(color online) Schematics of the controlled state-sensitive collisional interaction. Due to the dynamics in the state-dependent potential, the internal and motional states of the atoms are entangled. (a) Two trapped BECs in a coherent superposition of states and in the double-well OFMTs. (b), (c) Wavefunctions of state overlap leading to a collisional interaction while the unwanted interactions for state are shifted further apart.