  We theoretically investigate the generation of microscopic atomic NOON
states, corresponding to the coherent |N,0> + |0,N> superposition with N ~ 5
particles, via collective tunneling of interacting ultracold bosonic atoms
within a symmetric double-well potential in the self-trapping regime. We show
that a periodic driving of the double well with suitably tuned amplitude and
frequency parameters allows one to substantially boost this tunneling process
without altering its collective character. The time scale to generate the NOON
superposition, which corresponds to half the tunneling time and would be
prohibitively large in the undriven double well for the considered atomic
populations, can thereby be drastically reduced, which renders the realization
of NOON states through this protocol experimentally feasible. Resonance- and
chaos-assisted tunneling are identified as key mechanisms in this context. A
quantitative semiclassical evaluation of their impact onto the collective
tunneling process allows one to determine the optimal choice for the driving
parameters in order to generate those NOON states as fast as possible.
