Time evolution of the coherent state in a degenerate parametric amplifier

In this paper, we study the time evolution of the coherent state in a degenerate parametric amplifier by the technique of integration within an ordered product (IWOP) of operators. We investigate some interesting and important physical properties of this state, such as the quantum statistical properties and squeezing effects, both analytically and numerically. Furthermore, the fidelity between this state and the Schrödinger cat state is also given. It is interesting to find that this quantum state has not only squeezing effect, but also rotating effect by appropriately choosing the related parameters.