Fig. 2: Rotations induced while shuttling by the difference in quantization axes.

a Schematic explaining the effect of the change in quantization axis direction that the qubit experiences during the shuttling process. The difference in quantization axis between quantum dots (QDs) is caused by the strong spin-orbit interaction. b Oscillations in spin-up probabilities P_↑ induced by the change in quantization axis while shuttling diabatically a qubit in a \(\left\vert \downarrow \right\rangle\) state between QD₂ and QD₃. Ramp times of 4 ns are used for the detuning pulses. Note that the oscillations have a reduced visibility, meaning that the difference in quantization axes does not induce a full spin flip. The angle between the quantization axes of the two quantum dots can be estimated from the amplitude of the oscillations, see Supplementary Note 2A. c Oscillations due to the change in quantization axis at a fixed point in detuning, as function of the voltage pulse ramp time used to shuttle the spin. When the ramp time is long enough, typically above 30 ns, the spin is shuttled adiabatically and the oscillations vanish. d Magnetic-field dependence of the oscillations induced by the difference in quantization axis. e Frequency of the oscillations f_osc induced by the change in quantization axis as a function of magnetic field for different shuttling processes. The oscillation frequency f_osc for QD₃ is extracted from measurements displayed in d (and similar experiments for the other quantum dot pairs) and is plotted with points. f_osc scales linearly with the magnetic field. Comparing f_osc with resonance frequencies f_resonance measured using microwave pulses (data points depicted with stars) reveals that f_osc is given by the Larmor frequency of the quantum dot towards which the qubit is shuttled (black label).