  Nanobubbles formed in monolayers of transition metal dichalcogenides (TMDCs)
on top of a substrate feature localized potentials, in which electrons can be
captured. We show that the captured electronic density can exhibit a
non-trivial spatiotemporal dynamics, whose movements can be mapped to states in
a two-level system illustrated as points of an electronic Poincar\'e sphere.
These states can be fully controlled, i.e, initialized and switched, by
multiple electronic wave packets. Our results could be the foundation for novel
implementations of quantum circuits.
