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We characterize numerically and analytically the signatures of the spin-orbitinteraction in a two-electron GaAs double quantum dot in the presence of anexternal magnetic field. In particular, we obtain the return probability of thesinglet state by simulating Landau-Zener voltage detuning sweeps which traversethe singlet-triplet ($S-T_+$) resonance. Our results indicate thatnon-spin-conserving interdot tunneling processes arising from the spin-orbitinteraction have well defined signatures. These allow direct access to thespin-orbit interaction scales and are characterized by a frequency shift andFourier amplitude modulation of the Rabi flopping dynamics of thesinglet-triplet qubits $S-T_0$ and $S-T_+$. By applying the Bloch-Feshbachprojection formalism, we demonstrate analytically that the aforementionedeffects originate from the interplay between spin-orbit interaction andprocesses driven by the hyperfine interaction between the electron spins andthose of the GaAs nuclei.

Spin-orbit signatures in the dynamics of singlet-triplet qubits in double quantum dots