Control of a two-electron double quantum dot with an external magnetic field

We investigate the utilization of external magnetic field for the manipulation of the quantum states in a two-electron double quantum dot. The singlet and triplet states are coupled through the hyperfine interaction between the electrons and surrounding nuclei. When the magnetic field is changed as a function of time, the singlet-triplet transition is possible for certain values of magnetic field, when the singlet state becomes degenerate with the triplet state. The transition probability depends on the sweeping speed of the magnetic field through the averaged Landau-Zener formula. We evaluate proper time scales for efficient control of the quantum dot, evaluate the singlet probabilities for different time-dependent magnetic fields, and study the average of the final singlet probability, averaged over the orientations of the nuclear spins surrounding the quantum dot.