Decoherence in Bose-Einstein condensates: Towards bigger and better Schrodinger cats

We consider a quantum superposition of Bose-Einstein condensates (BEC's) in two immiscible internal states. A decoherence rate for the resulting Schrodinger cat is calculated and shown to be a significant threat to this macroscopic quantum superposition of BEC's. An experimental scenario is outlined where the decoherence rate due to the thermal cloud is dramatically reduced thanks to trap engineering and "symmetrization" of the environment, which allow the Schrodinger cat to be an approximate painter state.