  We argue that a Bose-Einstein condensate can be transformed into a Floquet
condensate, that is, into a periodically time-dependent many-particle state
possessing the coherence properties of a mesoscopically occupied
single-particle Floquet state. Our reasoning is based on the observation that
the denseness of the many-body system's quasienergy spectrum does not
necessarily obstruct effectively adiabatic transport. Employing the idealized
model of a driven bosonic Josephson junction, we demonstrate that only a small
amount of Floquet entropy is generated when a driving force with judiciously
chosen frequency and maximum amplitude is turned on smoothly.
