  A model for the coherent output coupler of the Bose-Einstein condensed atoms
from a trap in the recent MIT experiment (Phys. Rev. Lett., 78 (1997) 582) is
established with a simple many-boson system of two states with linear coupling.
Its exact solution for the many-body problem shows a factorization of dynamical
evolution process, i.e., the wave function initially prepared in a direct
product of a vacuum state and a coherent state remains in a direct product of
two coherent states at any instance in the evolution of the total system. This
conclusion always holds even for a system with a finite average particle number
in the initial state. Its thermodynamical limit can be directly dealt with in
the Bogoliubov approximation and manifests that an ideal condensate in the trap
will remain in a coherent state after the r.f. interaction while the
output-coupler pulse of atoms is also in a coherent state, which means a
coherent output of atomic beam to form a macroscopic quantum state in a
propagating mode.
