Demonstrating mesoscopic superpositions in double-well Bose-Einstein condensates

The availability of Bose-Einstein condensates as mesoscopic or macroscopic quantum objects has aroused new interest in the possibility of making and detecting coherent superpositions involving many atoms. We consider the important problem of distinguishing whether a coherent superposition or a statistical mixture is generated by a given experimental procedure, using the specific example of a double-well condensate. In this system, such a superposition state can be generated by using a Feshbach resonance to tune the inter-atomic interactions. We find that unambiguously distinguishing even a perfect ‘NOON’ state from a statistical mixture using standard detection methods will present experimental difficulties.