  Tunable synthetic spin-orbit coupling (s-SOC) is one of the key challenges in
various quantum systems, such as ultracold atomic gases, topological
superconductors, and semiconductor quantum dots. Here we experimentally
demonstrate controlling the s-SOC by investigating the anisotropy of
spin-valley resonance in a silicon quantum dot. As we rotate the applied
magnetic field in-plane, we find a striking nonsinusoidal behavior of resonance
amplitude that distinguishes s-SOC from the intrinsic spin-orbit coupling
(i-SOC), and associate this behavior with the previously overlooked in-plane
transverse magnetic field gradient. Moreover, by theoretically analyzing the
experimentally measured s-SOC field, we predict the quality factor of the spin
qubit could be optimized if the orientation of the in-plane magnetic field is
rotated away from the traditional working point.
