Production of Schrödinger macroscopic quantum-superposition states in a Kerr medium

We show how a special class of Schr\"odinger macroscopic quantum-superposition states can be produced by a coherent field propagating through a Kerr medium. We show that these states are eigenstates of the mth power of the photon-annihilation operator leading also to the possibility of producing these using multiphoton Jaynes-Cummings systems. We further show how superpositions of squeezed coherent states can be produced.