Properties of displaced idealized cat state

The Schrödinger-cat state, the quantum-mechanical superposition of two coherent states, has been investigated extensively due to its many nonclassical features. The properties of Schrödinger-cat state highly depend on the overlap between the two coherent states, i.e. the interference of the two coherent states. It has been shown that the interference is determined by the phase. The schrödinger-cat state can also be consider as the superposition of two coherent states with the same amplitudes, but different phase. In contrast, the superposition of two coherent states with the same phases but different amplitudes will produce the phase-cat states.