  In a parameter regime for which the mean-field (Gross-Pitaevskii) dynamics
becomes chaotic, mesoscopic quantum superpositions in phase space can occur in
a double-well potential which is shaken periodically. For experimentally
realistic initial states like the ground state of some 100 atoms, the emergence
of mesoscopic quantum superpositions in phase space is investigated
numerically. It is shown to be reproducible even if the initial conditions
slightly change. While the final state is not a perfect superposition of two
distinct phase-states, the superposition is reached an order of magnitude
faster than in the case of the collapse and revival phenomenon. Furthermore, a
generator of entanglement is identified.
