  We investigate superradiant-like dynamics of the nuclear-spin bath in a
single-electron quantum dot, by considering electrons cyclically shuttling
on/off an isotopically enriched `nuclear-spin island'. Assuming a uniform
hyperfine interaction, we discuss in detail the nuclear spin evolution under
shuttling and its relation to superradiance. We derive the minimum shuttling
time which allows to escape the adiabatic spin evolution. Furthermore, we
discuss slow/fast shuttling under the inhomogeneous field of a nearby
micromagnet. Finally, by comparing our scheme to a model with stationary
quantum dot, we stress the important role played by non-adiabatic shuttling in
lifting the Coulomb blockade and thus establishing the superradiant-like
behavior.
