Production of mesoscopic superpositions with ultracold atoms

We study mesoscopic superpositions of two component Bose-Einstein condensates. Atomic condensates, with long coherence times, are good systems in which to study such quantum phenomenon. We show that the mesoscopic superposition states can be rapidly generated in which the atoms dispersively interact with the photon field in a cavity. We also discuss the production of compass states which are generalized Schr"{o}dinger cat states. The physical realization of mesoscopic states is important in studying decoherence and precision measurement.