Havana (CNN) — President Barack Obama touched down in Cuba on Sunday, definitively ending a half-century of estrangement in a dramatic personal demonstration of his core foreign policy principle of engaging America's enemies. It's a shift that the change-minded president hopes will nudge the Communist government here to grant more freedoms to its people and open new economic channels for American businesses. The President and his allies also hope a successful détente will offer something bigger: a lasting example of diplomacy's power in dealing with longtime foes.