Magnetic and electrical control of electron-nuclear spin coupling in GaAs double quantum dots

We magnetically and electrically control spin coupling between electrons and nuclei in a vertical GaAs double quantum dot in the Pauli spin blockade regime to characterize the two-electron exchange energy and the dynamic nuclear polarization (DNP). The Pauli blockade is lifted by a hyperfine-mediated transition from an electron triplet state to the singlet state. This transition progressively occurs when the triplet-singlet separation or exchange energy J is compensated by tuning either Zeeman energy with external magnetic field (i.e., magnetic control) or inter-dot energy detuning with bias voltage (i.e., electrical control). The blockade is then lifted with a current step for sweeping up an external magnetic field. The J value, which is evaluated from the step position for various inter-dot detuning values, is consistent with calculation. DNP takes place through the hyperfine coupling near the current step, leading to a shifted current step to lower external magnetic field for the down-sweep. For the electrical control, a similar current step appears for sweeping bias voltage. In this case we are able to control the two-electron state energies in a relevant manner based on real time before DNP is significantly influenced, because the voltage sweep is much faster than the magnetic field sweep. We use this technique to distinguish the current step with and without DNP contributions, and therefore quantify the nuclear Overhauser fields with external magnetic field as a parameter. We present a simple phenomenological model to reproduce the experiment and also discuss a possible approach to realize the full DNP.