Shaped electric fields for fast optimal manipulation of electron spin and position in a double quantum dot

We use quantum optimal control theory algorithms to design external electric fields that drive the coupled spin and orbital dynamics of an electron in a double quantum dot, subject to the spin-orbit interaction and Zeeman magnetic fields. We obtain time-profiles of multi-frequency electric pulses which increase the rate of spin-flip transitions by several orders of magnitude in comparison with monochromatic fields, where the spin Rabi oscillations were predicted to be very slow. This precise, with the accuracy higher than $10^{-4}$, and fast, at the timescale of the order of 0.1 ns, simultaneous control of the electron spin orientation and position is achieved while keeping the electron in the four lowest tunneling- and Zeeman-split levels through the duration of the pulse, facilitating high fidelity and suggesting useful applications in spintronics and quantum information devices.