Dynamical Entanglment In The Model Of The Field Interacted With Atoms Of A Nonlinear Medium

Quantum entanglment is a striking feature of quantum systems and the key physical resource to realize quantum tasks, for instance, quantum cryptography, quantum teleportation,and quantum computation, which can not be accounded for classical physics. This has motivated strong interest in the study of quantification of entanglment. So, in the present paper the dynamical entanglment in a model of the field interacted with atoms of a nonlinear medium is studied in terms of concurrence, negativity and the reduced Neumann entropy for the pure state and mixed state. And some interesting conclusions are obtained. which is useful for quantum information theory.Firstly, the the reduced von Neumann entropy and concurrence of pure state in the system is investigated. It is showed that concurrence is dominantly positive correlated with the the reduced von Neumann entropy for the generalized binomial state of the field and the ground state of atoms,and the entanglment in suitable conditions is nearly unchanged for a long time. Meanwhile, we found that the reduced von Neumann entropy of the subsystems for three kinds of initial pure state,which are the pure density matrix of binomial states, fock states and coherent state on the two modes, show the periodical evolution in weak nonlinear condition. Moreover, the period can be influenced by nonlinearity.Then, we derive an analytical form of the von Neumann entropy for the two energy level mixed state of atoms and the thermal state of field. And the dynamics of concurrence, reduced Neumann entropy, mutual entropy, negativity are studied for the mixed thermal state of the field and the mixed four-level Fock state of atoms by numerical simulations. It is shown that in most of the time concurrence, mutual entropy, negativity are positively correlated with each other. Finally, by a detailed example we show that the low bound of concurrence based on the PPT and realignment criterion is better than that based on positive maps for the thermal state of field and state of atoms. Those are useful for the theory of quantum entanglement.