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

Recently it has been shown that ac-driven double quantum dots can act as spin pumps and spin filters. By calculating the current through the system for each spin polarization, by means of the time evolution of the reduced density matrix in the sequential tunneling regime (Born-Markov approximation), we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. Importantly, the pumped current as a function of the applied frequency presents a series of peaks which are uniquely associated with a definite spin polarization. We discuss how excited states participating in the current allow the system to behave as a bipolar spin filter by tuning the ac frequency and intensity. We also discuss spin relaxation and decoherence effects in the pumped current and show that measuring the width of the current vs frequency peaks allows to determine the spin decoherence time $T_{2}$., Comment: 10 pages. 5 figures

We propose and analyze a new scheme of realizing both spin filtering and spin pumping by using ac-driven double quantum dots in the Coulomb blockade regime. By calculating the current through the system we demonstrate that the spin polarization of the current can be controlled by tuning the parameters (amplitude and frequency) of the ac field. We also discuss spin relaxation and decoherence effects in the pumped current., Comment: 5 pages, 4 figures