  We propose a model for the creation of entangled number states (Schr\"odinger
cat states) of a Bose-Einstein condensate in a double well through simple phase
engineering. We show that a $\pi$-phase imprinted condensate in a double-well
evolves, with a simultaneous change of barrier height, to number states with
well defined and controlled entanglement. The cat state generation is
understood in terms of the underlying classical phase space dynamics of a
$\pi$-phase displaced coherent state put at the hyperbolic fixed point of the
separatrix of a physical pendulum. The extremity and sharpness of the final cat
state is determined by the initial barrier height and the rate at which it is
ramped during the evolution.
