Fig. 2.

MOS interface spin–orbit interaction. a Energy diagram and gate pulse schematic for controlling spin–orbit rotations. We initialize the qubit into the S(2, 0) ground state and transfer the system to the (1, 1) charge sector with a rapid adiabatic pulse, such that it remains a singlet. The difference in Zeeman splitting between the QDs drives X-rotations between the S(1, 1) and T₀(1, 1) states. A rapid adiabatic return pulse projects the states onto the S(2, 0) and T₀(1, 1) basis for measurement. b Change in charge sensor current as a function of X-rotation manipulation time as the magnetic field is varied along the $\left[1\overline{1}0\right]$ crystallographic direction. c The extracted rotation frequency as a function of magnetic field strength along the [110] and $\left[1\overline{1}0\right]$ crystallographic directions. d, e Magnetic field angular dependence of the SO-driven difference in g-factor between the dots for the in-plane, θ, and out-of-plane, ϕ, directions, respectively. Fits to the form $\left(\mathrm{\Delta }g\right){\mu }_{\mathrm{B}}B\mathrm{∕}h$ = $∣\mathbf{B}∣∣\mathrm{\Delta }\alpha -\mathrm{\Delta }\beta \sin \left(2\varphi \right)∣$ sin²(θ) are also plotted for θ = π/2 (black), ϕ = 3π/4 (blue) and ϕ = π/4 (red). f A cartoon representation of the angular dependence of the two QDs (left). The difference between the QD g-factors give an in-plane dependence represented by the cloverleaf plot on the right