  We consider a degenerate Bose gas confined in a double-well potential in
interaction with a trapped ion in one dimension and investigate the impact of
two relevant sources of imperfections in experiments on the system dynamics:
ion motion and thermal excitations of the bosonic ensemble. Particularly, their
influence on the entanglement generation between the spin state of the moving
ion and the atomic ensemble is analyzed. We find that the detrimental effects
of the ion motion on the entanglement protocol can be mitigated by properly
choosing the double-well parameters as well as timings of the protocol.
Furthermore, thermal excitations of the bosons affect significantly the
system's tunneling and self-trapping dynamics at moderate temperatures; i.e.,
thermal occupation of a few double-well quanta reduces the protocol performance
by about 10%. Hence, we conclude that finite temperature is the main source of
decoherence in such junctions and we demonstrate the possibility to entangle
the condensate motion with the ion vibrational state.
