Study On Entanglement In Optical Four Wave Mixing

The study of quantum entanglement is the basic information resource of quantum communication.It reflects the nonlocal and nonclassical correlation between two or more quantum systems.Quantum entanglement plays an important role in the field of quantum communication,including quantum dense coding,quantum secure communication,quantum teleportation,quantum computation and so on.In this paper,we consider a system of interaction between a two-mode cavity and a three-level lambda type atom.Under the condition of adiabatic and non adiabatic,the system produces two mode continuous variable entanglement in the four wave mixing process.The entanglement is analyzed by different criteria and the quantum discord is calculated.Firstly,we calculate the correlation matrix generated by the interaction between a two-mode cavity and a three-level lambda type atom.Three level lambda atoms are placed in a two mode cavity.We obtain the Hamiltonian of the cavity atom system by dipole approximation and choosing the appropriate rotating frame.Considering the dissipation of the system,the linearized Langevin equations of the field and atom are obtained by linearization.Then,Einstein equation and Lyapunov equation are used to calculate the correlation matrix of the cavity atom system.Then we discuss the properties of two cavity entanglement EN,two cavity EPR entanglement and quantum discord with cavity detuning.By using the logarithm criterion proposed by Vidal and Werner,we find that the system can exhibit the quantum entanglement and the quantum discord of the two mode field.The influence of spontaneous emission rate on entanglement and quantum is discussed.We find that EPR entanglement can not exceed half of its vacuum fluctuation in the case of strong and weak spontaneous emission.In addition,the definition of quantum discord is used to calculate and pass the image.We find that there is no entanglement between two cavities in the case of quantum discord.But if there is entanglement between the two cavities,there must be quantum discord.