| From the birth of quantum mechanics, after dozens of years, especially the rapid development in recent years, quantum mechanics has become a powerful tool to research micro world. It provides strong power for humanity to explore and understand the microscopic world and promotes the rapid development of modern science and technology of modern civilization.This article introduced the development history of quantum optics, and mainly included the development of quantum entanglement in the modern. It highlighted that quantum optics, especially quantum entanglement promotes the development of modern science and technology. We introduced some basic concepts of quantum optics, quantum entanglement and how to prepares and measures quantum entanglement. We also introduced some of applications for quantum entanglement in the present. Cavity quantum electrodynamics is a study of interaction between photons and atoms. It’s one of the effective ways to prepare reliable quantum entanglement. JC(Jaynes-Cummings) model is a simplified model of Rabi model with rotating wave approximation. This model usually be used to described the process that single-mode radiation field interacting with a two-level atom system.JC model was chosen as the basic framework. The time evolution of the photon statistical properties of two-level atom interacting with photons was obtained by using the theory of dressed state. We mainly focused on the research of the time evolution of the quantum statistical properties of two-level atom system interacting with the cavity field which Schrodinger-cat state as initial state. We characterized the atomic population by atomic inversion probability and showed the interference of the cavity field in the time evolution by relative average photon numbers. With Mandel Q parameters, the photon number distribution of the cavity field was characterized in the time evolution process. Using the ups and downs of the orthogonal component, we described the squeezing properties of the cavity field. Photon number distribution of the cavity field at a special moment was shown by photon number distribution. The evolution of entanglement degree in the process of cavity field interacting with the two-level atom by the quantum entropy of field was researched and the phase spaces of different initial state photon were shown with Wigner quasi-probability distribution.Through the analysis of the characteristic curves, we have found something in the process of coherent superposition state of coherent states which with same mode interact with two-level atom. The oscillation of the atomic inversion probability was disordered and cavity field was constructive interference with coherent states in small-amplitude. Photon number distribution changes among super-poisson distribution, poisson distribution and sub-poisson distribution in this process. But the squeezing of optical field cannot be observed with macroscopic distinguishing cat state photons. With small-amplitude coherent states, the entanglement degree of the cavity field and atom oscillate with ln2 as its up-limit. In Wigner distribution, for initial photon states, there were two separate peaks and interference peaks in the middle.For coherent states with larger-amplitude, the oscillation of atomic inversion probability becomes orderly with collapse-calm-revival and then chaos occurs later. The relative average photon number also becomes orderly, and the cavity field still constructive interference. Photon field distribution also changes among super-poisson distribution, poisson distribution and sub-poisson distribution but stable to sub-possion distribution in calm area with different photon number distributions. No squeezing of cavity field with more distinguishable of coherent states. The quantum entropy oscillates corresponding to the probability of the atomic inversion with value ln2 as its up-limit. In Wigner distribution, the initial state of cavity field showed two separate peaks with more distance and appear more intense interference peaks in the middle of them with larger-amplitude. |
