Phase engineering of controlled entangled number states in a single component Bose-Einstein condensate in a double well

We propose a model for the creation of entangled number states (Schrodinger 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.