  Polar bubble domains are complex topological defects akin to magnetic
skyrmions that can spontaneously form in ferroelectric thin films and
superlattices. They can be deterministically written and deleted and exhibit a
set of properties, such as sub-10 nm radius and room-temperature stability,
that are highly attractive for dense data storage and reconfigurable
nano-electronics technologies. However, possibilities of controlled motion of
electric bubble skyrmions, a critical technology requirement currently remains
missing. Here we present atomistic simulations that demonstrate how external
electric-field perturbations can induce two types of motion of bubble skyrmions
in low-dimensional tetragonal PbZr$_{0.4}$Ti$_{0.6}$O$_3$ systems under
residual depolarizing field. Specifically, we show that, depending on the
spatial profile and magnitude of the external field, bubble skyrmions can
exhibit either a continuous motion driven by the external electric field
gradient or a discontinuous, teleportation-like, skyrmion domain transfer.
These findings provide the first analysis of dynamics and controlled motion of
polar skyrmions that are essential for functionalization of these particle-like
domain structures.
