  The coupling of the spin and the motion of charge carriers stems directly
from the atomic structure of a conductor. It has become an important ingredient
for the emergence of topological matter, and, in particular, topological
superconductivity which could host non-abelian excitations such as Majorana
modes or parafermions. These modes are sought after mostly in semiconducting
platforms which are made of heavy atoms and therefore exhibit naturally a large
spin-orbit interaction. Creating domain walls in the spin orbit interaction at
the nanoscale may turn out to be a crucial resource for engineering topological
excitations suitable for universal topological quantum computing. For example,
it has been proposed for exploring exotic electronic states or for creating
hinge states. Realizing this in natural platforms remains a challenge. In this
work, we show how this can be alternatively implemented by using a synthetic
spin orbit interaction induced by two lithographically patterned magnetically
textured gates. By using a double quantum dot in a light material -- a carbon
nanotube -- embedded in a microwave cavity, we trigger hopping between two
adjacent orbitals with the microwave photons and directly compare the wave
functions separated by the domain wall via the light-matter coupling. We show
that we can achieve an engineered staggered spin-orbit interaction with a
change of strength larger than the hopping energy between the two sites.
