Mesoscopic superposition of states with sub-Planck structures in phase space

We propose the cavity quantum electrodynamics method, using dispersive interaction between atoms and a high-quality cavity to realize the mesoscopic superposition of coherent states that would exhibit sub-Planck structures in phase space, i.e., the structures at a scale smaller than the Plank's constant ((h) over bar). These structures are direct signatures of quantum coherence and are formed as a result of interference between the two superposed cat states. In particular we focus on a superposition involving four coherent states. We show interferences in the conditional measurements involving two atoms.