A linear quantum dynamical theory for squeezing the output of the trapped B
ose-Einstein condensate is presented with the Bogoliubov approximation. We
observe that the nonclassical properties, such as sub-Poisson distribution
and quadrature squeezing effect, mutually oscillate between the quantum sta
tes of the applied optical field and the resulting atom laser beam with tim
e. In particular, it is shown that an initially squeezed optical field will
lead to squeezing in the outcoupled atomic beam at later times.