measurements have only fairly recently become possible. Thus, theoretical models treat spin only through coupling to initial states and generally neglect the spin dynamics. However, the trend for longer wavelengths, e.g. in imaging process such as laser induced electron diffraction (LIED), means that spin dynamics may play an important role, through high energy rescattering. We explore spin, spin-orbit coupling, and relativistic corrections to the kinetic energy by modifying the path-integral model, the Coulomb quantum-orbit strong-field approximation (CQSFA). Spin is included into the path-integral formalism and solved exactly, while the remaining system is solved via the semi-classical saddle point method. We confirm the validity of the CQSFA method by comparing the non-relativistic model without spin-orbit coupling to a non-relativistic TDSE code, with exceptional agreement. At 1600 nm wavelengths, there are differences in the photoelectron momentum distributions when comparing with and without spin-orbit coupling or relativistic corrections, which are most apparent in the high-energy region of the photoelectron momentum distributions and centre around rescattered electron wavepackets. We demonstrate that these recolliding electrons undergo a very large momentum transfer, which warrants a relativistic treatment, and leads to large spin-orbit coupling. We demonstrate that this has an impact on both the phase and amplitude of these wavepackets. These results are a key step in accurate modelling of strong-field ionization at longer wavelengths and highlight effects that may have an impact on imaging processes such as LIED or photoelectron holography.